Chapter 4: Net Present Value
Concept Questions - Chapter 4
4.1 ? Define future value and present value.
Future value is the value of a sum after investing over one or more periods.
Present value is the value today of cash flows to be received in the future.
?How does one use net present value when making an investment decision?
One determines the present value of future cash flows and then subtracts the cost of the investment. If this value is positive, the investment should be undertaken.
If the NPV is negative, then the investment should be rejected.
4.2 ? What is the difference between simple interest and compound interest?
With simple interest, the interest on the original investment is not reinvested.
With compound interest, each interest payment is reinvested and one earns
interest on interest.
?What is the formula for the net present value of a project?
T
NPV = -C0 + ∑ C t /(1+I)t
t=1
4.3 ? What is a stated annual interest rate?
The stated annual interest rate is the annual interest rate without consideration of compounding.
? What is an effective annual interest rate?
An effective annual interest rate is a rate that takes compounding into account.
? What is the relationship between the stated annual interest rate and the
effective annual interest rate?
Effective annual interest rate = (1 + (r/m) )m - 1.
?Define continuous compounding.
Continuous compounding compounds investments every instant.
4.4 ? What are the formulas for perpetuity, growing-perpetuity, annuity, and
growing annuity?
Perpetuity: PV = C/r
Growing Perpetuity: PV = C/(r-g)
Annuity: PV = (C/r) [1-1/(1+r)T]
Growing Annuity: PV = [C/(r-g)] [1-((1+g) / (1+r))T ] ?What are three important points concerning the growing perpetuity formula?
1.The numerator.
2.The interest rate and the growth rate.
3.The timing assumption.
?What are four tricks concerning annuities?
1. A delayed annuity.
2.An annuity in advance
3.An infrequent annuity
4.The equating of present values of two annuities.
Answers to End-of-Chapter Problems
Questions And Problems
Annual Compounding
4.1 Compute the future value of $1,000 compounded annually for
a. 10 years at 5 percent.
b. 10 years at 7 percent.
c. 20 years at 5 percent.
d. Why is the interest earned in part c not twice the amount earned in part a?
4.1 a. $1,000 ? 1.0510 = $1,628.89
b. $1,000 ? 1.0710 = $1,967.15
c. $1,000 ? 1.0520 = $2,653.30
d. Interest compounds on the interest already earned. Therefore, the interest earned
in part c, $1,653.30, is more than double the amount earned in part a, $628.89.
4.2 Calculate the present value of the following cash flows discounted at 10 percent.
a. $1,000 received seven years from today.
b. $2,000 received one year from today.
c. $500 received eight years from today.
4.2 a. $1,000 / 1.17 = $513.16
b. $2,000 / 1.1 = $1,818.18
c. $500 / 1.18 = $233.25
4.3 Would you rather receive $1,000 today or $2,000 in 10 years if the discount rate is 8 percent?
96 Part II Value and Capital Budgeting
14The following conventions are used in the questions and problems for this chapter.
If more frequent compounding than once a year is indicated, the problem will either state: (1) both a stated annual interest rate and a compounding period, or (2) an effective annual interest rate.
If annual compounding is indicated, the problem will provide an annual interest rate. Since the stated annual interest rate and the effective annual interest rate are the same here, we use the simpler annual interest rate.
4.3 You can make your decision by computing either the present value of the $2,000 that you
can receive in ten years, or the future value of the $1,000 that you can receive now.
Present value: $2,000 / 1.0810 = $926.39
Future value: $1,000 ? 1.0810 = $2,158.93
Either calculation indicates you should take the $1,000 now.
4.4 The government has issued a bond that will pay $1,000 in 25 years. The bond will pay no interim coupon payments. What is the present value of the bond if the discount rate is 10 percent?
4.4 Since this bond has no interim coupon payments, its present value is simply the present
value of the $1,000 that will be received in 25 years. Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond.
PV = $1,000 /1.125 = $92.30
4.5 A firm has an estimated pension liability of $1.5 million due 27 years from today. If the
firm can invest in a risk-free security that has a stated annual interest rate of 8 percent, how
much must the firm invest today to be able to make the $1.5 million payment?
4.5 PV = $1,500,000 / 1.0827 = $187,780.23
4.6 You have won the Florida state lottery. Lottery officials offer you the choice of the following alternative payouts:
Alternative 1: $10,000 one year from now.
Alternative 2: $20,000 five years from now.
Which alternative should you choose if the discount rate is:
a. 0 percent?
b. 10 percent?
c. 20 percent?
d. What discount rate makes the two alternatives equally attractive to you?
4.6 a. At a discount rate of zero, the future value and present value are always the same.
Remember, FV = PV (1 + r) t. If r = 0, then the formula reduces to FV = PV.
Therefore, the values of the options are $10,000 and $20,000, respectively. You
should choose the second option.
b. Option one: $10,000 / 1.1 = $9,090.91
Option two: $20,000 / 1.15 = $12,418.43
Choose the second option.
c. Option one: $10,000 / 1.2 = $8,333.33
Option two: $20,000 / 1.25 = $8,037.55
Choose the first option.
d. You are indifferent at the rate that equates the PVs of the two alternatives. You
know that rate must fall between 10% and 20% because the option you would
choose differs at these rates. Let r be the discount rate that makes you indifferent
between the options.
$10,000 / (1 + r) = $20,000 / (1 + r)5
(1 + r)4 = $20,000 / $10,000 = 2
1 + r = 1.18921
r = 0.18921 = 18.921%
4.7 You are selling your house. The Smiths have offered you $115,000. They will pay you immediately. The Joneses have offered you $150,000, but they cannot pay you until three years from today. The interest rate is 10 percent. Which offer should you choose?
4.7 PV of Joneses’ offer = $150,000 / (1.1)3 = $112,697.22
Since the PV of Joneses’ offer is less than Smiths’ offer, $115,000, you should choose
Smiths’ offer.
4.8 Suppose you bought a bond that will pay $1,000 in 20 years. No intermediate coupon
payments will be made. If the appropriate discount rate for the bond is 8 percent,
a. what is the current price of the bond?
b. what will the price be 10 years from today?
c. what will the price be 15 years from today?
4.8 a. P0 = $1,000 / 1.0820 = $214.55
b. P10 = P0 (1.08)10 = $463.20
c. P15 = P0 (1.08)15 = $680.59
4.9 Suppose you deposit $1,000 in an account at the end of each of the next four years. If the account earns 12 percent, how much will be in the account at the end of seven years?
4.9 The $1,000 that you place in the account at the end of the first year will earn interest for six
years. The $1,000 that you place in the account at the end of the second year will earn
interest for five years, etc. Thus, the account will have a balance of
$1,000 (1.12)6 + $1,000 (1.12)5 + $1,000 (1.12)4 + $1,000 (1.12)3
= $6,714.61
4.10 Ann Woodhouse is considering the purchase of a house. She expects that she will own the house for 10 years and then sell it for $5 million. What is the most she would be willing to pay for the house if the appropriate discount rate is 12 percent?
4.10 PV = $5,000,000 / 1.1210 = $1,609,866.18
4.11 You have the opportunity to make an investment that costs $900,000. If you make this investment now, you will receive $120,000 one year from today, $250,000 and $800,000 two and three years from today, respectively. The appropriate discount rate for this investment is 12 percent.
a. Should you make the investment?
b. What is the net present value (NPV) of this opportunity?
c. If the discount rate is 11 percent, should you invest? Compute the NPV to support your answer.
4.11 a. The cost of investment is $900,000.
PV of cash inflows = $120,000 / 1.12 + $250,000 / 1.122 + $800,000 / 1.123
= $875,865.52
Since the PV of cash inflows is less than the cost of investment, you should not
make the investment.
b. NPV = -$900,000 + $875,865.52
= -$24,134.48
c. NPV = -$900,000 + $120,000 / 1.11 + $250,000 / 1.112 + $800,000 / 1.113
= $-4,033.18
Since the NPV is still negative, you should not make the investment.
4.12 You have the opportunity to invest in a machine that will cost $340,000. The machine will
generate cash flows of $100,000 at the end of each year and require maintenance costs of
$10,000 at the beginning of each year. If the economic life of the machine is five years and
the relevant discount rate is 10 percent, should you buy the machine? What if the relevant
discount rate is 9 percent?
4.12 NPV = -($340,000 + $10,000) + ($100,000 - $10,000) / 1.1
+ $90,000 / 1.12 + $90,000 / 1.13 + $90,000 / 1.14 + $100,000 / 1.15
= -$2,619.98
Since the NPV is negative, you should not buy it.
If the relevant cost of capital is 9 percent,
NPV = -$350,000 + $90,000 / 1.09 + $90,000 / 1.092 + $90,000 / 1.093
+ $90,000 / 1.094 + $100,000 / 1.095
= $6,567.93
Since the NPV is positive, you should buy it.
4.13 Today a firm signed a contract to sell a capital asset for $90,000. The firm will receive
payment five years from today. The asset costs $60,000 to produce.
a. If the appropriate discount rate is 10 percent, is the firm making a profit on this item?
b. At what appropriate discount rate will the firm break even?
