【免费下载】Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch12

Chapter 4Time Value of Money:Valuing Cash Flow StreamsNote: All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problemswith a higher level of difficulty. Editor’s Note: As we move forward to more complex financial analysis, the student will notice that someproblems may contain a large amount of data from different time periods that require more complicated and intensive analysis. Modern information technology has evolved in the form of financial calculators with built-in analysis functions and Time Value ofMoney functions that are built into computer-based electronic spreadsheet software such as Excel. The solutions for many data- and computationally intensive problems will be presented in formula form with a solution, as well as with the appropriate financialcalculator commands and Excel functions to produce the same correct answer. In this way, it is our expectation that students will develop proficiency in solving financial analysis problems by mathematical calculation as well as by using financial calculators and electronic spreadsheets.1. a.Year 1 2 3 4 5 CF1020304050()()()()23451020304050106.531.10 1.10 1.10 1.10 1.10PV =++++= b.()()()()23455040302010120.921.10 1.10 1.10 1.10 1.10PV =++++= Year 1 2 3 4 5 CF5040302010Chapter 4 Time Value of Money: Valuing Cash Flow Streams 27c. The present value is different because the timing of the cash flows is different. In the secondset, you get the larger cash flows earlier, so it is more valuable to you and shows up as a higher PV.2.Year 1 2 3 4 CF100-100200-200()()()23410010020020028.491.15 1.15 1.15 1.15PV =-+-=3.Year 1 2 3 4 5 CF10000-2000-3000-3500-3975()()()2342,0003,0003,5003,97510,000.121.085 1.085 1.085 1.085PV =+++=, so yes, the PV of your payments would just cover the loan amount (actually exceeding it by 12 cents). Thus, the maximum you could borrow would be 10,000.124. Month1 2 3 4 5 6 7 8 CF500 550 600 650 700 750 800 850()()()()()()()23456785005506006507007508008505,023.751.015 1.015 1.015 1.015 1.015 1.015 1.015 1.015PV =+++++++=So, the PV of your payments will exceed the loan balance. This means that your planned payments will be enough to payoff your credit card.5.From the bank’s perspective, the timeline is the same except all the signs are reversed.28 Berk/DeMarzo/Harford •Fundamentals of Corporate Finance, Third Edition, Global Edition6.0 1 2 3 4 48–300 –300 –300 –300 –300From the bank’s perspective, the timeline would be identical except with opposite signs.7. Plan: Draw the timeline and then compute the FV of these two cash flows.Execute:Timeline (because we are computing the future value of the account, we will treat the cashflows as positive—going into the account):800 600FV = ?FV = 800(1.05) + 600 = 1,440Evaluate:The timeline helps us organize our work so that we get the number of periods of compoundingcorrect. The first cash flow will have 1 year of compounding, but the second cash flow will bedeposited at the end of period 1, so it receives no compounding.8. Editor’s Note: In several previous problems, we used a financial calculator to solve a timevalue of money problem. Problems could be solved quickly and easily by manipulating the N,I/Y, PV, PMT, and FV keys. In each of these problems, there was a series of payments of equal amount over time, i.e., an annuity. All you had to do to input this series was enter the payment(PMT) and the number of payment (N).Many financial analysis problems involve a series of equal payments, but others involve aseries of unequal payments. A financial calculator can be used to evaluate an unequal series ofcash flows (using the cash flow (CF) key), but the process is cumbersome because each cashflow must be entered individually. I urge each student to study the Chapter 4 Appendix: “Usinga Financial Calculator,” as well as instructional materials that are prod uced by themanufacturers of the financial calculator.Here we will solve a problem with uneven cash flows mathematically and with a financialcalculator.Plan: It is wonderful that you will receive this windfall from your investment in your friend’sbusiness. Because the cash flow payments to you are of different amounts and paid over threeyears, there are different ways in which you can think about how much money you arereceiving.Chapter 4 Time Value of Money: Valuing Cash Flow Streams 29Execute:a. 2310,00020,00030,000PV 1.035 1.035 1.0359,66218,67027,05855,390=++=++=The Texas Instrument BA II PLUS calculator has a cash flow worksheet accessed with the CF key. To clear all previous values that might be stored in the calculator, press the CF, second, and CE/C buttons. The screen should show CF 0 = asking for the cash flow at time 0, which in this problem is 0. Press 0, then press enter, and then the down key button. Thescreen should show CO1 asking for the cash flow at time 1, which in this problem is 10,000. Input 10,000 followed by the enter key, followed by the down button. The screen should show FO1 = 1.0 asking for the frequency of this cash flow. Because it occurs only once, it is correct, and we press the down key. The screen now has CO2 asking for the time 2 cash flow, which is 20,000, which we input, followed by the enter key and the down key. The screen now has FO2 = 1.0, which is correct. Enter the down key, which asks for the third cash flow, which is 30,000. Input 30,000, followed by the enter and down keys. Now press the NPV key, and the calculator will display I = asking for the interest rate, which is 3.5. Input 3.5, press the enter key, and press the down key, and the screen will display NPV =. Then press the CPT button, and the screen should display 55,390.33, the Net Present Value.b. 3FV 55,390 1.03561,412=⨯=Evaluate: You may ask: “How much better off am I because of this windfall?” There are several answers to this question. The value today (i.e., the present value) of the cash you will receive over three years is $55,390. If you decide to reinvest the cash flows as you receive them, then in three years you will have $61,412 (i.e., future value) from your windfall.9. Plan: Use Eq. 4.3 to compute the PV of this stream of cash flows and then use Eq. 4.1 to compute the FV of that present value. To answer part (c), you need to track the new deposit made each year along with the interest on the deposits already in the bank.Execute: a. and b.233100100100257.71(1.08)(1.08)(1.08)257.71(1.08)324.64PV FV =++===30 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Editionc. ()11Year 1: 100Year 2: 1001.08100208Year 3: 208(1.08)100324.64+=+=Evaluate:By using the PV and FV tools, we are able to keep track of our balance as well as quicklycalculate the balance at the end. Whether we compute it step by step as in part (c) or directly as in part (b), the answer is the same.10. Plan: First, create a timeline to understand when the cash flows are occurring.Second, calculate the present value of the cash flows.Once you know the present value of the cash flows, compute the future value (of this present value) at date 3.Execute: 231,0001,0001,000PV 1.05 1.05 1.0595********,723=++=++=NI/Y PV PMT FV Excel FormulaGiven: 35.00% -1,000 0Solve for PV:2,723.25=PV(0.05,3,-1,000,0)33FV 2,723 1.053,152=⨯=NI/Y PV PMT FV Excel FormulaGiven: 35.00% -2,723.43Solve for FV:3,152.71=FV(0.05,3,0,-2,723.43)Evaluate: Because of the bank’s offer, you now hav e two choices as to how you will repay this loan. Either you will pay the bank $1,000 per year for the next three years as originallypromised, or you can decide to skip the three annual payments of $1,000 and pay $3,152 in year three.You now have the information to make your decision.11. a. The FV of 100,000 invested for 35 years at 9% is 100,000 × (1.09)35 = 2,041,397b. The FV of 100,000 invested for 25 years at 9% is 100,000 × (1.09)25 = 862,308Chapter 4 Time Value of Money: Valuing Cash Flow Streams 31c. The difference is so large because of the effect of compounding, which is exponential. Inthe scenario where you invest earlier, those 10 years are critical to the compound growthyou achieve on your investment.12. Plan: This scholarship is a perpetuity. The cash flow is $5,000 and the discount rate is 6%.Execute:Timeline:5,000 5,000 …PV 5,000/0.06 = 83,333.33Evaluate:With a donation of $83,333.33 today and 6% interest, the university can withdraw the interest every year ($5,000) and leave the endowment intact to generate the next year’s $5,000. It can keep doing this forever.13. P lan: This is a deferred perpetuity. Here is the timeline:Do this in two steps:1. Calculate the value of the perpetuity in year 9, when it will start in only one year(we already did this in problem 12).2. Discount that value back to the present.Execute:The value in year 9 is 5,000/0.06 = 83,333.33.The value today is 83,333.33/1.069 = 49,324.87Evaluate:Because your endowment will have 10 years to earn interest before making its first payment, you can endow the scholarship for much less. The value of your endowment must reach$83,333.33 the year before it starts (in 9 years). If you donate $49,324.87 today, it will grow at 6% interest for 9 years, just reaching $83,333.33, one year before the first payment.32 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition14. The timeline for this investment is:a. The value of the bond is equal to the present value of the cash flows. By the perpetuity formula, which assumes the first payment is at period 1, the value of the bond is:PV = 1,000 /0.08 = £12,500 b. The value of the bond is equal to the present value of the cash flows. The first payment will be received at time zero. The cash flows are the perpetuity plus the payment that will be received immediately.PV = 1,000 /0.08 + 1,000 = £13,50015. Plan: Draw the timeline of the cash flows for the investment opportunity. Compute the NPV ofthe investment opportunity at 7% interest per year to determine its value.Execute: The cash flows are a 100-year annuity, so by the annuity formula:1001,0001PV 10.07 1.0714,269.25⎛⎫=- ⎪⎝⎭=NI/Y PV PMT FV Excel FormulaGiven: 1007.00% 1,000 0Solve for PV:(14,269.25)=PV(0.07,100,1000,0)Evaluate: The PV of $1,000 to be paid every year for 100 years discount to the present at 7% is $14,269.25.16. Plan: Prepare a timeline of your grandmother’s deposits.The deposits are an 18-year annuity. Use Eq. 4.6 to calculate the future value of the deposits.Execute: 1811(1)11,000(1.03)123,414.430.03N FV C r r =⨯+-=-=⎡⎤⎡⎤⎣⎦⎣⎦Chapter 4 Time Value of Money: Valuing Cash Flow Streams 33NI/Y PV PMT FV Excel FormulaGiven: 183.00% 0 1,000Solve for FV:(23,414.43)=FV(0.03,18,1000,0)At age 18, you will have $23,414.43 in your account.Evaluate:The interest on the deposits and interest on that interest adds more than $5,414 to the account.17. a.First, we need to calculate the PV of $160,000 in 18 years.18160,000PV (1.08)40,039.84==NI/Y PV PMT FV Excel FormulaGiven: 188.00% 0 160,000Solve for PV:(40,039.84)=PV(0.08,18,0,160000)In order for the parents to have $160,000 in your college account by your 18th birthday, the 18-year annuity must have a PV of $40,039.84. Solving for the annuity payments:1840,039.841110.08 1.08$4,272.33C =⎛⎫- ⎪⎝⎭=which must be saved each year to reach the goal.NI/Y PV PMT FV Excel FormulaGiven: 188.00% 40,039.84Solve for PMT:(4,272)=PMT(0.08,18,40039.84,0)b. First, we need to calculate the PV of $200,000 in 18 years.18200,000PV (1.08)50,049.81==34 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global EditionNI/Y PV PMT FV Excel FormulaGiven: 188.00% 0 200,000Solve for PV:(50,049.81)=PV(0.08,18,0,200000)In order for the parents to have $200,000 in your college account by your 18th birthday, the 18-year annuity must have a PV of $50,049.81. Solving for the annuity payments:18$50,049.811110.08 1.08$5340.42C =⎛⎫- ⎪⎝⎭=which must be saved each year to reach the goal.N I/Y PV PMT FV Excel FormulaGiven: 18.00 0.08 50,049.810.00Solve for PMT:-5340.42=PMT(0.08,18,50049.81,0)*18. Plan:a. Draw the timeline of the cash flows for the loan.1 2 3 4 5To pay off the loan, you must repay the remaining balance. The remaining balance is equal to the present value of the remaining payments. The remaining payments are a four-year annuity, so:b.4 5Execute:a. 45,0001PV 10.06 1.0617,325.53⎛⎫=- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 4 6.00% 5000 0Solve for PV:(17,325.53)=PV(0.06,4,5000,0)Chapter 4 Time Value of Money: Valuing Cash Flow Streams 35b. 5,000PV 1.064,716.98==Evaluate: To pay off the loan after owning the vehicle for one year will require $17,325.53. To pay off the loan after owning the vehicle for four years will require $4,716.98.19. Plan: This is a deferred annuity. The cash flow timeline is:Calculate the value of the annuity in year 17, one period before it starts using Eq. 4.5 and then discount that value back to the present using Eq. 4.2.The value of the annuity in year 17, one period before it is to start is:41100,000111331,212.68(1)0.08(1.08)n CF PV r r ⎡⎤⎡⎤=-=-=⎢⎥⎢⎥+⎣⎦⎣⎦To get its value today, we need to discount that lump sum amount back 17 years to the present:17331,212.68$89,516.50(1.08)=Evaluate:Even though the cash flows are a little unusual (an annuity starting well into the future), we can still value them by combining the PV of annuity and PV of a FV tool. If we invest $89,516.50 today at an interest rate of 8%, it will grow to be enough to fund an annuity of $100,000 per year by the time it is needed for college expenses.20. Plan: This is a deferred annuity. The cash flow timeline is:Calculate the value of the annuity in year 44, one period before it starts using Eq. 4.5 and then discount that value back to the present using Eq. 4.2.Execute:The value of the annuity in year 44, one period before it is to start is:16140,000111377,865.94(1)0.07(1.07)n CF PV r r r ⎡⎤⎡⎤=-=-=⎢⎥⎢⎥+⎣⎦⎣⎦To get its value today, we need to discount that lump sum amount back 44 years to the present:44377,865.94$19,250.92(1.07)=Evaluate:Even though the cash flows are a little unusual (an annuity starting well into the future), we can still value them by combining the PV of annuity and PV of a FV tool. The total value to you today of Social Security’s promise is less than $20,000.