4.13 a. Profit = PV of revenue - Cost = NPV
NPV = $90,000 / 1.15 - $60,000 = -$4,117.08
No, the firm will not make a profit.
b. Find r that makes zero NPV.
$90,000 / (1+r)5 - $60,000 = $0
(1+r)5 = 1.5
r = 0.08447 = 8.447%
4.14 Your aunt owns an auto dealership. She promised to give you $3,000 in trade-in value
for your car when you graduate one year from now, while your roommate offered you
$3,500 for the car now. The prevailing interest rate is 12 percent. If the future value of
benefit from owning the car for one year is expected to be $1,000, should you accept
your aunt’s offer?
Compounding Periods
4.14 The future value of the decision to own your car for one year is the sum of the trade-in
value and the benefit from owning the car. Therefore, the PV of the decision to own the car for one year is
$3,000 / 1.12 + $1,000 / 1.12 = $3,571.43
Since the PV of the roommate’s offer, $3,500, is lower than the aunt’s offer, you should
accept aunt’s offer.
4.15 What is the future value three years hence of $1,000 invested in an account with a stated annual interest rate of 8 percent,
a. compounded annually?
b. compounded semiannually?
c. compounded monthly?
d. compounded continuously?
e. Why does the future value increase as the compounding period shortens?
4.15 a. $1.000 (1.08)3 = $1,259.71
b. $1,000 [1 + (0.08 / 2)]2 ? 3 = $1,000 (1.04)6 = $1,265.32
c. $1,000 [1 + (0.08 / 12)]12 ? 3 = $1,000 (1.00667)36 = $1,270.24
d. $1,000 e0.08 ? 3 = $1,271.25
e. The future value increases because of the compounding. The account is earning
interest on interest. Essentially, the interest is added to the account balance at the
end of every compounding period. During the next period, the account earns
interest on the new balance. When the compounding period shortens, the balance
that earns interest is rising faster.
4.16 Compute the future value of $1,000 continuously compounded for
a. 5 years at a stated annual interest rate of 12 percent.
b. 3 years at a stated annual interest rate of 10 percent.
c. 10 years at a stated annual interest rate of 5 percent.
d. 8 years at a stated annual interest rate of 7 percent.
4.16 a. $1,000 e0.12 ? 5 = $1,822.12
b. $1,000 e0.1 ? 3 = $1,349.86
c. $1,000 e0.05 ? 10 = $1,648.72
d. $1,000 e0.07 ? 8 = $1,750.67
4.17 Calculate the present value of $5,000 in 12 years at a stated annual interest rate of 10 percent, compounded quarterly.
4.17 PV = $5,000 / [1+ (0.1 / 4)]4 ? 12 = $1,528.36
4.18 Bank America offers a stated annual interest rate of 4.1 percent, compounded quarterly,
while Bank USA offers a stated annual interest rate of 4.05 percent, compounded monthly.
In which bank should you deposit your money?
Perpetuities and Growing Perpetuities
4.18 Effective annual interest rate of Bank America
= [1 + (0.041 / 4)]4 - 1 = 0.0416 = 4.16%
Effective annual interest rate of Bank USA
= [1 + (0.0405 / 12)]12 - 1 = 0.0413 = 4.13%
You should deposit your money in Bank America.
4.19 The market interest rate is 15 percent. What is the price of a consol bond that pays $120 annually? 4.19 The price of the consol bond is the present value of the coupon payments. Apply the
perpetuity formula to find the present value. PV = $120 / 0.15 = $800
4.20 A prestigious investment bank designed a new security that pays a quarterly dividend of $10 permanently. What is the price of the security if the stated annual interest rate is 12 percent, compounded quarterly?
4.20 Quarterly interest rate = 12% / 4 = 3% = 0.03
Therefore, the price of the security = $10 / 0.03 = $333.33
4.21 World Transportation, Inc., is expected to initiate its quarterly dividend of $1 five years
from today and the dividend is expected to remain constant permanently. What is the price
of World Transportation stock if the stated annual interest rate is 15 percent, compounded
quarterly?
4.21 The price at the end of 19 quarters (or 4.75 years) from today = $1 / (0.15 4) = $26.67
The current price = $26.67 / [1+ (.15 / 4)]19 = $13.25
4.22 Assuming an interest rate of 10 percent, calculate the present value of the following
streams of yearly payments:
a. $1,000 per year forever, with the first payment one year from today.
b. $500 per year forever, with the first payment two years from today.
c. $2,420 per year forever, with the first payment three years from today.
4.22 a. $1,000 / 0.1 = $10,000
b. $500 / 0.1 = $5,000 is the value one year from now of the perpetual stream. Thus,
the value of the perpetuity is $5,000 / 1.1 = $4,545.45.
c. $2,420 / 0.1 = $24,200 is the value two years from now of the perpetual stream.
Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.
4.23 Given an interest rate of 10 percent per year, what is the value at date t _ 5 (i.e., the end of
year 5) of a perpetual stream of $120 annual payments starting at date t _ 9?
4.23 The value at t = 8 is $120 / 0.1 = $1,200.
Thus, the value at t = 5 is $1,200 / 1.13 = $901.58.
4.24 Harris, Inc., paid a $3 dividend yesterday. If the firm raises its dividend at 5 percent every
year and the appropriate discount rate is 12 percent, what is the price of Harris stock?
4.24 P = $3 (1.05) / (0.12 - 0.05) = $4
5.00
4.25 In its most recent corporate report,Williams, Inc., apologized to its stockholders for not
paying a dividend. The report states that management will pay a $1 dividend next year.
That dividend will grow at 4 percent every year thereafter. If the discount rate is 10
percent, how much are you willing to pay for a share of Williams, Inc.?
4.25 P = $1 / (0.1 - 0.04) = $16.67
4.26 Mark Weinstein has been working on an advanced technology in laser eye surgery. The technology is expected to be available to the medical industry two years from today and
will generate annual income of $200,000 growing at 5 percent perpetually. What is the
present value of the technology if the discount rate is 10 percent?
Annuities and Growing Annuities
4.26 The first cash flow will be generated 2 years from today.
The value at the end of 1 year from today = $200,000 / (0.1 - 0.05) = $4,000,000.
Thus, PV = $4,000,000 / 1.1 = $3,636,363.64.
4.27 IDEC Pharmaceuticals is considering a drug project that costs $100,000 today and is
expected to generate end-of-year annual cash flow of $50,000 forever. At what discount
rate would IDEC be indifferent between accepting or rejecting the project?
4.27 A zero NPV
- $100,000 + $50,000 / r = 0
r = 0.5
4.28 Should you buy an asset that will generate income of $1,200 per year for eight years? The price of the asset is $6,200 and the annual interest rate is 10 percent.
4.28 Apply the NPV technique. Since the inflows are an annuity you can use the present value
of an annuity factor.
A
NPV = -$6,200 + $1,200 8
1.0
= -$6,200 + $1,200 (5.3349)
= $201.88
Yes, you should buy the asset.
4.29 What is the present value of end-of-year cash flows of $2,000 per year, with the first cash flow received three years from today and the last one 22 years from today? Use a discount rate of 8 percent.
4.29 Use an annuity factor to compute the value two years from today of the twenty payments.
Remember, the annuity formula gives you the value of the stream one year before the first payment. Hence, the annuity factor will give you the value at the end of year two of the
A
stream of payments. Value at the end of year two = $2,000 20
08
.0
= $2,000 (9.8181)
= $19,636.20
The present value is simply that amount discounted back two years.
PV = $19,636.20 / 1.082 = $16,834.88
4.30 What is the value of a 15-year annuity that pays $500 a year? The annuity’s first payment is at the end of year 6 and the annual interest rate is 12 percent for years 1 through 5 and 15 percent thereafter.
4.30 The value of annuity at the end of year five
A = $500 (5.84737) = $2,923.69
= $500 15
.0
15
The present value = $2,923.69 / 1.125 = $1,658.98
4.31 You are offered the opportunity to buy a note for $12,800. The note is certain to pay $2,000 at the end of each of the next 10 years. If you buy the note, what rate of interest will you receive?
4.31 The easiest way to do this problem is to use the annuity factor. The annuity factor must be
equal to $12,800 / $2,000 = 6.4; remember PV =C A t r. The annuity factors are in the
appendix to the text. To use the factor table to solve this problem, scan across the row
labeled 10 years until you find 6.4. It is close to the factor for 9%, 6.4177. Thus, the rate you will receive on this note is slightly more than 9%.
You can find a more precise answer by interpolating between nine and ten percent.
10% ? 6.1446 ?
a ? r ?
b
c ? 6.4 ? d
? 9% ?? 6.4177 ?
By interpolating, you are presuming that the ratio of a to b is equal to the ratio of c to d.
(9 - r ) / (9 - 10) = (6.4177 - 6.4 ) / (6.4177 - 6.1446)
r = 9.0648%
The exact value could be obtained by solving the annuity formula for the interest rate.
Sophisticated calculators can compute the rate directly as 9.0626%.
4.32 You need $25,000 five years from now. You budget to make equal payments at the end of every year into an account that pays an annual interest rate of 7 percent.
a. What are your annual payments?
b. Your rich uncle died and left you $20,000. How much of it must you put into the same
account as a lump sum today to meet your goal?
4.32 a. The annuity amount can be computed by first calculating the PV of the $25,000
which you need in five years. That amount is $17,824.65 [= $25,000 / 1.075].
Next compute the annuity which has the same present value.
A
$17,824.65 = C 5
07
.0
$17,824.65 = C (4.1002)
C = $4,347.26
Thus, putting $4,347.26 into the 7% account each year will provide $25,000 five
years from today.
b. The lump sum payment must be the present value of the $25,000, i.e., $25,000 /
1.075 = $17,824.65
The formula for future value of any annuity can be used to solve the problem (see
footnote 14 of the text).
4.33 Nancy Ferris bought a building for $120,000. She paid 15 percent down and agreed to pay the balance in 20 equal annual installments. What are the equal installments if the annual interest rate is 10 percent? 4.33 The amount of loan is $120,000 ? 0.85 = $102,000.
20
C A= $102,000
.0
10
The amount of equal installments is
A = $102,000 / 8.513564 = $11,980.88
C = $102,000 / 20
.0
10
4.34 Jack Ferguson has signed a three-year contract to work for a computer software company. He expects to receive a base salary of $5,000 a month and a bonus of $10,000 at year-end. All payments are made at the end of periods. What is the present value of the contract if the stated annual interest rate, compounded monthly, is 12 percent?
A = $150,537.53
4.34 The present value of salary is $5,000 36
01
.0
A = $23,740.42 (EAR = 12.68% is used since
The present value of bonus is $10,000 3
.0
1268
bonuses are paid annually.)
The present value of the contract = $150,537.53 + $23,740.42 = $174,277.94
4.35 Peter Green bought a $15,000 Honda Civic with 20 percent down and financed the rest with a four-year loan at 8 percent stated annual interest rate, compounded monthly. What is his monthly payment if he starts the payment one month after the purchase?
4.35
The amount of loan is $15,000 ? 0.8 = $12,000.
C 480067.0A = $12,000
The amount of monthly installments is C = $12,000 / 480067.0A = $12,000 / 40.96191 = $292.96
4.36 You have recently won the super jackpot in the Illinois state lottery. On reading the fine print, you discover that you have the following two options:
a. You receive $160,000 at the beginning of each year for 31 years. The income would be taxed at a rate of 28 percent. Taxes are withheld when the checks are issued.
b. You receive $1,750,000 now, but you do not have access to the full amount immediately. The
$1,750,000 would be taxed at 28 percent. You are able to take $446,000 of the after-tax amount now. The remaining $814,000 will be placed in a 30-year annuity account that pays $101,055 on a before-tax basis at the end of each year.
Using a discount rate of 10 percent, which option should you select?
4.36 Option one: This cash flow is an annuity due. To value it, you must use the after-tax
amounts. The after-tax payment is $160,000 (1 - 0.28) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of
$115,200 to obtain the value of this option.
Value = $115,200 + $115,200 30
10.0A
= $115,200 + $115,200 (9.4269)
= $1,201,178.88
Option two: This option is valued similarly. You are able to have $446,000 now; this is
already on an after-tax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those payments are taxable when you receive them, so your after-tax
payment is $72,759.60 [= $101,055 (1 - 0.28)].
Value = $446,000 + $72,759.60 30
10.0A
= $446,000 + $72,759.60 (9.4269)
= $1,131,897.47
Since option one has a higher PV, you should choose it.
4.37 On September 1, 1998, Susan Chao bought a motorcycle for $10,000. She paid $1,000 down and financed the balance with a five-year loan at a stated annual interest rate of 9.6 percent, compounded
monthly. She started the monthly payment exactly one month after the purchase, i.e., October, 1998. In the middle of October, 2000, she got a new job and decided to pay off the loan. If the bank charges her 1
percent prepayment penalty based on the loan balance, how much should she pay the bank on November 1, 2000?
4.37
The amount of loan is $9,000. The monthly payment C is given by solving the equation:
C 60008.0A = $9,000
C = $9,000 / 47.5042 = $189.46
In October 2000, Susan Chao has 35 (= 12 ? 5 - 25) monthly payments left, including the one due in October 2000.
Therefore, the balance of the loan on November 1, 2000
= $189.46 + $189.46 34008.0A
= $189.46 + $189.46 (29.6651)
= $5,809.81
Thus, the total amount of payoff = 1.01 ($5,809.81) = $5,867.91
4.38 Assume that the cost of a college education will be $20,000 per year when your child enters college 12 years from now. You currently have $10,000 to invest. What rate of interest must your investment earn to pay the cost of a four-year college education for your child? For simplicity, assume the entire cost of the college education must be paid when your child enters college.
4.38
Let r be the rate of interest you must earn.
$10,000(1 + r)12 = $80,000
(1 + r)12 = 8 r = 0.18921 = 18.921%
4.39 You are saving for the college education of your two children. They are two years apart in age; one will begin college in 15 years, the other will begin in 17 years. You estimate your children ’s college expenses to be $21,000 per year per child. The annual interest rate is 15 percent. How much money must you deposit in an account each year to fund your children ’s education? You will begin payments one year from today. You will make your last deposit when your oldest child enters college.
4.39 First compute the present value of all the paymen ts you must make for your children’s
education. The value as of one year before matriculation of one child’s education is
$21,000 415.0A = $21,000 (2.8550) = $59,955.
This is the value of the elder child’s education fourteen years from n ow. It is the value of
the younger child’s education sixteen years from today. The present value of these is
PV = $59,955 / 1.1514 + $59,955 / 1.1516
= $14,880.44
You want to make fifteen equal payments into an account that yields 15% so that the
present value of the equal payments is $14,880.44.
Payment = $14,880.44 / 15
15.0A = $14,880.44 / 5.8474 = $2,544.80
4.40 A well-known insurance company offers a policy known as the “Estate Creator Six Pay.” Typically the policy is bought by a parent or grandparent for a child at the child ’s birth.
The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company.
First birthday $750 Fourth birthday $800
Second birthday $750 Fifth birthday $800
Third birthday $750 Sixth birthday $800
No more payments are made after the child ’s sixth birthday. When the child reaches age 65, he or she receives $250,000. If the relevant interest rate is 6 percent for the first six years and 7 percent for all subsequent years, is the policy worth buying?
4.40 The NPV of the policy is
NPV = -$750 3
06.0A - $800 306.0A / 1.063 + $250,000 / [(1.066) (1.0759)]
= -$2,004.76 - $1,795.45 + $3,254.33
= -$545.88
Therefore, you should not buy the policy.
4.41 Your company is considering leasing a $120,000 piece of equipment for the next 10 years. Your company can buy the equipment outright or lease it. The annual lease payments of $15,000 are due at the beginning of each year. The lease includes an option for your company to buy the equipment for $25,000 at the end of the leasing period (i.e., 10 years). Should your company accept the lease offer if the appropriate discount rate is 8 percent a year?
4.41
The NPV of the lease offer is
NPV = $120,000 - $15,000 - $15,000 908.0A - $25,000 / 1.0810
= $105,000 - $93,703.32 - $11,579.84
= -$283.16 Therefore, you should not accept the offer.
4.42 You are saving for your retirement. You have decided that one year from today you will deposit 2 percent of your annual salary in an account which will earn 8 percent per year. Your salary last year was $50,000, and it will increase at 4 percent per year throughout your career. How much money will you have for your retirement, which will begin in 40 years?
4.42 This problem applies the growing annuity formula. The first payment is
$50,000(1.04)2(0.02) = $1,081.60.
PV = $1,081.60 [1 / (0.08 - 0.04) - {1 / (0.08 - 0.04)}{1.04 / 1.08}40]
= $21,064.28
This is the present value of the payments, so the value forty years from today is
$21,064.28 (1.0840) = $457,611.46
4.43 You must decide whether or not to purchase new capital equipment. The cost of the machine is $5,000. It will produce the following cash flows. The appropriate discount rate is 10 percent.
Year Cash Flow
1 $ 700
2 900
3 1,000
4 1,000
5 1,000
6 1,000
7 1,250
8 1,375
Should you purchase the equipment?
4.43 Use the discount factors to discount the individual cash flows. Then compute the NPV of
the project. Notice that the four $1,000 cash flows form an annuity. You can still use the factor tables to compute their PV. Essentially, they form cash flows that are a six year
annuity less a two year annuity. Thus, the appropriate annuity factor to use with them is
2.6198 (= 4.3553 - 1.7355).
Year Cash Flow Factor PV
1 $700 0.9091 $636.37
2 900 0.8264 743.76
3 1,000 ?
4 1,000 ? 2.6198 2,619.80
5 1,000 ?
6 1,000 ?
7 1,250 0.5132 641.50
8 1,375 0.4665 641.44
Total $5,282.87
NPV = -$5,000 + $5,282.87
= $282.87
Purchase the machine.