*21. Plan: Clearly, Mr. Rodriguez’s contract is complex, calling for payments over many years.Assume that an appropriate discount rate for A-Rod to apply to the contract payments is 7% per year.a. Calculate the true promised payments under this contract, including the deferred payments with interest.b. Draw a timeline of all of the payments.c. Calculate the present value of the contract.d. Compare the present value of the contract to the quoted value of $252 million. What explains the difference?Execute: Determine the PV of each of the promised payments discounted to the present at 7%.2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 $18M 19M19M19M21M19M23M27M27M27M20112012 2013 2014 2015 2016 2017 2018 2019 2020 6.7196M 5.3757M 4.0317M 4.0317M 4.0317M 4.0317M 4.0317M 4.0317M 4.0317M 4.0317MThe PV of the promised cash flows is $165.77 million.Evaluate: The PV of the contract is much less than $252 million. The $252 million value does not discount the future cash flows or adjust deferred payments for accrued interest. *22. a.0 1 2343The amount in the retirement account in 43 years would be:43435,000FV (1.10)10.10$2,962,003.46=-⎡⎤⎣⎦=NI/Y PV PMT FV Excel FormulaGiven: 4310.00%0.00 -5,000Solve for FV:2,962,003.46=FV(0.1,43,-5000,0)b. To solve for the lump sum amount today, find the PV of the $2,962,003.46.432,962,003.46PV (1.10)$49,169.99==N I/Y PV PMT FV Excel FormulaGiven: 43 10.00%0 2,962,003Solve for PV:(49,169.99) =PV(0.1,43,0,2962003.46) c.Solve for the annuity cash flow that, after 20 years, exactly equals the starting value of the account.202,962,003.461110.10 1.10347,915.81C =⎛⎫-⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 20.00 0.10 2,962,003.460.00Solve for PMT:-347,915.81=PMT(0.1,20,2962003.46,0)d.We want to solve for N , which is the length of time in which the PV of annual payments of $300,000 will equal $2,962,003.46. Setting up the PV of an annuity formula and solving for N :300,000112,962,003.460.10 1.1012,962,003.460.1010.98733451.10300,000110.98733450.01266551.101.1078.95456Log(78.95456)45.84Log(1.10)N N NN N ⎛⎫-= ⎪⎝⎭⨯⎛⎫-== ⎪⎝⎭=-==== e. If we can only invest $1,000 per year, then set up the PV formula using $1 million as the FV and $1,000 as the annuity payment. 431,000111,000,000(1)r r ⎛⎫-= ⎪+⎝⎭To solve for r , we can either guess or use the annuity calculator. You can check and see that r = 11.74291% solves this equation. So the required rate of return must be 11.74291%.N I/Y PV PMT FV Excel FormulaGiven: 43 0.00 -1,000 1,000,000Solve for Rate: 11.74291%=RATE(43,-1000,0,1000000)23. Plan: The bequest is a perpetuity growing at a constant rate. The bequest is identical to a firmthat pays a dividend that grows forever at a constant rate. We can use the constant dividend growth model to determine the value of the bequest.Execute: a.Using the formula for the PV of a growing perpetuity gives1,000PV 0.120.0825,000⎛⎫= ⎪-⎝⎭=which is the value today of the bequest.b.1 2 3 4Using the formula for the PV of a growing perpetuity gives:1,000(1.08)PV 0.120.0827,000=-=which is the value of the bequest after the first payment is made.Evaluate: The bequest is worth $25,000 today and will be worth $27,000 in 1 year’s time. *24. Plan: The machine will produce a series of savings that are growing at a constant rate. The rateof growth is negative, but the constant growth model can still be used.Execute:The timeline for the saving would look as follows:We must value a growing perpetuity with a negative growth rate of – 0.03:2,000PV 0.08(0.03)$18,181.82=--= Evaluate: The value of the savings produced by the machine is worth $18,181.82 today.25. Plan: Nobel’s bequest is a perpetu ity. The total amount is 5 ⨯ $45,000 = $225,000. With a cashflow of $225,000 and an interest rate of 7% per year, we can use Eq. 4.4 to solve for the total amount he would need to use to endow the prizes. In part (b), we will need to use the formula for a growing perpetuity (Eq. 4.7) to find the new value he would need to leave. Finally, in part (c), we can use the FV equation (Eq. 4.1) to solve for the future value his descendants would have had if they had kept the money and invested it at 7% per year.a. In order to endow a perpetuity of $225,000 per year with a 7% interest rate per year, he would need to leave $225,000/0.07 = $3,214,285.71.b. In order to endow a growing perpetuity with an interest rate of 7% and a growth rate of 4% and an initial cash flow of $225,000, he would have to leave:1225,0007,500,0000.070.04CF PV r g ===-- c. FV = PV (1 + r )n = 7,500,000(1.07)118 = $ 21,996,168,112Evaluate:The prizes that bear Nobel’s name were very expensive to endow—$3 million was an enormous sum in 1896. However, Nobel’s endowment has been able to generate enough interest each year to fund the prizes, which now have a cash award of approximately $1,500,000 each!26. Plan: The drug will produce 17 years of cash flows that will grow at 5% annually. The value ofthis stream of cash flows today must be determined. We can use the formula for a growing annuity (Eq. 4.8) or Excel to solve this. C = 2, r = 0.10, g = 0.05, N = 17Execute: 171 1.052121.860.100.05 1.10PV ⎛⎫⎛⎫⎛⎫=-= ⎪ ⎪ ⎪ ⎪-⎝⎭⎝⎭⎝⎭Because the cash flows from this investment will continue for 17 years, we decided to solve for the Net Present Value by using the NPV function in Excel. This is shown on the next page. The 17 cash flows are presented in columns C, D,…S. The initial cash flow of $2M is presented in cell C8, and each subsequent cash flow grows at 5% until $4.365749M is presented in year 17 in cell S8. (Note that columns G through Q are not presented.) The NPV of the project is calculated using the NPV formula = NPV(C3,C8:S8) in cell B10. The NPV of the future cash flows is $21.86M.ABCDEFR S 1 2 1+g 1.05 3 r 0.1 4 5 6 T 0 1 2 3 4 16 17 7 8 2 2.1 2.205 2.31525 4.1578564.3657499 10 NPV $21.86 11 12 EXCEL NPV FORMULA =NPV(C3,C8:S8) 13Evaluate: The value today of the cash flows produced by the drug over the next 17 years is $21.86 million. Because the cash flows are expected to grow at a constant rate, we can use the growing annuity formula as a shortcut.27. Plan: Your rich aunt is promising you a series of cash flows over the next 20 years. You mustdetermine the value of those cash flows today. This is a growing annuity and we can use Eq.4.8 to solve it, or we can also solve it in Excel. C= 5, r= 0.03, g= 0.05 and N= 20Execute:201 1.035179.820.050.03 1.05PV⎛⎫⎛⎫⎛⎫=-=⎪⎪ ⎪⎪-⎝⎭⎝⎭⎝⎭Because the cash flows from this investment will continue for 20 years, we decided to solve for the Net Present Value by using the NPV function in Excel. This is shown on the next page. The 20 cash flows are presented in columns C, D,…V. The initial cash flow of $5,000 is presented in cell C8, and each subsequent cash flow grows at 3% until $8,767.53 is presented in year 20 in cell V8. (Note that columns G through R are not presented.) The NPV of the project is calculated using the NPV formula =NPV(C3,C8:V8) in cell B10. The NPV of the future cash flows is $79,824.A B C D E …S T U V12 1 + g 1.033 r 0.05456 T 0 1 2 3 17 18 19 2078 5 5.15 5.3045 8.023532 8.264238 8.512165 8.76753910 NPV $79.821112 EXCEL NPV FORMULA =NPV(C3,C8:V8)13Evaluate: Because your aunt will be increasing what she gives each year at a constant rate, we can use the growing perpetuity formula as a shortcut to value the stream of cash flows. Her gift is quite generous: It is equivalent to giving you almost $80,000 today!28. Plan: This problem is asking us to solve for the rate of return (r). Because there are norecurring payments, we can use Eq. 4.1 to represent the problem and then just solvealgebraically for r. We have FV = 200, PV = 100, n = 10.Execute:FV = PV(1 +r)n200 = 100(1 +r)10, so r = (200/100) 1/10– 1 = 0.072 or 7.2%Evaluate:The implicit return we earned on the savings bond was 7.2%. Our money doubled in 10 years, which by the rule of 72 meant that we earned about 72/10 = 7.2% and our calculationconfirmed that.29. Plan: This problem is again asking us to solve for r. We will represent the investment with Eq.4.1 and solve for r. We have PV = 2,000, FV = 10,000, n = 10. The second part of the problemasks us to change the rate of return going forward and calculate the FV in another 10 years.Execute:a. FV= PV(1 + r)n10,000 = 2,000(1 +r)10, so r = (10,000/2,000) 1/10– 1 = 0.1746, or 17.46%b.FV = 10,000(1.12)10= $31,058.4830. Plan: Draw a timeline and determine the IRR of the investment.Execute:–IRR is the r that solves:15,000 = 20,000/(1 +r), so r = (20,000/15,000) – 1 = 33.33%Evaluate: You are making a 33.33% IRR on this investment.31. Plan: Draw a timeline to demonstrate when the cash flows will occur. Then solve the problemto determine the payments you will receive.Execute:–P = C/r,So, C = P × r= 500 × 0.08= $40Evaluate: You will receive $40 per year into perpetuity.32. Plan: Draw a timeline to determine when the cash flows occur. Solve the problem to determinethe annual payments. Timeline (from the perspective of the bank):Execute:–203,000,000$240,727.761110.05 1.05==⎛⎫- ⎪⎝⎭Cwhich is the annual payment.NI/YPVPMTFVExcel FormulaGiven: 205.00% -3000000Solve for PMT:$240727.76=PMT(0.05,20,-3000000,0)Evaluate: You will have to pay the bank $240,727.76 per year for 20 years in mortgage payments.*33. Plan: Draw a timeline to demonstrate when the cash flows will occur. Determine the annualpayments.Execute:0 2 4 6 20–This cash flow stream is an annuity. First, calculate the two-year interest rate: The one-year rate is 4%, and $1 today will be worth (1.04)2 = 1.0816 in two years, so the two-year interest rate is 8.16%. Using the equation for an annuity payment:1050,0001110.0816(1.0816)$7,505.34C =⎛⎫- ⎪⎝⎭=which is the payment you must make every two years.N I/Y PV PMT FV Excel Formula Given: 10 8.16% -50,000.00Solve for PMT: $7,505.34=PMT(0.0816,10,-50000,0)Evaluate: You must pay the art dealer $7505.34 every two years for 20 years.*34. Plan: Draw a timeline to determine when the cash flows occur. Timeline (where X is the balloon payment):0 1 2330–+ X Note that the PV of the loan payments must be equal to the amount borrowed.Execute:303023,5001300,00010.07 1.07(1.07)X⎛⎫=-+ ⎪⎝⎭ Solving for X :303023,5001300,0001(1.07)0.07 1.07$63,848X ⎡⎛⎫⎤=-- ⎪⎢⎥⎣⎝⎭⎦= NI/Y PV PMT FV Excel Formula Given: 307.00%-23,500Solve for PV:291,612.47=PV(0.07,30,-23500,0)The present value of the annuity is $291,612.47, which is $8,387.53 less than the $300,000.00. To make up for this shortfall with a balloon payment in year 30 would require a payment of $63,848.02.N I/YPVPMT FVExcel FormulaGiven: 30 7.00% 8,387.53 0Solve for FV:(63,848.02) =FV(0.07,30,0,8387.53)Evaluate: At the end of 30 years you would have to make a $63,848 single (balloon) payment to the bank.*35. Plan: Draw a timeline to demonstrate when the cash flows occur. We know that you intend tofund your retirement with a series of annuity payments and the future value of that annuity is $2 million.22 23 24 25 65 0 1 2343CC CCCExecute: FV = $2 million.The PV of the cash flows must equal the PV of $2 million in 43 years. The cash flows consist of a 43-year annuity, plus the contribution today, so the PV is:()431PV 10.05 1.05C C ⎛⎫=-+ ⎪⎝⎭The PV of $2 million in 43 years is:432,000,000$245,408.80(1.05)=N I/Y PV PMT FV Excel Formula Given: 43 5.00% 0 2,000,000Solve for PV: (245,408.80)=PV(0.05,43,0,2000000)Setting these equal gives434311245,408.800.05(1.05)245,408.80$13,232.5011110.05(1.05)C C C ⎛⎫-+= ⎪⎝⎭⇒==⎛⎫-+ ⎪⎝⎭We need $245,408.80 today to have $2,000,000 in 43 years. If we do not have $245,408.80 today, but wish to make 44 equal payments (the first payment is today, making the payments an annuity due) then the relevant Excel command is:=PMT(rate,nper,pv,(fv),type =PMT(.05,44,245,408.80,0,1) = 13,232.50Type is set equal to 1 for an annuity due as opposed to an ordinary annuity.Evaluate: You would have to put aside $13,232.50 annually to have the $2 million you wish to have in retirement.36. Plan: This problem is asking you to solve for n . You can do this mathematically using logs, orwith a financial calculator or Excel. Because the problem happens to be asking how long it will。