4.44 When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. A bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $5 when she died in 1962. Based on actuarial tables, “Joltin’ Joe”could expect to live for 30 years after the actress died. Assume that the stated annual interest rate, compounded weekly, is 10.4 percent. Also, assume that the rate of inflation is 3.9 percent per year, when expressed as a stated annual inflation rate, compounded weekly. Assuming that each year has exactly 52 weeks, what is the present value of this commitment?
4.44 Weekly inflation rate = 0.039 / 52 = 0.00075
Weekly interest rate = 0.104 / 52 = 0.002
PV = $5 [1 / (0.002 - 0.00075)] {1 – [(1 + 0.00075) / (1 + 0.002)]52 ? 30}
= $3,429.38
4.45 Your younger brother has come to you for advice. He is about to enter college and has two options open to him. His first option is to study engineering. If he does this, his undergraduate degree would cost him $12,000 a year for four years. Having obtained this, he would need to gain two years of practical experience: in the first year he would earn $20,000, in the second year he would earn $25,000. He would then need to obtain his master ’s degree, which will cost $15,000 a year for two years. After that he will be fully qualified and can earn $40,000 per year for 25 years.
His other alternative is to study accounting. If he does this, he would pay $13,000 a year for four years and then he would earn $31,000 per year for 30 years.
The effort involved in the two careers is the same, so he is only interested in the earnings the jobs provide. All earnings and costs are paid at the end of the year. What advice would you give him if the market interest rate is 5 percent? A day later he comes back and says he took your advice, but in fact, the market interest rate was 6 percent. Has your brother made the right choice?
100 Part II Value and Capital Budgeting
4.45 Engineer:
NPV = -$12,000 405.0A + $20,000 / 1.055 + $25,000 / 1.056 - $15,000 / 1.057
- $15,000 / 1.058 + $40,000 2505.0A / 1.058
= $352,533.35
Accountant:
NPV = -$13,000 4
05.0A + $31,000 3005.0A / 1.054
= $345,958.81
Become an engineer.
After your brother announces that the appropriate discount rate is 6%, you can recalculate the NPVs. Calculate them the same way as above except using the 6% discount rate.
Engineer NPV = $292,419.47
Accountant NPV = $292,947.04 Your brother made a poor decision. At a 6% rate, he should study accounting. 4.46 In January 1984, Richard “Goose ” Gossage signed a contract to play for the San Diego Padres that guaranteed him a minimum of $9,955,000. The guaranteed payments were $875,000 for 1984, $650,000 for 1985, $800,000 in 1986, $1 million in 1987, $1 million in 1988, and $300,000 in 1989. In addition, the contract called for $5,330,000 in deferred money payable at the rate of $240,000 per year from 1990
through 2006 and then $125,000 a year from 2007 through 2016. If the effective annual rate of interest is 9 percent and all payments are made on July 1 of each year, what would the present value of these guaranteed payments be on January 1, 1984? Assume an interest rate of 4.4 percent per six months. If he were to
receive an equal annual salary at the end of each of the five years from 1984 through 1988, what would his equivalent annual salary be? Ignore taxes
throughout this problem.
4.46 Since Goose receives his first payment on July 1 and all payments in one year intervals
from July 1, the easiest approach to this problem is to discount the cash flows to July 1 then use the six month discount rate (0.044) to discount them the additional six months. PV = $875,000 / (1.044) + $650,000 / (1.044)(1.09) + $800,000 / (1.044)(1.092)
+ $1,000,000 / (1.044)(1.093) + $1,000,000/(1.044)(1.094) + $300,000 / (1.044)(1.095)
+ $240,000 17
09.0A / (1.044)(1.095) + $125,000 1009.0A / (1.044)(1.0922)
= $5,051,150
Remember that the use of annuity factors to discount the deferred payments yields the value of the annuity stream one period prior to the first payment. Thus, the annuity factor applied to the first set of deferred payments gives the value of those payments on July 1 of 1989. Discounting by 9% for five years brings the value to July 1, 1984. The use of the six month discount rate (4.4%) brings the value of the payments to January 1, 1984. Similarly, the annuity factor applied to the second set of deferred payments yields
the value of those payments in 2006. Discounting for 22 years at 9% and for six months at 4.4% provides the value at January 1, 1984.
The equivalent five-year, annual salary is the annuity that solves:
A
$5,051,150 = C5
09
.0
C = $5,051,150/3.8897
C = $1,298,596
The student must be aware of possible rounding errors in this problem. The difference between 4.4% semiannual and 9.0% and for six months at 4.4% provides the value at
January 1, 1984.
4.47 Ms. Adams has received a job offer from a large investment bank as an assistant to the vice president. Her base salary will be $35,000. She will receive her first annual salary payment one year from the day she begins to work. In addition, she will get an immediate $10,000 bonus for joining the company. Her salary will grow at 4 percent each year. Each year she will receive a bonus equal to 10 percent of her salary. Ms. Adams is expected to work for 25 years. What is the present value of the offer if the discount rate is 12 percent?
4.47 PV = $10,000 + ($35,000 + $3,500) [1 / (0.12 - 0.04)] [1 - (1.04 / 1.12) 25 ]
= $415,783.60
4.48 Justin Leonard has just arranged to purchase a $400,000 vacation home in the Bahamas with a 20% down payment. The mortgage has an 8% annual percentage rate (APR) and calls for equal monthly payments over the next 30 years. His first payment will be due one month from now. However, the mortgage has an 8-year balloon payment, meaning that the loan must be paid off then. There were no other transaction costs or finance charges. How big will Justin’s balloon payment be in 8 years?
4.48 NPV = -$40,000 + $10,000 [1 / (0.10 - 0.07)] [1 - (1.07 / 1.10)5 ]
= $3,041.91
Revise the textbook.
4.49 You want to lease a set of golf clubs from Pings Ltd. for $4,000. The lease contract is in the form of 24 months of equal payments at a 12% annual percentage rate (APR). Suppose payments are due in the beginning of the month and your first payment is due immediately. What will your monthly lease payment be?
4.49The amount of the loan is $400,000 (0.8) = $320,000
A= $ 2,348.10
The monthly payment is C = $320,000 / 360
.
0067
.
Thirty years of payments $ 2,348.10 (360) = $ 845,316.00
Eight years of payments $2,348.10 (96) = $225,417.60
The difference is the balloon payment of $619,898.40
4.50 A 10-year annuity pays $900 per year, with payments made at the end of each year. The first $900 will be paid 5 years from now. If the APR is 8% and interest is compounded quarterly, what is the present value of this annuity? What Is a Firm Worth?
4.50The lease payment is an annuity in advance
A = $4,000
C + C 23
.0
01
C (1 + 20.4558) = $4,000
C = $186.42
4.51 Southern California Publishing Company is trying to decide whether or not to revise its popular textbook, Financial Psychoanalysis Made Simple. They have estimated that the revision will cost $40,000. Cash flows from increased sales will be $10,000 the first year. These cash flows will increase by 7 percent per year. The book will go out of print five years from now. Assume the initial cost is paid now and all revenues are received at the end of each year. If the company requires a 10 percent return for such an investment, should it undertake the revision?
4.51The effective annual interest rate is
[ 1 + (0.08 / 4) ] 4 – 1 = 0.0824
The present value of the ten-year annuity is
A = $5,974.24
PV = 900 10
0824
.0
Four remaining discount periods
PV = $5,974.24 / (1.0824) 4 = $4,352.43
4.52 Ernie Els wants to save money to meet two objectives. First, he would like to be able to retire 30 years from now with a retirement income of $300,000 per year for 20 years beginning at the end of the 31 years from now. Second, he would like to purchase a cabin in the mountains 10 years from now at an estimated cost of $350,000. He can afford to save only $40,000 per year for the first 10 years. He expects to earn 7 percent per year from investments. Assuming he saves the same amount each year, what must Ernie save annually from years 11 to 30 to meet his objectives?