Fundamentals of Corporate Finance, 12e (Ross)Chapter 22 Behavioral Finance: Implications for Financial Management1) Nadine made a business decision that turned out badly. In reflecting upon her decision, she decided it was a reasoning error that led to the faulty decision. Which one of the following areas of study best applies to this situation?A) Corporate ethicsB) Financial statement analysisC) Managerial financeD) Debt managementE) Behavioral financeAnswer: EDifficulty: 1 EasyTopic: Behavioral financeLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation2) Peter has successfully managed the finances of A.D. Leadbetter in a manner that has yielded abnormally high returns. Due to this success, Peter has decided to publish a newsletter for financial executives so that he can share his superior financial wisdom with others. There is a very real probability that Peter has which one of the following characteristics?A) Gambler's fallacyB) Frame dependenceC) OverconfidenceD) Representativeness heuristicE) Sentiment-based risk attitudesAnswer: CDifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation3) Jeremy believes he excels at picking stock winners and thus trades frequently. Which characteristic does he most likely represent?A) Confirmation biasB) Frame dependenceC) OverconfidenceD) Representativeness heuristicE) Break-even effectAnswer: CDifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation4) Anytime Ted analyzes a proposed project, he always assigns a much higher probability of success to the project than is warranted by the information he has gathered. Ted suffers from which one of the following?A) Frame dependenceB) Mental accountingC) Endowment effectD) Confirmation biasE) OveroptimismAnswer: EDifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation5) The tendency for a decision maker to search for reassurance that a recent decision he or she made was a good decision represents which one of the following characteristics?A) OverconfidenceB) OveroptimismC) Affect heuristicD) Confirmation biasE) Representativeness heuristicAnswer: DDifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation6) Which one of the following best illustrates an error which you, as a project manager, might make due to confirmation bias?A) Overestimating the best outcome expected from a project while underestimating the possibility of a less favorable outcomeB) Assuming that a new project will be profitable since similar projects in the past were successfulC) Assuming that your expectations of the future outcome from a project are more accurate than the expectations of others within your organizationD) Listening to the advice of subordinates with whom you agree while ignoring the advice of subordinates with whom you tend to disagreeE) Downplaying the cost of future failure of an existing project since the project has already paid for itselfAnswer: DDifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation7) Assume you are an overconfident manager. You are most apt to do which one of the following more so than you would if you were not overconfident?A) Research a project more thoroughly before committing funds to commence itB) Accept risky projects that turn out to be less profitable than you expectedC) Wait until new technology proves its worth before incorporating it into your firm's operationsD) Avoid mergers and acquisitionsE) Invest excess company cash more conservatively than your peers at other firmsAnswer: BDifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation8) Marzella Corp. is analyzing a project that involves expanding the firm into a new product line. The project's financial projections will tend to have which one of the following characteristics if the person compiling those projections suffers from overoptimism?A) Overestimated construction costsB) Overestimated expensesC) Overestimated net present valuesD) Underestimated profitsE) Underestimated sales estimatesAnswer: CDifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation9) Alice believes she can accurately forecast the future and makes business decisions based on this belief. Which characteristics does this belief represent?A) OverconfidenceB) OveroptimismC) Affect heuristicD) Confirmation biasE) Representativeness heuristicAnswer: ADifficulty: 1 EasyTopic: BiasesLearning Objective: 22-01 Describe how behaviors such as overconfidence, overoptimism, and confirmation bias can affect decision making.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation10) Kate tends to hold onto assets that have lost value in the hope that their values will increase in the future. Kate illustrates which one of the following?A) Frame dependenceB) Self-attribution biasC) Gambler's fallacyD) Break-even effectE) Regret aversionAnswer: DDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation11) Which one of the following refers to the fact that an individual may reply differently if a question is asked in an equivalent but different manner?A) Loss aversionB) Gambler's fallacyC) Frame dependenceD) OverconfidenceE) Format referenceAnswer: CDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation12) Aivree wants to accumulate great wealth but she invests all of her funds in U.S. Treasury bills because she wants to avoid the potential losses she knows can occur in the stock markets. Aivree best illustrates which one of these characteristics?A) Loss aversionB) Gambler's fallacyC) Disposition effectD) Law of small numbersE) Mental accountingAnswer: ADifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation13) Consumer Marketing just conducted a two-phase survey. In the first phase, the survey questions were worded such that the answers tended to sound positive. In the second phase, the survey questions were reworded so the answers tended to convey a negative feeling. Both sets of survey questions should have resulted in similar results as the information solicited was essentially identical. However, the survey results varied significantly. This survey best illustrates which one of the following?A) Mental accountingB) OverconfidenceC) Self-attribution biasD) Confirmation biasE) Frame dependenceAnswer: EDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation14) Recently, a neighbor you have known for years won a lottery and received a $250,000 prize. This neighbor decided to invest all of his winnings in a new business venture that he knew only had a 5 percent chance of success. Previous to this, the neighbor had always been ultra conservative with his money and had refused to invest in this business venture as recently as last week. Which one of the following behaviors most applies to your neighbor's decision to invest in this business venture now?A) Disposition effectB) Affect heuristicC) Gambler's fallacyD) House moneyE) Get-evenitisAnswer: DDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation15) The tendency to sell winners and hold losers is known as the:A) representativeness heuristic.B) disposition effect.C) house money effect.D) self-attribution bias.E) affect heuristic.Answer: BDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation16) Steve purchased a stock last year for $34 a share. The stock increased in value to $36 a share before declining to its current value of $30. Steve has decided to sell the stock, but only if he can receive $34 a share or better. Steve is primarily suffering from which one of the following behavioral conditions?A) Representativeness heuristicB) House moneyC) Loss aversionD) RandomnessE) Myopic loss aversionAnswer: CDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation17) Over the past six months, you have watched as your parent's retirement savings have declined in value by 25 percent due to a severe financial market downturn. As a result, you have decided that you will never invest in stocks for your own retirement but will instead keep all of your money in an insured bank account. Which behavioral characteristic have you acquired as a result of the market downturn?A) Myopic loss aversionB) Get-evenitisC) Self-attribution biasD) Mental accountingE) Regret aversionAnswer: ADifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation18) Ramon opened a combination laundry and dry cleaning establishment three years ago that is quite successful. He has considered expanding this business by opening another location but keeps putting off that decision for fear that the second location will not be a success. Ramon is currently displaying which one of the following behavioral characteristics?A) Self-attribution biasB) OverconfidenceC) Regret aversionD) House money effectE) Frame dependenceAnswer: CDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation19) Phyllis is planning for her retirement in 15 years. She currently lives comfortably on $38,000a year given that she is debt-free. Based on her family history she only expects to live ten years after she retires. Thus, she computes her retirement need as $38,000 a year for ten years. Which one of the following behaviors applies to Phyllis?A) Regret aversionB) Money illusionC) Self-attribution biasD) Endowment effectE) Myopic loss aversionAnswer: BDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation20) Kate is attempting to sell her house for $260,000. Fred lives across the street in an identical house. Fred recently stated to his wife that Kate's house is probably worth only $250,000 but that once she sells her house, he would like to put their house on the market at $285,000 and then move into a condominium. Which one of the following behaviors applies to Fred?A) Myopic loss aversionB) House money effectC) Money illusionD) Self-attribution biasE) Endowment effectAnswer: EDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation21) You have a tendency to take credit for the decisions you make that have good outcomes even when those outcomes are out of your control. On the other hand, you blame bad luck for your decisions that turn out badly. Which of these terms applies to you?A) Myopic loss aversionB) House money effectC) Money illusionD) Self-attribution biasE) Endowment effectAnswer: DDifficulty: 1 EasyTopic: Framing effectsLearning Objective: 22-02 Demonstrate how framing effects can result in inconsistent and/or incorrect decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation22) A tendency to be overly conservative when faced with new information is referred to as:A) anchoring and adjustment.B) heuristics.C) self-attribution.D) loss aversion.E) regret aversion.Answer: ADifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation23) Bill feels that he possesses a good dose of "street smarts." Thus, he makes his business decisions based on how a project feels to him rather than taking the time to financially analyze a project. This type of behavior is referred to as:A) overconfidence.B) endowment effect.C) money illusion.D) affect heuristic.E) sentiment-based risk.Answer: DDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation24) Which term refers to the tendency to shy away from the unknown?A) Aversion to ambiguityB) Clustering illusionC) Anchoring and adjustmentD) Recency biasE) Availability biasAnswer: ADifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation25) You recently overheard your boss telling someone that if he'd actually crunched some numbers and done some analysis instead of just going with his instincts, he never would have opened the new store in Centre City. Which one of the following caused your boss to make a bad decision?A) Regret aversionB) Endowment effectC) Money illusionD) Affect heuristicE) Representativeness heuristicAnswer: DDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation26) Roger's Meat Market is a chain of retail stores that limits its sales to fresh-cut meats. The stores have been very profitable in northern cities. However, when two stores were opened in the south, both lost money and had to be closed. Roger, the owner, has now concluded that no southern-based store should be opened as it would not be profitable. Which one of the following applies to Roger?A) Confirmation biasB) Endowment effectC) Money illusionD) Affect heuristicE) Representativeness heuristicAnswer: EDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation27) Up until three years ago, A.C. Dime opened an average of ten new retail stores a year. One of every ten new stores had to be closed within two years due to poor sales. This 90 percent success ratio was fairly steady for over 30 years. Starting three years ago, the firm has opened 40 new stores and every one had significant profits within six months. Management believes their recent success is not just a random event and that all future stores will be profitable. Thus, the managers have decided to open a minimum of 15 new stores each year. The managers are suffering from:A) arbitrage limitations.B) anchoring and adjustment.C) aversion to ambiguity.D) the clustering illusion.E) myopic aversion.Answer: DDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation28) You are employed as a commission-based sales clerk for a cosmetics retail store. You know that, on average, exactly 50 percent of the customers that enter your store will make at least one purchase. Thus far this morning, you have waited on eight customers without making a single sale. You are convinced that the next customer you wait on will buy something. This belief is known as:A) aversion to ambiguity.B) the law of small numbers.C) anchoring and adjusting.D) gambler's fallacy.E) false consensus.Answer: DDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation29) The last six times you purchased a stock you earned high returns within one year. Thus, you believe you will have the same result with your next stock purchase. This is an example of which one of the following?A) Recency biasB) Anchoring and adjustmentC) Frame dependenceD) Aversion to ambiguityE) Clustering illusionAnswer: ADifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation30) You started an online business two weeks ago. Thus far, you have averaged ten sales a day, which is one sale for every five hits. You are now considering giving up your day job and becoming a full-time online retailer. You have calculated the amount of income you can earn based on ten sales a day and know that level of income would support you in a comfortable fashion. The belief that you will have ten sales per day if this becomes your full-time occupation is based on which one of the following?A) Mental accountingB) Anchoring and adjustmentC) Law of small numbersD) Bubble and crash theoryE) Confirmation biasAnswer: CDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation31) You are a hard-charging manager who doesn't really like to sit at a desk for too long. You prefer to gather information quickly, make a decision, and move on to the next item on your agenda. Which one of the following applies to you?A) Availability biasB) Arbitrage limitsC) Law of small numbersD) Representativeness heuristicE) Regret aversionAnswer: ADifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation32) Your friends are all investing in a start-up company. You, on the other hand, refuse to invest in the company because you don't know the odds of it becoming successful. Which behavioral characteristic are you displaying?A) Aversion to ambiguityB) Recency biasC) Sentiment-based risk aversionD) Clustering illusionE) Money illusionAnswer: ADifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation33) You are the manager of a retail store. You believe the economy is in a recession and that sales for the month will be unusually slow. Since you have complete discretion over the pricing at your location, you decide to have a storewide sale and offer ten percent off all merchandise for a three-day period. You don't expect your superiors to criticize this decision as you believe they, along with the majority of the other store managers, feel the same way about the economy as you do. Which one of the following applies to you?A) Recency biasB) Law of small numbersC) Gambler's fallacyD) False consensusE) Money illusionAnswer: DDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation34) The last two promotions within a firm involved individuals who completed the same advanced managerial program. As a result, the company president has stipulated that all future management hires must be graduates of that program. This behavior is typical of someone who has which one of the following characteristics?A) Endowment effectB) Framing effectC) Representativeness heuristicD) Narrow framingE) Affect heuristicAnswer: CDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation35) Which term refers to the reliance on stereotypes or limited samples to form opinions about an entire class?A) Clustering illusionB) Law of small numbersC) Representativeness heuristicD) False consensusE) Recency biasAnswer: CDifficulty: 1 EasyTopic: HeuristicsLearning Objective: 22-03 Show how the use of heuristics can lead to suboptimal financial decisions.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation36) It is believed by some individuals that, in an efficient market, the actions of traders who constantly buy and sell on any perceived market mispricing will in effect cause market prices to correctly reflect asset values. A person who believes that the actions of these traders will not result in correctly valued prices are most apt to believe in which one of the following?A) Gambler's fallacyB) Limits to arbitrageC) Availability biasD) False consensusE) Clustering illusionAnswer: BDifficulty: 1 EasyTopic: Arbitrage and its limitsLearning Objective: 22-04 Define the shortcomings and limitations to market efficiency from the behavioral finance view.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation37) Which one of the following is an investment risk that investors face in addition to firm-based risk and market-based risk?A) Management-related riskB) Inflation riskC) Supply chain riskD) Interest rate riskE) Sentiment-based riskAnswer: EDifficulty: 1 EasyTopic: Behavioral financeLearning Objective: 22-04 Define the shortcomings and limitations to market efficiency from the behavioral finance view.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation38) Which word best describes the stock market during the month of October 1987?A) CrashB) CircleC) BubbleD) LimitE) FlatAnswer: ADifficulty: 1 EasyTopic: Historical performanceLearning Objective: 22-04 Define the shortcomings and limitations to market efficiency from the behavioral finance view.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation39) All of the following create limits to arbitrage except:A) firm-specific risk.B) noise traders.C) thinly traded securities.D) rational traders.E) implementation costs.Answer: DDifficulty: 1 EasyTopic: Arbitrage and its limitsLearning Objective: 22-04 Define the shortcomings and limitations to market efficiency from the behavioral finance view.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation40) AB Industries is an all-equity firm that has $10 per share in cash and a book value per share of $12. At which one of the following market prices would you know with absolute certainty that the stock was mispriced?A) $9B) $10C) $11D) $12E) $13Answer: ADifficulty: 1 EasyTopic: Market efficiencyLearning Objective: 22-04 Define the shortcomings and limitations to market efficiency from the behavioral finance view.Bloom's: UnderstandAACSB: Reflective ThinkingAccessibility: Keyboard Navigation41) Approximately what percent of its total value did the stock market lose on "Black Monday"?A) 19B) 10C) 23D) 30E) 38Answer: CDifficulty: 1 EasyTopic: Historical performanceLearning Objective: 22-04 Define the shortcomings and limitations to market efficiency from the behavioral finance view.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation42) Which one of the following statements related to market crashes is correct?A) Financial market crashes are unique to the United States.B) A market crash tends to occur within a week but have effects that last many years.C) Once the market finally crashed in 1929, stock prices began a long period of steady increases.D) The market crash of 1987 occurred on a day when trading volume was light indicating there were a limited number of irrational investors involved.E) Actions in Washington, D.C., may have helped contribute to the market crash in 1929 but not to the 1987 crash.Answer: BDifficulty: 1 EasyTopic: Historical performanceLearning Objective: 22-04 Define the shortcomings and limitations to market efficiency from the behavioral finance view.Bloom's: RememberAACSB: Reflective ThinkingAccessibility: Keyboard Navigation。

Fundamentals of Corporate Finance, 12e (Ross)Chapter 3 Working with Financial Statements1) Which one of the following is a source of cash for a tax-exempt firm?A) Increase in accounts receivableB) Increase in depreciationC) Decrease in accounts payableD) Increase in common stockE) Increase in inventory2) Which one of the following is a use of cash?A) Decrease in fixed assetsB) Decrease in inventoryC) Increase in long-term debtD) Decrease in accounts receivablesE) Decrease in accounts payable3) Which one of the following is a source of cash?A) Repurchase of common stockB) Acquisition of debtC) Purchase of inventoryD) Payment to a supplierE) Granting credit to a customer4) Which one of the following is a source of cash?A) Increase in accounts receivableB) Decrease in common stockC) Increase in fixed assetsD) Decrease in accounts payableE) Decrease in inventory5) On the statement of cash flows, which one of the following is considered a financing activity?A) Increase in inventoryB) Decrease in accounts payableC) Increase in net working capitalD) Dividends paidE) Decrease in fixed assets6) On the statement of cash flows, which one of the following is considered an operating activity?A) Increase in net fixed assetsB) Decrease in accounts payableC) Purchase of equipmentD) Dividends paidE) Repayment of long-term debt7) According to the statement of cash flows, an increase in inventory will ________ the cash flow from ________ activities.A) increase; operatingB) decrease; financingC) decrease; operatingD) increase; financingE) increase; investment8) According to the statement of cash flows, an increase in interest expense will ________ the cash flow from ________ activities.A) decrease; operatingB) decrease; financingC) increase; operatingD) increase; financingE) Increase; investment9) Activities of a firm that require the spending of cash are known as:A) sources of cash.B) uses of cash.C) cash collections.D) cash receipts.E) cash on hand.10) The sources and uses of cash over a stated period of time are reflected on the:A) income statement.B) balance sheet.C) tax reconciliation statement.D) statement of cash flows.E) statement of operating position.11) A common-size income statement is an accounting statement that expresses all of a firm's expenses as a percentage of:A) total assets.B) total equity.C) net income.D) taxable income.E) sales.12) Which one of the following standardizes items on the income statement and balance sheet relative to their values as of a chosen point in time?A) Statement of standardizationB) Statement of cash flowsC) Common-base year statementD) Common-size statementE) Base reconciliation statement13) On