4.52The present value of Ernie’s retirement income
A / (1.07) 30 = $417,511.54
PV = $300,000 20
07
.0
The present value of the cabin
PV = $350,000 / (1.07) 10 = $177,922.25
The present value of his savings
A = $280,943.26
PV = $40,000 10
07
.0
In present value terms he must save an additional $313,490.53
In future value terms
FV = $313,490.53 (1.07) 10 = $616,683.32
He must save
A = $58,210.54
C = $616.683.32 / 20
07
.0
公司理财（11.04） 第一章公司理财概述 一、单项选择题 1、在筹资理财阶段，公司理财的重点内容是（ B ）。 A有效运用资金 B如何设法筹集到所需资金 C研究投资组合 D国际融资 二、多项选择题 1、公司财务活动的内容包括（ ABCDE ）。 A资金的筹集 B资金的运用 C资金的耗费 D资金的收回 E资金的分配 三、填空题 1、在内部控制理财阶段，公司理财的重点内容是如何有效地（运用资金）。 2、西方经济学家和企业家以往都以（利润最大化）作为公司的经营目标和理财目标。 3、现代公司理财的目标是（股东财富最大化）。 4、公司资产价值增加，生产经营能力提高，意味着公司具有持久的、强大的获利能力和（偿 债能力）。 5、当（股票价格）达到最高时，意味着股东财富达到最大化。 6、公司筹资的渠道主要有两大类，一是（自有资本）的筹集，二是（借入资本）的筹集。 四、简答题 1、为什么以股东财富最大化作为公司理财目标？P14 （1）考虑到了货币时间价值和风险价值；（2）体现了对公司资产保值增值的要求；（3）有利于克服公司经营上的短期行为，促使公司理财当局从长远战略角度进行财务决策，不断增加公司财富。 2、公司理财的具体内容是什么？P16-17 （1）筹资决策；（2）投资决策；（3）股利分配决策。 第二章财务报表分析 一、单项选择题 1、资产负债表为（ B ）。 A动态报表 B静态报表 C动态与静态相结合的报表 D既不是动态报表也不是静态报表 2、下列负债中属于长期负债的是（ D ）。 A应付账款 B应交税金 C预计负债 D应付债券 3、公司流动性最强的资产是（）。A A货币资金 B短期投资 C应收账款 D存货 4、利润表中的收入是按（ B ）确认的。 A收付实现制 B权责发生制 C永续盘存制 D实地盘存制 5、下列各项费用中属于财务费用的是（ C ）。 A广告费 B劳动保险费 C利息支出 D坏账损失 6、反映公司所得与所费的比例关系的财务指标是（）。D A销售利润率 B总资产周转率 C资产利润率 D成本费用利润率 二、多项选择题 1、与资产负债表中财务状况的计量直接联系的会计要素有（ ABC ）。 A资产 B负债 C所有者权益 D成本费用 E收入利润 2、与利润表中经营成果的计量有直接联系的会计要素有（ BCD ）。 A资产 B收入 C成本和费用 D利润 E所有者权益 3、反映偿债能力的财务指标主要有（ ABCD ）。 A资产负债率 B流动比率 C速动比率 D现金比率 E存货周转率 三、填空题 1、资产的实质是（经济资源）。 2、公司所有者权益的金额为（资产）减去（负债）后的余额。 3、公司的法定盈余公积在转增资本后，一般不得低于注册资金的（25% ）。C 4、固定资产的计价标准有原始价值、重置价值和（净值）三种。
公司理财（财务治理） 第一章、公司理财概述 《财务与成本治理》教材一书共十五章、632页、44万字。其中前十章是讲财务治理，后四章是讲成本治理。财务治理与成本治理本是两门学科，没有内在的必定联系，实际上它是两门完全独立的学科。 《财务治理》的特点是公式专门多，有的公式需要死背硬记，有的在理解后就能记住。第一章是总论，这章的内容是财务治理内容的总纲，是理解各章内容的一个起点，对掌握各章之间的联系有重要意义。因此，学习这一章重点是掌握财务治理知识的体系，理解每一个财务指标、公式、名词的概念，掌握它，对以后各章在整个知识体系中的地位和作用有专门大关心。 第一节财务治理的目标 一、企业的财务目标 有四个问题：企业目标决定了财务治理目标；财务治理目标的三种主张及其理由和问题；讨论财务目标的重要意义；什么缘故要以利
润大小作为财务目标。这四个问题是财务治理中的差不多问题，是组织财务治理工作的动身点。 公司理财是指公司在市场经济条件下，如何低成本筹措所需要的资金并进行各种筹资方式的组合；如何高效率地投资，并进行资源的有效配置；如何制定利润分配政策，并合理地进行利润分配。公司理财确实是要研究筹资决策、投资决策及利润分配决策。 1、企业治理的目标 包括三个方面内容：一是生存，企业只有生存，才可能获利，企业 还到期债务的能力，减少破产的风险，使企业长期稳定地生存下去，是对公司理财的第一个要求；二是进展，企业是在进展中求得生存的。筹集企业进展所需的资金，是对公司理财的第二个要求；三是获利，企业必须获利，才有存在的价值。通过合理有效地使用资金使企业获利，是对公司理财的第三个要求。总之，企业的目标（企业治理的目标）确实是生存、进展和获利。 2、公司理财的目标 三种观点 ①、利润最大化
第一章．公司理财导论 1.企业组织形态：单一业主制、合伙制、股份公司（所有权和管理相分离、相对容易转让 所有权、对企业债务负有限责任，使企业融资更加容易。企业寿命不受限制，但双重课税） 2.财务管理的目标：为了使现有股票的每股当前价值最大化。或使现有所有者权益的市场 价值最大化。 3.股东与管理层之间的关系成为代理关系。代理成本是股东与管理层之间的利益冲突的成 本。分直接和间接。 4.公司理财包括三个领域：资本预算、资本结构、营运资本管理 第二章． 1.在企业资本结构中利用负债成为“财务杠杆”。 2.净利润与现金股利的差额就是新增的留存收益。 3.来自资产的现金流量=经营现金流量（OCF）-净营运资本变动-资本性支出 4.OCF=EBIT+折旧-税 5.净资本性支出=期末固定资产净值-期初固定资产净值+折旧 6.流向债权人的现金流量=利息支出-新的借款净额 7.流向股东的现金流量=派发的股利-新筹集的净权益 第三章 1.现金来源：应付账款的增加、普通股本的增加、留存收益增加 现金运用：应收账款增加、存货增加、应付票据的减少、长期负债的减少 2.报表的标准化：同比报表、同基年度财报 3.ROE=边际利润（经营效率）X总资产周转率（资产使用效率）X权益乘数（财务杠杆） 4.为何评价财务报表： 内部：业绩评价。外部：评价供应商、短期和长期债权人和潜在投资者、信用评级机构。第四章． 1.制定财务计划的过程的两个维度：计划跨度和汇总。 2.一个财务计划制定的要件：销售预测、预计报表、资产需求、筹资需求、调剂、经济假设。 3.销售收入百分比法：
提纯率=再投资率=留存收益增加额/净利润=1-股利支付率 资本密集率=资产总额/销售收入 4.内部增长率=(ROAXb)/(1-ROAXb) 可持续增长率=ROE/(1-ROEXb):企业在保持固定的债务权益率同时没有任何外部权益筹资的情况下所能达到的最大的增长率。是企业在不增加财务杠杆时所能保持的最大的增长率。（如果实际增长率超过可持续增长率，管理层要考虑的问题就是从哪里筹集资金来支持增长。如果可持续增长率始终超过实际增长率，银行家最好准备讨论投资产品，因为管理层的问题是怎样处理所有的这些富余的现金。） 5.增长率的决定因素 利润率、股利政策（提纯率）、筹资政策（财务杠杆）、总资产周转率 6.如果企业不希望发售新权益，而且它的利润率、股利政策、筹资政策和总资产周转率（资 本密集率）是固定的，那么就只会有一个可能得增长率 7.如果销售收入的增长率超过了可持续增长率，企业就必须提高利润率，提高总资产周转 率，加大财务杠杆，提高提纯率或者发售新股。 第六章． 1.贷款的种类：纯折价贷款、纯利息贷款、分期偿还贷款 纯折价贷款：国库券（即求现值即可） 纯利息贷款：借款人必须逐期支付利息，然后在未来的某时点偿还全部本金。 如：三年期，利率为10%的1000美元纯利息贷款，第一年第二年要支付1000X0.1的利息，第三年末要支付1100元。 分期偿还贷款：每期偿还利息加上一个固定的金额。其中每期支付的利息是递减的，而且相等总付款额情况下的总利息费用较高。 第7章 1.市场对某一债券所要求的利率叫做该债券的到期收益率。 2.如果债券低于或高于面值的价格出售，则为折价债券或溢价债券。 折价：票面利率为8%，市场利率（到期收益率）为10% 溢价：票面利率为8%，市场利率为6%（投资者愿意多支付价款以获得额外的票年利息） 3.债券的价值=票面利息的现值+面值的现值（与利率呈相反变动） 4.利率风险：债券的利率风险的大小取决于该债券的价格对利率变动的敏感性。其他条件相同，到期期限越长，利率风险越大；其他条件相同，票面利率越低，利率风险越大。 5.债券的当期收益率是债券的年利息除以它的价格。折价债券中，当期收益率小于到期收益率，因为没有考虑你从债券折价中获取的利得。溢价相反。 6.公司发行的证券：权益性证券和债务证券。 7.权益代表一种所有权关系，而且是一种剩余索取权，对权益的支付在负债持有人后。拥有债务和拥有权益的风险和利率不一样。 8.债务性证券通常分为票据、信用债券和债券。长期债务的两种主要形式是公开发行和私下募集 9．债务和权益的差别： 1.债务并不代表公司的所有权的一部分。债权人通常不具有投票权。 2.公司对债务支付的利息属于经营成本，因此可以再税前列支，派发给股东的股利则不能抵税。 3.未偿还的债务是公司的负债。如果公司没有偿还，债权人对公司的资产就有合法的索取权。这种行为可能导致两种可能的破产：清算和重组。 4.债券合约是公司和债券人之间的书面协议，有时也叫做信用证书，里面列示了债券的各种