a common-size balance sheet all accounts for the current year are expressed as a percentage of:A) sales for the period.B) the base year sales.C) total equity for the base year.D) total assets for the current year.E) total assets for the base year.14) On a common-base year financial statement, accounts receivables for the current year will be expressed relative to which one of the following?A) Current year salesB) Current year total assetsC) Base-year salesD) Base-year total assetsE) Base-year accounts receivables15) Which one of the following ratios is a measure of a firm's liquidity?A) Cash coverage ratioB) Profit marginC) Debt-equity ratioD) Quick ratioE) NWC turnover16) An increase in current liabilities will have which one of the following effects, all else held constant? Assume all ratios have positive values.A) Increase in the cash ratioB) Increase in the net working capital to total assets ratioC) Decrease in the quick ratioD) Decrease in the cash coverage ratioE) Increase in the current ratio17) An increase in which one of the following will increase a firm's quick ratio without affecting its cash ratio?A) Accounts payableB) CashC) InventoryD) Accounts receivableE) Fixed assets18) A supplier, who requires payment within 10 days, should be most concerned with which one of the following ratios when granting credit?A) CurrentB) CashC) Debt-equityD) QuickE) Total debt19) A firm has an interval measure of 48. This means that the firm has sufficient liquid assets to do which one of the following?A) Pay all of its debts that are due within the next 48 hoursB) Pay all of its debts that are due within the next 48 daysC) Cover its operating costs for the next 48 hoursD) Cover its operating costs for the next 48 daysE) Meet the demands of its customers for the next 48 hours20) Ratios that measure a firm's liquidity are known as ________ ratios.A) asset managementB) long-term solvencyC) short-term solvencyD) profitabilityE) book value21) Which one of the following statements is correct?A) If the total debt ratio is greater than .50, then the debt-equity ratio must be less than 1.0.B) Long-term creditors would prefer the times interest earned ratio be 1.4 rather than 1.5.C) The debt-equity ratio can be computed as 1 plus the equity multiplier.D) An equity multiplier of 1.2 means a firm has $1.20 in sales for every $1 in equity.E) An increase in the depreciation expense will not affect the cash coverage ratio.22) If a firm has a debt-equity ratio of 1.0, then its total debt ratio must be which one of the following?A) 0B) .5C) 1.0D) 1.5E) 2.023) The cash coverage ratio directly measures the ability of a company to meet its obligation to pay:A) an invoice to a supplier.B) wages to an employee.C) interest to a lender.D) principal to a lender.E) a dividend to a shareholder.24) All-State Moving had sales of $899,000 in 2017 and $967,000 in 2018. The firm's current accounts remained constant. Given this information, which one of the following statements must be true?A) The total asset turnover rate increased.B) The days' sales in receivables increased.C) The net working capital turnover rate increased.D) The fixed asset turnover decreased.E) The receivables turnover rate decreased.25) The Corner Hardware has succeeded in increasing the amount of goods it sells while holding the amount of inventory on hand at a constant level. Assume that both the cost per unit and the selling price per unit also remained constant. This accomplishment will be reflected in the firm's financial ratios in which one of the following ways?A) Decrease in the inventory turnover rateB) Decrease in the net working capital turnover rateC) Increase in the fixed asset turnover rateD) Decrease in the day's sales in inventoryE) Decrease in the total asset turnover rate26) RJ's has a fixed asset turnover rate of 1.26 and a total asset turnover rate of .97. Sam's has a fixed asset turnover rate of 1.31 and a total asset turnover rate of .94. Both companies have similar operations. Based on this information, RJ's must be doing which one of the following?A) Utilizing its fixed assets more efficiently than Sam'sB) Utilizing its total assets more efficiently than Sam'sC) Generating $1 in sales for every $1.26 in net fixed assetsD) Generating $1.26 in net income for every $1 in net fixed assetsE) Maintaining the same level of current assets as Sam's27) Ratios that measure how efficiently a firm manages its assets and operations to generate net income are referred to as ________ ratios.A) asset managementB) long-term solvencyC) short-term solvencyD) profitabilityE) turnover28) If a company produces a return on assets of 14 percent and also a return on equity of 14 percent, then the firm:A) may have short-term, but not long-term debt.B) is using its assets as efficiently as possible.C) has no net working capital.D) has a debt-equity ratio of 1.0.E) has an equity multiplier of 1.0.29) Which one of the following will decrease if a firm can decrease its operating costs, all else constant?A) Return on equityB) Return on assetsC) Profit marginD) Total asset turnoverE) Price-earnings ratio30) Al's has a price-earnings ratio of 18.5. Ben's also has a price-earnings ratio of 18.5. Which one of the following statements must be true if Al's has a higher PEG ratio than Ben's?A) Al's has more net income than Ben's.B) Ben's is increasing its earnings at a faster rate than Al's.C) Al's has a higher market value per share than does Ben's.D) Ben's has a lower market-to-book ratio than Al's.E) Al's has a higher earnings growth rate than Ben's.31) Tobin's Q relates the market value of a firm's assets to which one of the following?A) Initial cost of creating the firmB) Current book value of the firmC) Average asset value of similar firmsD) Average market value of similar firmsE) Today's cost to duplicate those assets32) The price-sales ratio is especially useful when analyzing firms that have:A) volatile market prices.B) negative earnings.C) positive PEG ratios.D) a high Tobin's Q.E) increasing sales.33) Mortgage lenders probably have the most interest in the ________ ratios.A) return on assets and profit marginB) long-term debt and times interest earnedC) price-earnings and debt-equityD) market-to-book and times interest earnedE) return on equity and price-earnings34) Relationships determined from a company's financial information and used for comparison purposes are known as:A) financial ratios.B) identities.C) dimensional analysis.D) scenario analysis.E) solvency analysis.35) DL Farms currently has $600 in debt for every $1,000 in equity. Assume the company uses some of its cash to decrease its debt while maintaining its current equity and net income. Which one of the following will decrease as a result of this action?A) Equity multiplierB) Total asset turnoverC) Profit marginD) Return on assetsE) Return on equity36) Which one of these identifies the relationship between the return on assets and the return on equity?A) Profit marginB) Profitability determinantC) Balance sheet multiplierD) DuPont identityE) Debt-equity ratio37) Which one of the following accurately describes the three parts of the DuPont identity?A) Equity multiplier, profit margin, and total asset turnoverB) Debt-equity ratio, capital intensity ratio, and profit marginC) Operating efficiency, equity multiplier, and profitability ratioD) Return on assets, profit margin, and equity multiplierE) Financial leverage, operating efficiency, and profitability ratio38) An increase in which of the following must increase the return on equity, all else constant?A) Total assets and salesB) Net income and total equityC) Total asset turnover and debt-equity ratioD) Equity multiplier and total equityE) Debt-equity ratio and total debt39) Which one of the following is a correct formula for computing the return on equity?A) Profit margin × ROAB) ROA × Equity multiplierC) Profit margin × Total asset turnover × Debt-equity ratioD) Net income/Total assetsE) Debt-equity ratio × ROA40) The DuPont identity can be used to help managers answer which of the following questions related to a company's operations?I. How many sales dollars are being generated per each dollar of assets?II. How many dollars of assets have been acquired per each dollar in shareholders' equity? III. How much net profit is being generating per dollar of sales?IV. Does the company have the ability to meet its debt obligations in a timely manner?A) I and III onlyB) II and IV onlyC) I, II, and III onlyD) II, III and IV onlyE) I, II, III, and IV41) The U.S. government coding system that classifies a company by the nature of its business operations is known as the:A) Centralized Business Index.B) Peer Grouping codes.C) Standard Industrial Classification codes.D) Governmental ID codes.E) Government Engineered Coding System.42) Which one of the following statements is correct?A) Book values should always be given precedence over market values.B) Financial statements are rarely used as the basis for performance evaluations.C) Historical information is useful when projecting a company's future performance.D) Potential lenders place little value on financial statement information.E) Reviewing financial information over time has very limited value.43) The most acceptable method of evaluating the financial statements is to compare the company's current financial:A) ratios to the company's historical ratios.B) statements to the financial statements of similar companies operating in other countries.C) ratios to the average ratios of all companies located within the same geographic area.D) statements to those of larger companies in unrelated industries.E) statements to the projections that were created based on Tobin's Q.44) All of the following issues represent problems encountered when comparing the financial statements of two separate entities except the issue of the companies:A) being conglomerates with unrelated lines of business.B) having geographically varying operations.C) using differing accounting methods.D) differing seasonal peaks.E) having the same fiscal year.45) Which one of these is the least important factor to consider when comparing the financial situations of utility companies that generate electric power and have the same SIC code?A) Type of ownershipB) Government regulations affecting the firmC) Fiscal year endD) Methods of power generationE) Number of part-time employees46) At the beginning of the year, Brick Makers had cash of $183, accounts receivable of $392, accounts payable of $463, and inventory of $714. At year end, cash was $167, accounts payables was $447, inventory was $682, and accounts receivable was $409. What is the amount of the net source or use of cash by working capital accounts for the year?A) Net use of $16 cashB) Net use of $17 cashC) Net source of $17 cashD) Net source of $15 cashE) Net use of $15 cash47) During the year, Al's Tools decreased its accounts receivable by $160, increased its inventory by $115, and decreased its accounts payable by $70. How did these three accounts affect the sources of uses of cash by the firm?A) Net source of cash of $120B) Net source of cash of $205C) Net source of cash of $45D) Net use of cash of $115E) Net use of cash of $2548) Lani's generated net income of $911, depreciation expense was $47, and dividends paid were $25. Accounts payables increased by $15, accounts receivables increased by $28, inventory decreased by $14, and net fixed assets decreased by $8. There was no interest expense. What was the net cash flow from operating activity?A) $776B) $865C) $959D) $922E) $98549) For the past year, Jenn's Floral Arrangements had taxable income of $198,600, beginning common stock of $68,000, beginning retained earnings of $318,750, ending common stock of $71,500, ending retained earnings of $316,940, interest expense of $11,300, and a tax rate of 21 percent. What is the amount of dividends paid during the year?A) $157,280B) $159,935C) $163,200D) $153,555E) $158,70450) The Floor Store had interest expense of $38,400, depreciation of $28,100, and taxes of $19,600 for the year. At the start of the year, the firm had total assets of $879,400 and current assets of $289,600. By year's end total assets had increased to $911,900 while current assets decreased to $279,300. What is the amount of the cash flow from investment activity for the year?A) −$51,150B) $21,850C) $29,300D) −$70,900E) −$89,40051) Williamsburg Market is an all-equity firm that has net income of $96,200, depreciation expense of $6,300, and an increase in net working capital of $2,800. What is the amount of the net cash from operating activity?A) $91,300B) $99,700C) $93,400D) $105,300E) $113,70052) The accounts payable of a company changed from $136,100 to $104,300 over the course of a year. This change represents a:A) use of $31,800 of cash as investment activity.B) source of $31,800 of cash as an operating activity.C) source of $31,800 of cash as a financing activity.D) source of $31,800 of cash as an investment activity.E) use of $31,800 of cash as an operating activity.53) Oil Creek Auto has sales of $3,340, net income of $274, net fixed assets of $2,600, and current assets of $920. The firm has $430 in inventory. What is the common-size statement value of inventory?A) 12.22 percentB) 44.16 percentC) 16.54 percentD) 13.36 percentE) 46.74 percent54) Pittsburgh Motors has sales of $4,300, net income of $320, total assets of $4,800, and total equity of $2,950. Interest expense is $65. What is the common-size statement value of the interest expense?A) .89 percentB) 1.51 percentC) 1.69 percentD) 2.03 percentE) 1.35 percent55) Last year, which is used as the base year, a firm had cash of $52, accounts receivable of $223, inventory of $509, and net fixed assets of $1,107. This year, the firm has cash of $61,accounts receivable of $204, inventory of $527, and net fixed assets of $1,216. What is this year's common-base-year value of inventory?A) .67B) .91C) .88D) 1.04E) 1.1856) Duke's Garage has cash of $68, accounts receivable of $142, accounts payable of $235, and inventory of $318. What is the value of the quick ratio?A) 2.25B) .53C) .71D) .89E) 1.3557) Uptown Men's Wear has accounts payable of $2,214, inventory of $7,950, cash of $1,263, fixed assets of $8,400, accounts receivable of $3,907, and long-term debt of $4,200. What is the value of the net working capital to total assets ratio?A) .31B) .42C) .47D) .51E) .5658) DJ's has total assets of $310,100 and net fixed assets of $168,500. The average daily operating costs are $2,980. What is the value of the interval measure?A) 31.47 daysB) 47.52 daysC) 56.22 daysD) 68.05 daysE) 104.62 days59) Corner Books has a debt-equity ratio of .57. What is the total debt ratio?A) .36B) .30C) .44D) 2.27E) 2.7560) SS Stores has total debt of $4,910 and a debt-equity ratio of 0.52. What is the value of the total assets?A) $16,128.05B) $7,253.40C) $9,571.95D) $11,034.00E) $14,352.3161) JK Motors has sales of $96,400, costs of $53,800, interest paid of $2,800, and depreciation of $7,100. The tax rate is 21 percent. What is the value of the cash coverage ratio?A) 15.21B) 12.14C) 17.27D) 23.41E) 12.6862) Terry's Pets paid $2,380 in interest and $2,200 in dividends last year. The times interest earned ratio is 2.6 and the depreciation expense is $680. What is the value of the cash coverage ratio?A) 1.42B) 2.72C) 2.94D) 2.89E) 2.4663) The Up-Towner has sales of $913,400, costs of goods sold of $579,300, inventory of $123,900, and accounts receivable of $78,900. How many days, on average, does it take the firm to sell its inventory assuming that all sales are on credit?A) 74.19 daysB) 84.69 daysC) 78.07 daysD) 96.46 daysE) 71.01 days64) Flo's Flowers has accounts receivable of $4,511, inventory of $1,810, sales of $138,609, and cost of goods sold of $64,003. How many days does it take the firm to sell its inventory and collect the payment on the sale assuming that all sales are on credit?A) 11.88 daysB) 22.20 daysC) 16.23 daysD) 14.50 daysE) 18.67 days65) The Harrisburg Store has net working capital of $2,715, net fixed assets of $22,407, sales of $31,350, and current liabilities of $3,908. How many dollars' worth of sales are generated from every $1 in total assets?A) $1.08B) $1.14C) $1.19D) $84E) $9366) TJ's has annual sales of $813,200, total debt of $171,000, total equity of $396,000, and a profit margin of 5.78 percent. What is the return on assets?A) 8.29 percentB) 6.48 percentC) 9.94 percentD) 7.78 percentE) 8.02 percent67) Frank's Used Cars has sales of $807,200, total assets of $768,100, and a profit margin of 6.68 percent. The firm has a total debt ratio of 54 percent. What is the return on equity?A) 13.09 percentB) 12.04 percentC) 11.03 percentD) 8.56 percentE) 15.26 percent68) Bernice's has $823,000 in sales. The profit margin is 4.2 percent and the firm has 7,500 shares of stock outstanding. The market price per share is $16.50. What is the price-earnings ratio?A) 3.58B) 3.98C) 4.32D) 3.51E) 4.2769) Hungry Lunch has net income of $73,402, a price-earnings ratio of 13.7, and earnings per share of $.43. How many shares of stock are outstanding?A) 13,520B) 12,460C) 165,745D) 171,308E) 170,70270) A firm has 160,000 shares of stock outstanding, sales of $1.94 million, net income of $126,400, a price-earnings ratio of 21.3, and a book value per share of $7.92. What is the market-to-book ratio?A) 2.12B) 1.84C) 1.39D) 2.45E) 2.6971) Taylor's Men's Wear has a debt-equity ratio of 48 percent, sales of $829,000, net income of $47,300, and total debt of $206,300. What is the return on equity?A) 19.29 percentB) 11.01 percentC) 15.74 percentD) 18.57 percentE) 14.16 percent72) Nielsen's has inventory of $29,406, accounts receivable of $46,215, net working capital of $4,507, and accounts payable of $48,919. What is the quick ratio?A) 1.55B) .49C) 1.32D) .94E) .9273) The Strong Box has sales of $859,700, cost of goods sold of $648,200, net income of $93,100, and accounts receivable of $102,300. How many days of sales are in receivables?A) 57.60 daysB) 40.32 daysC) 54.53 daysD) 29.41 daysE) 43.43 days74) Corner Books has sales of $687,400, cost of goods sold of $454,200, and a profit margin of 5.5 percent. The balance sheet shows common stock of $324,000 with a par value of $5 a share, and retained earnings of $689,500. What is the price-sales ratio if the market price is $43.20 per share?A) 4.28B) 12.74C) 6.12D) 4.07E) 14.5175) Gem Jewelers has current assets of $687,600, total assets of $1,711,000, net working capital of $223,700, and long-term debt of $450,000. What is the debt-equity ratio?A) .87B) .94C) 1.21D) 1.15E) 1.0676) Russell's has annual sales of $649,200, cost of goods sold of $389,400, interest of $23,650, depreciation of $121,000, and a tax rate of 21 percent. What is the cash coverage ratio for the year?A) 8.43B) 10.99C) 11.64D) 5.87E) 18.2277) Lawn Care, Inc., has sales of $367,400, costs of $183,600, depreciation of $48,600, interest of $39,200, and a tax rate of 25 percent. The firm has total assets of $422,100, long-term debt of $102,000, net fixed assets of $264,500, and net working capital of $22,300. What is the return on equity?A) 24.26 percentB) 15.38 percentC) 38.96 percentD) 29.96 percentE) 17.06 percent78) Frank's Welding has net fixed assets of $36,200, total assets of $51,300, long-term debt of $22,000, and total debt of $29,700. What is the net working capital to total assets ratio?A) 12.18 percentB) 16.82 percentC) 14.42 percentD) 17.79 percentE) 9.90 percent79) The Green Fiddle has current liabilities of $28,000, sales of $156,900, and cost of goods sold of $62,400. The current ratio is 1.22 and the quick ratio is .71. How many days on average does it take to sell the inventory?A) 128.13 daysB) 74.42 daysC) 199.81 daysD) 147.46 daysE) 83.53 days80) Green Yard Care has net income of $62,300, a tax rate of 21 percent, and a profit margin of 6.7 percent. Total assets are $1,100,500 and current assets are $328,200. How many dollars of sales are being generated from every dollar of net fixed assets?A) $2.83B) $1.37C) $.84D) $1.20E) $1.2381) Jensen's Shipping has total assets of $694,800 at year's end. The beginning owners' equity was $362,400. During the year, the company had sales of $711,000, a profit margin of 5.2 percent, a tax rate of 21 percent, and paid $12,500 in dividends. What is the equity multiplier at year-end?A) 1.67B) 1.72C) 1.93D) 1.80E) 1.8682) Western Gear has net income of $12,400, a tax rate of 21 percent, and interest expense of $1,600. What is the times interest earned ratio for the year?A) 9.63B) 7.75C) 10.81D) 14.97E) 10.9783) Big Tree Lumber has earnings per share of $1.36. The firm's earnings have been increasing at an average rate of 2.9 percent annually and are expected to continue doing so. The firm has 21,500 shares of stock outstanding at a price per share of $23.40. What is the firm's PEG ratio?A) 2.27B) 11.21C) 4.85D) 3.94E) 5.9384) Townsend Enterprises has a PEG ratio of 5.3, net income of $49,200, a price-earnings ratio of 17.6, and a profit margin of 7.1 percent. What is the earnings growth rate?A) 2.48 percentB) 1.06 percentC) 3.32 percentD) 5.20 percentE) 10.60 percent85) A firm has total assets with a current book value of $71,600, a current market value of $82,300, and a current replacement cost of $90,400. What is the value of Tobin's Q?A) .85B) .87C) .90D) .94E) .9186) Dixie Supply has total assets with a current book value of $368,900 and a current replacement cost of $486,200. The market value of these assets is $464,800. What is the value of Tobin's Q?A) .79B) .76C) .96D) 1.26E) 1.0587) Dandelion Fields has a Tobin's Q of .96. The replacement cost of the firm's assets is $225,000 and the market value of the firm's debt is $101,000. The firm has 20,000 shares of stock outstanding and a book value per share of $2.09. What is the market-to-book ratio?A) 2.75 timesB) 3.18 timesC) 3.54 timesD) 4.01 timesE) 4.20 times88) The Tech Store has annual sales of $416,000, a price-earnings ratio of 18, and a profit margin of 3.7 percent. There are 12,000 shares of stock outstanding. What is the price-sales ratio?A) .97B) .67C) 1.08D) 1.15E) .8689) Lassiter Industries has annual sales of $328,000 with 8,000 shares of stock outstanding. The firm has a profit margin of 4.5 percent and a price-sales ratio of 1.20. What is the firm's price-earnings ratio?A) 21.9B) 17.4C) 18.6D) 26.7E) 24.390) Drive-Up has sales of $31.4 million, total assets of $27.6 million, and total debt of $14.9 million. The profit margin is 3.7 percent. What is the return on equity?A) 6.85 percentB) 9.15 percentC) 11.08 percentD) 13.31 percentE) 14.21 percent91) Corner Supply has a current accounts receivable balance of $246,000. Credit sales for the year just ended were $2,430,000. How many days on average did it take for credit customers to pay off their accounts during this past year?A) 44.29 daysB) 55.01 daysC) 55.50 daysD) 36.95 daysE) 41.00 days92) BL Industries has ending inventory of $302,800, annual sales of $2.33 million, and annual cost of goods sold of $1.41 million. On average, how long did a unit of inventory sit on the shelf before it was sold?A) 47.43 daysB) 22.18 daysC) 78.38 daysD) 61.78 daysE) 83.13 days93) Billings Inc. has net income of $161,000, a profit margin of 7.6 percent, and an accounts receivable balance of $127,100. Assume that 66 percent of sales are on credit. What is the days' sales in receivables?A) 21.90 daysB) 27.56 daysC) 33.18 daysD) 35.04 daysE) 36.19 days94) Stone Walls has a long-term debt ratio of .6 and a current ratio of 1.2. Current liabilities are $800, sales are $7,800, the profit margin is 6.5 percent, and return on equity is 15.5 percent. What is the amount of the firm's net fixed assets?A) $8,880.15B) $8,017.43C) $7,666.67D) $5,848.15E) $8,977.43。