公司理财第十一版课后答案第一章 第1篇概论 第］章公司理财导论 1.1复习笔记 公司的首要目标——股东财富最大化决定了公司理财的目标。公司理财研究的是稀缺资金如何在企业和市场内进行有效配置，它是在股份有限公司已成为现代企业制度最主要组织形式的时代背景下，就公司经营过程中的资金运动进行预测、组织、协调、分析和控制的一种决策与管理活动。从决策角度来讲，公司理财的决策内容包括投资决策、筹资决策、股利决策和净流动资金决策；从管理角度来讲，公司理财的管理职能主要是指对资金筹集和资金投放的管理。公司理财的基本内容包括：投资决策（资本预算）、融资决策（资本结构）、短期财务管理（营运资本）。 1.资产负债表 资产负债表是总括反映企业某一特定日期财务状况的会计报表，它是根据资产、负债和所有者权益之间的相互关系，按照一定的分类标准和一定的顺序，把企业一定日期的资产、负债和所有者权益各项目予以适当排列，并对日常工作中形成的大量数据进行高度浓缩整理后编制而成的。资产负债表可以反映资本预算、资本支出、资本结构以及经营中的现金流量管理等方面的内容。 2.资本结构 资本结构是指企业各种资本的构成及其比例关系，它有广义和狭义之分。广义资本结构，亦称财务结构，指企业全部资本的构成，既包括长期资本，也包括短期资本（主要指短期债务资本）。狭义资本结构，主要指企业长期资本的构成，而不包括短期资本。通常人们将资本结构表示为债务资本与权益资本的比例关系（D/E）或债务资本在总资本中的构成（D/A）。准确地讲，企业的资本结构应定义为有偿负债与所有者权益的比例。 资本结构是由企业采用各种筹资方式筹集资本形成的。筹资方式的选择及组合决定着企业资本结构及其变化。资本结构是企业筹资决策的核心问题。企业应综合考虑影响资本结构的因素，运用适当方法优化资本结构，从而实现最佳资本结构。资本结构优化有利于降低资本成本，获取财务杠杆利益。 3.财务经理 财务经理是公司管理团队中的重要成员，其主要职责是通过资本预算、融资和资产流动性管理为公司创造价值。 【例1.1】公司财务经理的责任是增加（）。［清华大学2014金融硕士］ A.公司规模 B.公司增长速度 C.经理人的能力 D.股东权益价值 【答案】D 【解析】公司的财务经理为公司的股东做决策。财务经理通过增加股票价值的财务决策，最大限度地保护股东的利益。财务管理的目标是最大化现有股票的每股价值，因此财务经理的责任是增加股东权益价值。 4.公司制企业 企业有个人独资企业、合伙制企业和公司三种组织形式。公司制企业简称"公司”，即实行公司制的企业，以有限责任公司和股份有限公司为典型形式，是解决筹集大量资金的一种标准方法。 5.现金流的重要性 公司创造的现金流必须超过它所使用的现金流。公司支付给债权人和股东的现金流必须大于债权人和股东投入公司的现金流。当支付给债权人和股东的现金大于从金融市场上筹集的资金时，公司的价值就增加了。公司投资的价值取决于现金流量的时点。 6.财务管理的目标
1、FV=PV*(1+R)^T，PV= FV/(1+R)^T，所以时间长度增加时，终值会 增加，现值会减少。 2、FV=PV*(1+R)^T，PV= FV/(1+R)^T，利率增加时，年金的终值会增 加，现值会减少。 3、第一种情况：PV=C*{[1-1/(1+r)^T]/r}=1000*{[1-1/(1+r)^10]/r} 第二种情况：PV=C*{[1-(1+g)^T/(1+r)^T]/(r-g)}= 1000*{[1-(1+5%)^10/(1+r)^10]/(r-5%)} 1000*{[1-1/(1+r)^10]/r}>1000*{[1-(1+5%)^10/(1+r)^10]/(r-5%)} 所以第一种情况分十次等分支付更好。 4、是，因为名义利率通常不提供相关利率。唯一的优势就是方便 计算，但是随着现在计算机设备的发展，这种优势已经不明显。 5、新生将收到更多的津贴。因为新生到偿还贷款的时间较长。 6、因为货币具有时间价值。GMAC当期获得五百美元的使用权， 如果投资得当，三十年后的收益将会高于一千美元。 7、除非出现通货紧缩，资金成本成为负值，否则GMAC有权利在 任意时候以10000美元的价格赎回该债券，都会增加投资者的持有该债券的意愿。 8、我不愿意今天支付五百美元来换取三十年后的一万美元。关键 因素：一是同类投资相比的回报率是否较高，二是投资的回报率和风险是否相匹配。回答取决于承诺偿还人，因为必须评估其三十年后存续的风险。 9、财政部的债券价格应该更高，因为财政部发行债券是以国家信
用为担保，违约风险最小，基本可视为无风险债券。 10、应该超过。因为货币具有时间价值，债券的价格会随着时间的 发展逐渐上升，最终达到一万美元。所以2010年，债券的价格 应该会更高。但是这具有很大的不确定性，因为宏观经济环境 和公司微观环境会发生变化，都有可能造成债券价格发生变化。 11、 a 1000*（1+6%）^10=1791美元 b 1000*（1+9%）^10=1967美元 c 1000*（1+6%）^20=3207美元 d 因为在按照复利计算时，不仅本金会产生利息，本金的利息 也会产生利息。 12、PV=FV/（1+r）^t=7.5/(1+8.2%)^20=1.55亿美元 13、PV=C/r=120/5.7%=2105美元 14、FV=C*e^（rT） a FV=1900*e^（12%*5）=1900*1.8221=3462美元 b FV=1900*e^（10%*3）=1900*1.3499=2565美元 c FV=1900*e^（5%*10）=1900*1.6487=3133美元 d FV=1900*e^（7%*8）=1900*1.7507=3326美元 15、有限年限支付下PV= C*{[1-1/(1+r)^T]/r} 当T=15时， PV=4300*{[1-1/(1+9%)^15]/9%}=4300*8.0607=34661美元 当T=40时， PV=4300*{[1-1/(1+9%)^40]/9%}=4300*10.7574=46257美元
第1章公司理财概述 一、单项选择题 1.公司财务经理的基本职能不包括（）。 A.投资管理 B.核算管理 C.收益分配管理 D.融资管理 2.股东是公司的所有者，是公司风险的主要承担者，因此，一般来说，股东对于公司收益的 索取权是（）。 A.剩余索取权 B.固定索取权 C.法定索取权 D.或有索取权 3.无论从市场功能上还是从交易规模上看，构成整个金融市场核心部分的是（）。 A.外汇市场 B.商品期货市场 C.期权市场 D.有价证券市场 4.下列不属于公司财务管理内容的是（）。 A.资本预算管理 B.长期融资管理 C.营运资本管理 D.业绩考核管理 5.由于剩余收益索取权赋予股东的权利、义务、风险、收益都大于公司的债权人、经营者和 其他员工。因此，公司在确定财务管理目标时，应选择（）。 A.利润最大化 B.每股收益最大化 C.股东财富最大化 D.公司价值最大化 6.下列不属于股东财富最大化理财目标的优点之处是（）。 A.考虑了获取收益的时间因素和风险因素 B.克服了追求利润的短期行为 C.能够充分体现所有者对资本保值与增值的要求 D.适用于所有公司 7.股东通常用来协调自己和经营者利益的方法主要是（）。 A.监督和激励 B.解聘和激励 C.激励和接收 D.解聘和接收 8.根据资产负债表模式，可将公司财务分为长期投资管理、长期融资管理和营运资本管理三 部分，股利政策应属于（）。 A.营运资本管理 B.长期投资管理 C.长期融资管理 D.以上都不是 9.“所有包含在过去证券价格变动的资料和信息已完全反映在证券的现行市价中；证券价格 的过去变化和未来变化是不相关的。”下列各项中符合这一特征的是（）。 A. 弱式效率性的市场 B.半强式效率性的市场 C. 强式效率性的市场 D.以上都不是 10.股东与债权人之间矛盾与冲突的根源所在是（）。 A.风险与收益的“不对等契约” B.提供资本的性质不同 C.在公司治理中的作用不同 D.以上都不是 11.在金融市场上，投资者无法通过任何方法利用历史信息和公开信息获得超额利润，只有 公司的内线人物通过掌握公司内幕消息买卖自己公司的股票，而获得超额利润。该金融市场的效率程度是（）。