Chapter 5Interest RatesNote: All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problemswith a higher level of difficulty. 1. a. Because six months is 61244= of two years, using our rule 1/4(10.2) 1.0466.+= So the equivalent six-month rate is 4.66%.b. Because one year is half of two years 1/2(1.2) 1.0954.=So the equivalent one-year rate is 9.54%.c. Because one month is 1/24 of two years, using our rule 1/24(10.2) 1.00763.+=So the equivalent one-month rate is 0.763%.2. a. 0.06/12 = 0.005 or 0.5%b. (1.005)12 – 1 = 0.0617 or 6.17%3. Plan: The only way to compare these two rates is to convert them into their effective annual rates (EARs). To compute the EAR, you must first convert to the true rate at the appropriatecompounding interval and then compound that rate over one year. The first rate is given as 15% compounded monthly, so you have to first compute the true monthly rate. The second rate is already given as a six-month rate (8% every six months), so you just have to compound it to get the EAR:Execute: 122APR 0.150.0125(1.0125)10.16075compounding periods 120.08,compounding periods 2(1.08)10.1664r EAR r EAR ====-====-=Evaluate:You should use your credit card because the effective annual rate is lower.52 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition4. Plan: Because the interest rates are quoted over different intervals, the only way to compare them is to compute the interest over a common interval. Here, the natural common interval to choose is three years. Execute:If you deposit $1 into a bank account that pays 5% per year for three years, you will have 3(1.05) 1.15763= after three years.a. If the account pays 21/2% per six months, then you will have 6(1.025) 1.15969= afterthree years, so you prefer 21/2% every six months. b. If the account pays 71/2% per 18 months, then you will have 2(1.075) 1.15563= afterthree years, so you prefer 5% per year.c. If the account pays 1/2% per month then you will have 36(1.005) 1.19668= after three years,so you prefer 1/2% every month. Evaluate:The comparisons are very difficult to make unless you put them on an equal footing (common interval). Once you do so, the better choice becomes clear.*5. Plan: Draw a timeline to fully understand the timing of the cash flows. Determine the presentvalue of the bonus payments.Execute:B ecause 1.086 = 1.8509, the equivalent discount rate for a 6-year period is 85.09%.Using the annuity formula811(1.8509)PV 50,000$26,817.761.8509⎛⎫⎛⎫- ⎪ ⎪⎝⎭ ⎪== ⎪ ⎪⎝⎭NI/YPVPMT FVExcel FormulaGiven: 885.09%50,000 0Solve for PV:(26817.76)=PV(0.8509,8,50000,0)Evaluate: The PV of the annuity is $26,817.76.Chapter 5 Interest Rates 536. Plan: Determine the EAR for each investment option.Execute: For $1 invested in an account with 10% APR with monthly compounding you will have120.11$1.10471.12⎛⎫+= ⎪⎝⎭So the EAR is 10.471%.For $1 invested in an account with 10% APR with annual compounding, you will have (10.1)$1.10.+= So the EAR is 10%.For $1 invested in an account with 9% APR with daily compounding, you will have3650.091 1.09416.365⎛⎫+= ⎪⎝⎭So the EAR is 9.416%.Evaluate: One dollar invested at 10% APR compounded monthly will grow to $1.10471 in one year. This is greater than the values for the other two investments and, therefore, is superior.7. Plan: Use the formula for converting from an EAR to an APR quote (Eq. 5.3).APR 1 1.05kk ⎛⎫+= ⎪⎝⎭Execute:Solving for the APR1/APR (1.05)1kk ⎡⎤=-⎣⎦With annual payments k = 1, so APR = 5%. With semiannual payments k = 2, so APR = 4.939%. With monthly payments k = 12, so APR = 4.889%. Evaluate:The same effective annual rate can be quoted many different ways using different compoundingperiods.54 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition8. Plan: Determine the present value of the annuity.Execute: Using the PV of an annuity formula with N = 30 payments and C = $500 with r = 4.06% per 4-month interval because there is a 12% APR with monthly compounding: 12%/12 = 1% per month, or (1.01)4 - 1 = 4.06% per four months.()30111 4.06%PV 500 4.06%$8,583.38⎛⎫-⎪+ ⎪=⨯ ⎪ ⎪⎝⎭=NI/Y PV PMT FV Excel FormulaGiven: 304.06% 500 0Solve for PV:(8583.38)=PV(0.0406,30,500,0)Evaluate: The PV of the annuity is $8583.38.9. The fee is just an interest payment. If you pay $30 for a $200 loan, that’s $30/$200 = 15%interest FOR TWO WEEKS! So your effective annual interest rate for this loan compounds the 15% over the 26 two-week periods in the year: (1.15)26 – 1 = 36.8568, or 3,685.68% !! 10. Plan: Draw a timeline to demonstrate when the tuition payments will be needed. Thencalculate the PV of the tuition payments.Execute:0 1214Four percent APR (semiannual) implies a semiannual discount rate of 4%2%.2=So,810,0001PV 10.02(1.02)$73,254.81⎛⎫=- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 8 2.000%10000 0Solve for PV:(73,254.81)=PV(0.02,8,10000,0)Chapter 5 Interest Rates 55Evaluate: You will have to deposit $73,254.81 in the bank today in order to be able to make the tuition payments over the next four years.11. Plan: Compute the discount rate from the APR formula.Execute: Using the formula for computing the discount rate from an APR quote:8Discount Rate 2% per month.4==Evaluate: The interest rate is 2% per month.12. Plan: Draw a timeline for the cash flows. Given that $12,000 is the present value of an annuityof payments, determine the amount of the payments.Execute:-12,0006% APR monthly implies a discount rate of 6% / 12 = 0.5%Using the formula for computing a loan payment200.5%11(10.5%)12,000632-+=⨯=CNI/YPVPMT FVExcel FormulaGiven: 200.5% 12000 0Solve for PMT:(632)=PMT(0.005,20,12000,0)Evaluate: Your monthly payment for the motorcycle loan is $154.63.13. Plan: Draw a timeline to better understand when the cash flows are occurring. Because$150,000 is the present value of an annuity of mortgage payments, determine the amount of the mortgage payments.Execute:The monthly interest rate is: ()1/121.06810.5497367%-=56 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global EditionSolve for the annuity payments that give the PV of the mortgage (150,000).360150,000$957.661110.005497367(1.005497367)C ==⎛⎫- ⎪⎝⎭N I/Y PV PMT FV Excel FormulaGiven: 360 0.550% 150,000.00Solve for PMT:(957.68)=PMT(0.00549736708252291,360,150000,0)Evaluate: The monthly mortgage payment is $957.66.14. Plan: Plan: First, compute the payments. Because the payments are monthly, you need themonthly interest rate. An APR of 12%, compounded monthly is a monthly rate of 0.12/12 = 0.01, or a percent per month. You can use Eq. 4.9 to calculate the loan payment. We can break that payment into the interest (principal of the loan × the interest rate) and the remainder, which reduces the principal.Execute:9696PMT 12000010.01(10.01)(28000)(0.01)455.0811(10.01)⎡⎤=-⎢⎥+⎣⎦==⎡⎤-⎢⎥+⎣⎦PMTThe interest in the first month will be the $28,000 borrowed multiplied by 1% per month:(28,000)(0.01) = $280. So, of your first payment of $455.08, $280 will go toward interest and $175.08 will go toward principal.Evaluate:Typically, early in loans, much of the payment goes toward interest, but as the principal decreases and the payments stay the same, more and more of each payment goes toward principal.*15. Plan: Determine the present value of the savings on mortgage payments and the additionalprincipal paid you would make by paying the point. Compare that to the cost of the point.Execute: First, solve for the monthly mortgage payment at 6.5% APR. The 6.5% APR implies a monthly rate of3606.5%0.541667%12400,000$2,528.27.1110.00541667(1.00541667)C ===⎛⎫- ⎪⎝⎭Chapter 5 Interest Rates 57N I/Y PV PMT FV Excel FormulaGiven: 360 0.542% 400,000.00Solve for PMT:(2,528.27) = PMT(0.065/12,360,400000,0)Next, solve for the monthly mortgage payment at 6.25% APR. The 6.25% APR implies a monthly rate of3606.25%0.520833%12400,000$2,462.87.1110.00520833(1.00520833)C ===⎛⎫- ⎪⎝⎭N I/Y PV PMT FV Excel FormulaGiven: 360 0.521% 400,000.00Solve for PMT:(2,462.87) = PMT(0.06525/12,360,400000,0)So the lower interest rate on the mortgage results in a savings of $65.40 each month. If weknow that we will stay in the house at least five years, is this monthly savings worth the initial cost of $4,000? Solve for the PV of the mortgage payments, using the 6.25% APR as the interest rate (because this is the opportunity cost of the money):benefits 6065.401PV 10.00520833(1.00520833)3,362.60⎛⎫=- ⎪⎝⎭=NPV = PV benefits - PV costsNPV = 3362.60 - 4000 = -637.40.N I/Y PV PMT FV Excel FormulaGiven: 60 0.521%65.4 0Solve for PV:(3,362.60)=PV(0.00520833333333333,60,65.4,0)Balance of the 6.5% loan at the end of five years (with 300 payments remaining):3002,528.2711374,443.460.00541667(1.00541667)PV ⎡⎤=-=⎢⎥⎣⎦N I/Y PVPMTFV Excel Formula Given: 60 0.541667% (400,000) 2528.27Solve for PV:374,444.15 = FV(0.065/12,60,2528.27,–400000)58 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global EditionBalance of the 6.25% loan at the end of five years (with 300 payments remaining):3002,462.8711373,349.300.00520833(1.00520833)PV ⎡⎤=-=⎢⎥⎣⎦N I/YPVPMT FV Excel Formula Given: 60 0.520833% (400,000) 2462.87Solve for PV:373348.79= FV(.0625/12,60,2462.87,–400000)Difference in principal = 374,444.15 – 373,348.79 = 1,094.17()601,094.17801.161.00520833PV ==PV(benefits) = 3,362.60 +801.16 = 4,163.76 Cost = 4,000Net = 4,163.76 – 4,000 = 163.76Evaluate: The net is positive; therefore, you should pay the point. The small net benefit showsthat the decision is sensitive to how long you will be in the house —if you move in less than five years, you will not have benefited enough to offset the $4,000 cost.16. Plan: Draw a timeline to better understand the timing and amounts of the cash flows. Calculatethe loan balance after four years and eight months of payments.Execute:56 57 58360To find out what is owed, compute the PV of the remaining payments using the loan interest rate to compute the discount rate:3046.375Discount Rate 0.53125%122,3561PV 10.0053125(1.0053125)$354,900==⎛⎫=- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 304 0.531%2356 0Solve for PV:(354,899.99)=PV(0.0053125,304,2356,0)Evaluate: You would owe $354,900 on the mortgage at the end of four years and eight months.Chapter 5 Interest Rates 59*17. Plan: Compute the original loan payment. Then determine how much you owe to the bank atthe end of 18 years.First, we need to compute the original loan payment.Execute: 145% APR (monthly) implies a discount rate of 5.25120.4375%.=Using the formula for a loan payment360800,0000.00437511(1.004375)$4,417.63C ⨯=⎛⎫- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 360 0.438% 800,000.00Solve for PMT:(4,417.63)=PMT(0.004375,360,800000,0)Now we can compute the PV of continuing to make these payments.The timeline is:222 223 224 225 360Using the formula for the PV of an annuity1384,417.631PV 10.004375(1.004375)$456,931.41⎛⎫=- ⎪⎝⎭=So, you would keep $1,000,000 - $456,931 = $543,069.N I/Y PV PMT FV Excel FormulaGiven: 138 0.438%4,417.63Solve for PV:(456,931.45)=PV(0.004375,138,4417.63,0)Evaluate: You would keep $543,069 from the sale of the home.60 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition18. Plan: Draw a timeline and compute the sums that are indicated.Execute: a. Timeline:0 1 2 3 60F irst, solve for the monthly mortgage payment at 6% APR. The 6% APR implies a monthly rate of 6%120.50%=. 6050,000$966.641110.005(1.005)C ==⎛⎫- ⎪⎝⎭N I/Y PV PMT FV Excel FormulaGiven: 60 0.500%50,000.00Solve for PMT:(966.64)=PMT(0.005,60,50000,0)Each monthly payment is $966.64. After one month, the balance (principal) of the loan willbe the PV of the 59 remaining payments.59966.641PV 1$49,283.360.005(1.005)⎛⎫=-= ⎪⎝⎭N I/Y PV PMT FV Excel FormulaGiven: 59 0.500%966.64 0Solve for PV:(49,283.36)=PV(0.005,59,966.64,0)50,000 - 49,283.36 = 716.64 is amount of the payment that went to paying the principal,while 966.64 = 716.64 = 250 was interest.F or the second month, solve for the value of the remaining 58 payments:58966.641PV 1$48,563.140.005(1.005)⎛⎫=-= ⎪⎝⎭N I/Y PV PMT FV Excel FormulaGiven: 58 0.500%966.64 0Solve for PV:(48,563.13)=PV(0.005,58,966.64,0)49,283.36 - 48,563.14 = 720.22 is the amount of the payment that went to paying theprincipal, while 966.64 – 720.22 = 246.42 was interest.F or the first year, solve for the value of the remaining 48 payments:48966.641PV 10.005(1.005)$41,159.84⎛⎫=- ⎪⎝⎭=50,000 - 41,159.84 = 8,840.16 is amount of the payment that went to paying the principal, while (966.64 ⨯ 12) - 8,840.416 = 2,759.52 was interest.b. At the end of year 3, there are 24 payments remaining. The balance of the loan is:24966.641PV 10.005(1.005)$21,810.17⎛⎫=- ⎪⎝⎭=A t the end of year 4, there are only 12 payments remaining. The balance of the loan at the end of the four year is:12966.641PV 10.005(1.005)$11,231.33⎛⎫=- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 12 0.500%966.64 0Solve for PV:(11,231.33)=PV(0.005,12,966.64,0)21,810.17 - 11,231.33 = 10,578.86 is amount of the payment that went to paying the principal, while (966.64 ⨯ 12) - 10,578.86 = 1,020.82 was interest.Evaluate: A financial analyst can determine the amount of any loan payment. The financial analyst can also determine the outstanding amount on the loan at any time over its life.19. Plan: You can think of a lease as a loan with a balloon payment at the end (when you return the car or give them the residual value). The CF timeline is:1 …36 +30,000 -PMT … -PMT-15,000First, get the present value of the residual value of the car (you will give them $15,000 to keep the car or instead give them the car, which they agree to assign a value of $15,000). Subtract this from the price of the car, and what is left is what you have to cover with your annuity of payments.Execute:363615,00012,534.6730,00012,534.6717,465.331.005117,465.331.005(1.005)531.33PV CF CF ==-=⎡⎤=-⎢⎥⎣⎦=Evaluate:Your lease payment will be $531.33, which is less than it would be if you were buying the car with a three-year loan. Lease payments reduce the monthly cost of using the car, but at the end of the lease, you do not own the car.