第一章公司理财导论 ?.公司财务管理的三个基本问题？ 1.资本预算：企业长期的投资计划和管理过程。 2.资本结构：是企业用来为其经营融资的长期债务和权益的特定组合。 3.营运资本：指企业的短期资产(例如存货)和短期负债(例如欠供应商的款 项)。 资本运算，第一个问题着眼于企业的长期投资。 资本结构，财务经理的第二个问题着眼于企业对支持其长期投资需要长期筹资的获取和管理方式。 营运资本管理，第三个问题着眼于营运资本管理。 第二章财务报表税和现金流量 ?.市场价值与账面价值出现差异的原因？ 1.历史成本记账原则 2.折旧 3.资产的机会成本 4.未能列入资产负债表的一些项目，如企业的声誉，企业的文化， 品牌。 ?.净营运资本 企业流动资产与流动负债之差 ?.现金流量 来自资产的现金流量=流向债权人的现金流量+流向股东的现金流量
第三章利用财务报表 ?.财务报表标准化的原因： 第一很难直接比较， 第二，货币单位不同。 ?.流动比率 等于流动资产比流动负债 ?.长期偿债能力比率 揭示企业在长期内偿还其债务的能力，也被称为财务杠杆比率，或者干脆叫做杠杆比率。 主要指标： 1.资产负债率=（总资产-总权益）/总资产 2.权益乘数=总资产/总权益 3.债务权益比（产权比率）=总负债/总权益 4.已获利息倍数=息税前利润（EBIT）/ 利息 5.现金对利息的保障倍数=（ EBIT +折旧）/利息 ?.市场价值的衡量指标: 市盈率（P / E）=每股市价 / 每股收益 市值面值比=每股市场价值/每股账面价值 基于股票的每股市价，仅适用于公开上市交易的公司。 ?.杜邦恒等式 权益报酬率(ROE)=利润率x总资产周转率x权益乘数 ?.杜邦恒等式告诉我们ROE受三个要素影响 1.经营效率(用利润率计量);
第１章公司理财概述 一、单项选择题 1、公司财务经理得基本职能不包括( ）. A、投资管理 B、核算管理 C、收益分配管理 D、融资管理 2、股东就是公司得所有者，就是公司风险得主要承担者，因此，一般来说，股东对于公司 收益得索取权就是( ）。 A、剩余索取权Ｂ、固定索取权 C、法定索取权 D、或有索取权 3、无论从市场功能上还就是从交易规模上瞧，构成整个金融市场核心部分得就是（）。 A、外汇市场Ｂ、商品期货市场 C、期权市场 D、有价证券市场 4、下列不属于公司财务管理内容得就是（）. A、资本预算管理 B、长期融资管理 C、营运资本管理 D、业绩考核管理 5、由于剩余收益索取权赋予股东得权利、义务、风险、收益都大于公司得债权人、经营者 与其她员工。因此,公司在确定财务管理目标时，应选择（)。 Ａ、利润最大化Ｂ、每股收益最大化 C、股东财富最大化 D、公司价值最大化 6、下列不属于股东财富最大化理财目标得优点之处就是( )。 A、考虑了获取收益得时间因素与风险因素 B、克服了追求利润得短期行为 C、能够充分体现所有者对资本保值与增值得要求 D、适用于所有公司 7、股东通常用来协调自己与经营者利益得方法主要就是( ）。 Ａ、监督与激励B、解聘与激励 C、激励与接收 D、解聘与接收 8、根据资产负债表模式,可将公司财务分为长期投资管理、长期融资管理与营运资本管理三 部分，股利政策应属于( ）. A、营运资本管理 B、长期投资管理 C、长期融资管理 D、以上都不就是 9、“所有包含在过去证券价格变动得资料与信息已完全反映在证券得现行市价中；证券价格 得过去变化与未来变化就是不相关得.”下列各项中符合这一特征得就是（ )。 A、弱式效率性得市场Ｂ、半强式效率性得市场 Ｃ、强式效率性得市场 D、以上都不就是 1０、股东与债权人之间矛盾与冲突得根源所在就是( ）。 A、风险与收益得“不对等契约" B、提供资本得性质不同 C、在公司治理中得作用不同 D、以上都不就是 11、在金融市场上,投资者无法通过任何方法利用历史信息与公开信息获得超额利润，只有 公司得内线人物通过掌握公司内幕消息买卖自己公司得股票，而获得超额利润.该金融市场得效率程度就是（ )。 A、弱式效率性得市场 B、半强式效率性得市场 C、强式效率性得市场Ｄ、以上都不就是
第一章导论 1. 公司目标：为所有者创造价值，公司价值在于其产生现金流能力。 2. 财务管理的目标：最大化现有股票的每股现值。 3. 公司理财可以看做对一下几个问题进行研究： 1. 资本预算：公司应该投资什么样的长期资产。 2. 资本结构：公司如何筹集所需要的资金。 3. 净运营资本管理：如何管理短期经营活动产生的现金流。 4. 公司制度的优点：有限责任，易于转让所有权，永续经营。缺点：公司税对股东的双重课税。第二章会计报表与现金流量 资产= 负债+ 所有者权益（非现金项目有折旧、递延税款） EBIT（经营性净利润）= 净销售额- 产品成本- 折旧 EBITDA = EBIT + 折旧及摊销 现金流量总额CF(A) = 经营性现金流量- 资本性支出- 净运营资本增加额= CF(B) + CF(S) 经营性现金流量OCF = 息税前利润+ 折旧- 税 资本性输出= 固定资产增加额+ 折旧 净运营资本= 流动资产- 流动负债 第三章财务报表分析与财务模型 1. 短期偿债能力指标（流动性指标） 流动比率= 流动资产/流动负债（一般情况大于一） 速动比率= (流动资产- 存货)/流动负债（酸性实验比率） 现金比率= 现金/流动负债 流动性比率是短期债权人关心的，越高越好；但对公司而言，高流动性比率意味着流动性好，或者现金等短期资产运用效率低下。对于一家拥有强大借款能力的公司，看似较低的流动性比率可能并非坏的信号 2. 长期偿债能力指标（财务杠杆指标） 负债比率= (总资产- 总权益)/总资产or (长期负债+ 流动负债)/总资产 权益乘数= 总资产/总权益= 1 + 负债权益比 利息倍数= EBIT/利息 现金对利息的保障倍数(Cash coverage radio) = EBITDA/利息 3. 资产管理或资金周转指标 存货周转率= 产品销售成本/存货存货周转天数= 365天/存货周转率 应收账款周转率= （赊）销售额/应收账款 总资产周转率= 销售额/总资产= 1/资本密集度 4. 盈利性指标 销售利润率= 净利润/销售额 资产收益率ROA = 净利润/总资产 权益收益率ROE = 净利润/总权益 5. 市场价值度量指标 市盈率= 每股价格/每股收益EPS 其中EPS = 净利润/发行股票数 市值面值比= 每股市场价值/每股账面价值
Chapter 04 Introduction to Valuation: The Time Value of Money Multiple Choice Questions 1. Martha is investing $5 today at 6 percent interest so she can have $10 later. The $10 is referred to as the: A. true value. B. future value. C. present value. D. discounted value. E. complex value. 2. Tom earned $120 in interest on his savings account last year. Tom has decided to leave the $120 in his account so that he can earn interest on the $120 this year. This process of earning interest on prior interest earnings is called: A. discounting. B. compounding. C. duplicating. D. multiplying. E. indexing. 3. Jamie earned $180 in interest on her savings account last year. She has decided to leave the $180 in her account so that she can earn interest on the $180 this year. The interest Jamie earns this year on this $180 is referred to as: A. simple interest. B. complex interest. C. accrued interest. D. interest on interest. E. discounted interest.