*20. Plan: Draw a timeline to better understand the timing and amount of the cash flows. Thendetermine how much faster the loan would be paid off with a one-time additional $1,000 payment.0 1 2 3 36First, calculate the remaining balance on the loan, which is the PV of the remaining payments on the loan.Execute: The 7% APR implies a monthly rate of367%0.58333%126001PV 10.0058333(1.0058333)$19,431.88=⎛⎫=- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 36 0.583%600 0Solve for PV:(19,431.88)=PV(0.00583333333333333,36,600,0)If you plan on paying an additional $1,000 next month, the timeline changes to this:0 1 2 3N –1,000We want to know how long the payments will last if you include an additional $1,000 in next month’s payment. The principal of the loan must equal the PV of the payments made on the loan, so we can solve for the remaining length of time on the loan:60011,00019,431.8810.0058333(1.0058333) 1.0058333600118,437.6810.0058333(1.0058333)10.1792541(1.0058333)110.1792540.820746(1.0058333)1.0058333 1.218404log(1.218404)log(1.00NN NNN N ⎛⎫=-+ ⎪⎝⎭⎛⎫=- ⎪⎝⎭=-=-===58333)33.96=Evaluate: Thus, you reduce the amount of time remaining on the loan by slightly more than two months (from 36 to 34).*21. Plan: Draw a timeline to better understand the timing and amount of the cash flows. Thendetermine how much a one-time additional $100 payment today will reduce your last payment.Execute: We begin with the timeline of our required payments.Let’s compute our remaining balance on the student loan. As we pointed out earlier, theremaining balance equals the present value of the remaining payments. The loan interest rate is 9% APR, or 9%/12 = 0.75% per month, so the present value of the payments is:485001PV 10.0075 1.0075$20,092.39⎛⎫=- ⎪⎝⎭= Using the annuity spreadsheet to compute the present value, we get the same number: N I/Y PV PMT FV 480.75%20,092.39-500Thus, your remaining balance is $20,092.39.47–5000 2 –5001 –50048 –500If you prepay an extra $100 today, you will lower your remaining balance to $20,092.39 - 100 = $19,992.39. Though your balance is reduced, your required monthly payment does not change. Instead, you will pay off the loan faster; that is, it will reduce the payments you need to make at the very end of the loan. How much smaller will the final payment be? With the extra payment, the timeline changes:That is, we will pay off by paying $500 per month for 47 months, and some smaller amount, $500 - X , in the last month. To solve for X , recall that the PV of the remaining cash flows equals the outstanding balance when the loan interest rate is used as the discount rate:4848500119,992.3910.0075(10.0075) 1.0075X ⎛⎫=-- ⎪+⎝⎭ Solving for X gives4819,992.3920,092.39 1.0075$143.14XX =-=So the final payment will be lower by $143.14.You can also use the annuity spreadsheet to determine this solution. If you prepay $100 today, and make payments of $500 for 48 months, then your final balance at the end will be a credit of $143.14: N I/Y PV PMT FV 480.75%19,992.39-500143.14The extra payment effectively lets us exchange $100 today for $143.14 in four years. Weclaimed that the return on this investment should be the loan interest rate. Let’s see if this is the case:48$100(1.0075)$143.14,so it is.⨯=Thus, you earn a 9% APR (the rate on the loan).Evaluate: Your last payment will be reduced by $143.14.47 –5000 19,992.392 –5001 –50048 –(500 – X)*22. Plan: Draw a timeline to better understand the timing and amount of the cash flows. Thendetermine how much faster the loan would be paid off if you increase each additional payment by $250.And we want to determine the number of monthly payments N that we will need to make. That is, we need to determine what length an annuity with a monthly payment of $750 has the same present value as the loan balance, using the loan interest rate as the discount rate. As we did in Chapter 4, we set the outstanding balance equal to the present value of the loan payments and solve for N .Execute:()()7501120,092.390.00751.0075120,092.390.007510.2009241.0075750110.2009240.7990761.00751.0075 1.25145Log(1.25145)30.02Log(1.0075)NNNN N -=⨯-===-====We can also use the annuity spreadsheet to solve for N :N I/Y PV PMT FV 30.020.75%20,092.39-750Evaluate: So, by prepaying the loan, we will pay off the loan in about 30 months or 2 ½ years, rather than the four years originally scheduled. Because N of 30.02 is larger than 30, we could either increase the 30th payment by a small amount or make a very small 31st payment. We can use the annuity spreadsheet to determine the remaining balance after 30 payments: N I/Y PV PMT FV 300.75%20,092.39-750-13.86If we make a final payment of $750.00 + $13.87 = $763.87, the loan will be paid off in 30 months.N –7500 20,092.392 –7501 –750*23. Plan: Draw a timeline to determine the amount and timing of the cash flows. Then determinehow much more quickly the loan would be paid off with payments made every two weeks versus every month.Evaluate: From the solution to Problem 5.11, the monthly payment on the mortgage is $957.66.So if we make 957.662$478.83= every two weeks the timeline is:0 1 2 3 NNow because there are 26 weeks in a year1/26(1.0680)=1.0025335So, the discount rate is 0.25335%.To compute N we set the PV of the loan payments equal to the outstanding balance478.831150,00010.0025335(1.0025335)N⎛⎫=- ⎪⎝⎭And solve for N1150,0000.002533510.7936041.0025335478.8610.2063961.0025335log(0.206396)623.631log 1.0025335NN N ⨯⎛⎫-== ⎪⎝⎭⎛⎫= ⎪⎝⎭==⎛⎫⎪⎝⎭N I/Y PV PMTFVExcel FormulaGiven:0.253% 0.00 478.83150,00Solve for NPER: -623.72=NPER(0.00253350161796617,478.83,0,150000)Evaluate: So it will take 624 payments to pay off the mortgage. Because the payments occurevery two weeks, this will take 62421,248⨯= weeks, or approximately 24 years. (It is shorter because there are approximately two extra payments every year.)*24. Plan: Draw a timeline to determine the amount and timing of the cash flows. Then determinehow much more quickly the loan would be paid off with a double payment made January 1. Execute: The principal balance does not matter, so just pick 100,000. Begin by computing the monthly payment. The discount rate is 12%/12 = 1%.Timeline #1: 0 1 2 360Execute: Using the formula for the loan payment360100,0000.01$1,028.6111 1.01C ⨯==⎛⎫- ⎪⎝⎭NI/Y PV PMT FV Excel FormulaGiven: 3601.000% 100,000.00Solve for PMT:(1,028.61)=PMT(0.01,360,100000,0)Next we write out the cash flows with the extra payment:Timeline #2:0 1 6 718 19N -- -1,028.61-1,028.61The cash flow consists of two annuities.a. The original payments. The PV of these payments is:org1,028.611PV 10.01 1.01N⎛⎫⎛⎫=- ⎪ ⎪ ⎪⎝⎭⎝⎭b. The extra payment is every Christmas. There are m such payments, where m is the number of years you keep the loan. (For the moment we will not worry about the possibility that m is not a whole number.) Because the time period between payments is one year, we first have to compute the discount rate()121.01 1.12683.=So the discount rate is 12.683%.Now the present value of the extra payments in month 6 consists of the remaining m – 1 payments (an annuity) and the payment in month 6. So the PV is:611028.611PV 11028.610.12683(1.12683)m -⎛⎫=-+ ⎪⎝⎭To get the value today, we must discount these cash flows to month zero. Recall that themonthly discount rate is 1%. So the value today of the extra payment is:6extra 6616PV 1028.6111028.61PV 1(1.01)0.12683(1.01)(1.12683)(1.01)m -==⎛⎫-+ ⎪⎝⎭To find out how long it will take to repay the loan, we need to determine the number of yearsuntil the value of our loan payments has a present value at the loan rate equal to the amount we borrowed. Because the number of monthly payments N = 12 ⨯ m , we can write this as the following expression which we need to solve for m :org extra12616100,000PV PV 1,028.611100,00010.01 1.011,028.6111,028.6110.12683(1.01)(1.12683)(1.01)mm -=+⎛⎫⎛⎫=-⎪ ⎪⎝⎭⎝⎭⎛⎫+-+ ⎪⎝⎭The only way to find m is to iterate (guess). The answer is 19.04 years,m =or approximately19 years. In fact, after exactly 19 years, the PV of the payment is:22861861,028.6111028.6111,028.61PV 110.01 1.010.12683(1.01)(1.12683)(1.01)$99,939⎛⎫⎛⎫⎛⎫=-+-+⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭=Because you initially borrowed $100,000, the PV of what you still owe at the end of 19 years is $100,000 - $99,939 = $61. The future value of this in 19 years and 1 month is:22961(1.01)$596⨯=Evaluate: So you will have a partial payment of $596 in the first month of the 19th year. Because the mortgage will take about 19 years to pay off this way —which is close to 2/3 of its life of 30 years —your friend is right.25. Plan: a. First we deal with analyzing the existing mortgage, and analyzing several other financing alternatives. E xecute: First, we calculate the outstanding balance of the mortgage. There are 25 ⨯ 12 = 300 months remaining on the loan, so the timeline is as follows. T imeline 1:0 1 2 300T o determine the outstanding balance, we discount at the original rate, i.e., 10120.8333%.=3001,4021PV 10.008333(1.008333)$154,286.22⎛⎫=- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 300 0.833%1402 0Solve for PV:(154,286.22)=PV(.10/12,300,1402,0)N ext we calculate the loan payment on the new mortgage.T imeline 2:0 1 2 360 T he discount rate on the new loan is the new loan rate: 6.625120.5521%.=U sing the formula for the loan payment:360154,286.220.00552111 1.005521$987.93C ⨯=⎛⎫⎛⎫- ⎪ ⎪⎝⎭⎝⎭=NI/Y PV PMT FV Excel FormulaGiven: 360 0.552% 154,286.22Solve for PMT:(987.91) =PMT(.06625/12,360,154286.22,0)b. 300154,286.220.005521$1,053.8511 1.005521C ⨯==⎛⎫⎛⎫-⎪ ⎪⎝⎭⎝⎭NI/Y PV PMT FV Excel FormulaGiven: 300 0.552% 154,286.22Solve for PMT:(1,053.83) =PMT(.06625/12,300,154286.22,0)c. 14021PV 1$154,286.22170 months 0.005521(1.005521)N N ⎛⎫=-=⇒= ⎪⎝⎭(You can use trial and error or the annuity calculator to solve for N .)N I/Y PV PMT FV Excel FormulaGiven:0.552% 0.00 1,402 154,286Solve for NPER: -169.89=NPER(0.06625/12,1402,0,154286.22)d. ()30014021PV 1$205,2550.005521 1.005521you can keep 205,259154,286$50,969⎛⎫=-= ⎪⎝⎭⇒-=(Note: Results may differ slightly due to rounding. If you don’t round at all, the answer will be 205,259, so you could keep 50,973.)N I/Y PV PMT FV Excel FormulaGiven: 300 0.552%1,402 0Solve for PV:(205,259.23)=PV(0.06625/12,300,1402,0)E valuate: In considering this mortgage refinancing, it is clear that the homeowner has several alternatives that will depend on the amount of monthly payments to be made and how long it will take to pay off the mortgage.26. Plan: Use a timeline and financial analysis to determine how much more you could borrow at the lower rate and keep the same payments. Execute: The discount rate on the original card is 15121.25%.=Assuming that your current monthly payment is the interest that accrues, it equals:0.15$25,000$312.5012⨯= 01 2This is a perpetuity. So the amount you can borrow at the new interest rate is this cash flowdiscounted at the new discount rate. The new discount rate is 12121%.=So,312.50PV 0.01$31,250==Evaluate: So by switching credit cards you are able to spend an extra 31,25025,000$6,250.-= You do not have to pay taxes on this amount of new borrowing, so this is your after-tax benefit of switching cards.27. Plan: Draw a timeline to determine the amount and timing of the cash flows. Then determine how much you would owe at the end of five years.Execute:a. The payments are established as if the loan will last 15 years. Thus, the “timeline” for determining the payments looks like this:0 1 2 180T he discount rate is 9%/12 = 0.75% per month.180500,0000.007511 1.0075$5,071.33C ⨯=⎛⎫- ⎪⎝⎭=N I/Y PV PMT FV Excel FormulaGiven: 180 0.750% 500,000.00Solve for PMT:(5,071.33)=PMT(0.0075,180,500000,0)b. The actual timeline of payments is:0 1 2 60To solve for X , set the PV of the payments equal to $500,000:596060605,071.331500,0001500,000241,064.020.0075(1.0075) 1.0075258,935.98 1.0075258,935.98 1.0075405,411.15X XX ⎛⎫=-+- ⎪⎝⎭===⨯=。