1.当你增加时间的长度时，终值会发生什么变化，现值会发生什么变化？ 答：当增加时间长度时根据公司PV=C/(1+r)^t得到现值会减少（dwindle，diminish），而终值FV=C*(1+r)^t会增加。 2.如果利率增加，年金的终值会有什么变化？现值会有什么变化？ 答：当利率增加时，终值增大，现值FV=C(1/r-1/(r*(1+r)^t))得现值会减小分析这两道题都考察了对终值和现值的概念的理解:终值：一笔资金经过一个时期或者多个时期的以后的价值，如果考察终值就是在现在或将来我得到一笔资金C那么这笔资金在更远的未来将会价值多少，如果考察现值则是将来我得到一笔钱那么它现在的价值是多少（在某个固定的折现率下） 3.假设有两名运动员签署了一份10年8000万的合同，一份是每年支付800万，一份是 答：计算过程如下图： u 由上图的应该选第一种 4.贷款法是否应该要求贷款者报告实际利率而不是名义利率？为什么？ 答：他们应该报告实际利率，名义利率的优势只是在于它们方便计算，可是在计算机技术发达的今天，计算已经不再是一个问题 5.有津贴的斯坦福联邦贷款是为大学生提供帮助的一种普遍来源，直到偿还贷款才开始付 息。谁将收到更多的津贴，新生还是高年级的学生？请解释 答：新生将获得跟多的津贴，因为新生使用无息贷款的时间比高年级学生长。详细数据如下：
由此可见新生的津贴=22235-20000=2235；而高年级的学生为1089 根据下面的信息回答接下去的5个题： 6.由计算得到如果500美金若在30年后要变成10000则实际年利率是10.5%,我想应该 是GMAC的决策者认为公司的投资收益率大于10.5% 7.如果公司可以在30年内的任意时间内以10000元的价格购买该债券的话，将会使得该 债券更具有吸引力 8.1）这500元不能影响我后面30年的正常生活，也就是我说我是否有500元的多余资 金； 2）该公司是否能够保证在30年后我能收到10000元 3）当前我认为的投资收益率是否高于10.5%，若高于10.5%则不应该考虑投资该债券我的回答是：是取决的承诺偿还的人 9.财政部的发行该种债券的价格较高因为财政部在所有的债券发行者中信用最好 10.价格会超过之前的500美元，因为如果随着时间的推移，该债券的价值就越接近10000 美元，如果在2010年的看价格有可能会更高，但不能确定，因为GMAC有财务恶化
第 1 章公司理财概述一、单项选择题 1. 公司财务经理的基本职能不包括（ A. 投资管理 B. C. 收益分配管理 D.）。 核算管理 融资管理 2.股东是公司的所有者，是公司风险的主要承担者，因此，一般来说，股东对于公司收益的 索取权是（）。 A. 剩余索取权 B.固定索取权 C. 法定索取权 D.或有索取权 3.无论从市场功能上还是从交易规模上看，构成整个金融市场核心部分的是（）。 A. 外汇市场 B.商品期货市场 C. 期权市场 D.有价证券市场 4.下列不属于公司财务管理内容的是（）。 A. 资本预算管理 B.长期融资管理 C. 营运资本管理 D.业绩考核管理 5.由于剩余收益索取权赋予股东的权利、义务、风险、收益都大于公司的债权人、经营者和 其他员工。因此，公司在确定财务管理目标时，应选择（）。 A. 利润最大化 B.每股收益最大化 C. 股东财富最大化 D.公司价值最大化 6. 下列不属于股东财富最大化理财目标的优点之处是（）。 A.考虑了获取收益的时间因素和风险因素 B.克服了追求利润的短期行为 C.能够充分体现所有者对资本保值与增值的要求 D.适用于所有公司 7. 股东通常用来协调自己和经营者利益的方法主要是（ A. 监督和激励 B.解聘和激励 C. 激励和接收 D.解聘和接收 ）。 8.根据资产负债表模式，可将公司财务分为长期投资管理、长期融资管理和营运资本管理三 部分，股利政策应属于（）。 A. 营运资本管理 B.长期投资管理 C. 长期融资管理 D.以上都不是 9.“所有包含在过去证券价格变动的资料和信息已完全反映在证券的现行市价中； 的过去变化和未来变化是不相关的。”下列各项中符合这一特征的是（ A. 弱式效率性的市场 B.半强式效率性的市场 C. 强式效率性的市场 D.以上都不是 证券价格）。 10. 股东与债权人之间矛盾与冲突的根源所在是（）。 A. 风险与收益的“不对等契约” B.提供资本的性质不同 C. 在公司治理中的作用不同 D.以上都不是 11.在金融市场上，投资者无法通过任何方法利用历史信息和公开信息获得超额利润，只有公 司的内线人物通过掌握公司内幕消息买卖自己公司的股票，而获得超额利润。该金融市场的效率程度是（）。
第一章公司理财导论 1.代理问题 谁拥有公司?描述所有者控制公司管理层的过程。代理关系在公司的组织形式中存在的主要原因是什么?在这种环境下，可能会出现什么样的问题? 解：股东拥有公司;股东选举董事会，董事会选举管理层(股东→董事会→管理层);代理关系在公司的组织形式中存在的主要原因是所有权和控制权的分离;在这种情况下，可能会产生代理问题(股东和管理层可能因为目标不一致而使管理层可能追求自身或别人的利益最大化，而不是股东的利益最大化)。 2.非营利企业的目标 假设你是一家非营利企业(或许是非营利医院)的财务经理，你认为什么样的财务管理目标将会是恰当的? 解：所有者权益的市场价值的最大化。 3.公司的目标 评价下面这句话：管理者不应该只关注现在的股票价值，因为这么做将会导致过分强调短期利润而牺牲长期利润。 解：错误;因为现在的股票价值已经反应了短期和长期的的风险、时间以及未来现金流量。 4.道德规范和公司目标 股票价值最大化的目标可能和其他目标，比如避免不道德或者非法的行为相冲突吗?特别是，你认为顾客和员工的安全、环境和社会的总体利益是否在这个框架之内，或者他们完全被忽略了?考虑一些具体的情形来阐明你的回答。 解：有两种极端。一种极端，所有的东西都被定价。因此所有目标都有一个最优水平，包括避免不道德或非法的行为，股票价值最大化。另一种极端，我们可以认为这是非经济现象,最好的处理方式是通过政治手段。 一个经典的思考问题给出了这种争论的答案：公司估计提高某种产品安全性的成本是30万美元。然而，该公司认为提高产品的安全性只会节省20万美元。请问公司应该怎么做呢?” 5.跨国公司目标
2班 《公司理财》考试要点 一、单选题(10分:课件上有答案 二、判断题(10分:课件上有答案 三、简答题(10分:一个题目,课件上有答案 四、论述题(20分:一个题目,课件上有答案 五、案例分析与计算(50分 1、资本预算【第七章】 ①投资回收期(属静态计算,不考虑货币时间价值(P7-10 ②净现值(P5-6 2、复利终值(计算货币时间价值【第二章(P4-10,公式P6】 3、债券发行定价(注意利息支付时间【第四章】 4、股票定价(固定股利增长模型,套公式【第四章P18-19】 5、信用政策【第九章P58-63】 1、资本预算【第七章】 ①投资回收期(属静态计算,不考虑货币时间价值(P7-10 ②净现值(P5-6 回收期法(payback period
企业利用投资项目产生的净现金流量来回收项目初始投 资所需的年限 假设你是西蒙电子公司的财务分析师,资本预算部门的主任请 你对两个计划中的资本投资项目进行财务分析。两个项目的成本皆为10 000美元,必要投资报酬率皆为12%。项目的预期现金流量如下: 要求: 1、计算两个项目的投资回收期、净现值、部报酬率; 2、如果是相互独立的,哪个或哪些项目可以接受? 3、如果是互斥的,应该选择哪个项目?
4、如果是必要报酬率发生变化,IRR 和NPV 方法衡量的结果之间是否会发生冲突?如果必要报酬率是5%呢? 5、为什么会存在这种冲突? 投资回收期一般以年表示,对于开发投资,从建设开始年 算起,对于置业投资,从首次投入资金算起。其表达式为:年 投资回收期 年投资回收期86.235003000 217.23000500 2=+==+ =Y X % 0.15%0.1872 .630$412 .13500 $312.13500$212.13500$112.13500$10000$01.966$412.11000 $312.13000$212.13000$112.16500$10000$===++++-==++++ -=Y X IRR
1. 当你增加时间的长度时，终值会发生什么变化，现值会发生什么变化？ 答：当增加时间长度时根据公司PV=C/(1+r)A t得到现值会减少(dwindle，diminish)，而终值FV=C*(1+r)At会增加。 2. 如果利率增加，年金的终值会有什么变化？现值会有什么变化？ 答：当利率增加时，终值增大，现值FV=C(1/r-1/(r*(1+rFt))得现值会减小分析这两道题都考察了对终值和现值的概念的理解：终值：一笔资金经过一个时期或者多个时期的以后的价值，如果考察终值就是在现在或将来我得到一笔资金C那么这笔资金在更远的未来将会价值多少，如果考察现值则是将来我得到一笔钱那么它现在的价值是多少(在某个固定的折现率下) 3. 假设有两名运动员签署了一份10年8000万的合同，一份是每年支付800万，一份是8000 万分十次，支付金额每年递增 5% ，哪种情况最好答：计算过程如下图： u 12. 5T733354舉一忡t*况*■二沖耆况 63S. <4e>3& 04 年 1 667. M Oflfc-蠹 ML D虽百嘶fiOQi m.sa49& 97 sao TSh.294沮0鼻1 115 m.^6髯& 29S zaSr 钿亍 晒L弊TT E 颐 d 72監BL EB审 60496th 70191. 23IQ 旦计9CW0, 003H 也69 由上图的应该选第一种 4. 贷款法是否应该要求贷款者报告实际利率而不是名义利率？为什么？ 答：他们应该报告实际利率，名义利率的优势只是在于它们方便计算，可是在计算机技术发达的今天，计算已经不再是一个问题 5. 有津贴的斯坦福联邦贷款是为大学生提供帮助的一种普遍来源，直到偿还贷款才开始付 息。谁将收到更多的津贴，新生还是高年级的学生？请解释 答：新生将获得跟多的津贴，因为新生使用无息贷款的时间比高年级学生长。详细数据如下： 输入变童 APR 6. 25% 备朗金额5000 期限<1) 4 期眼(2) 3 实師利率8. 57% 借款总瓠< 1 >20000 借款总颔< 2 > 15000 输出变崖 终值(1) 贮厶235. 67 终值(2)￥1? 089. 51 由此可见新生的津贴=22235-20000=2235 ;而高年级的学生为1089 根据下面的信息回答接下去的5个题： 6. 由计算得到如果500美金若在30年后要变成10000则实际年利率是10.5%,我想应该是 GMAC的决策者认为公司的投资收益率大于10.5% 7. 如果公司可以在 30年内的任意时间内以 10000元的价格购买该债券的话，将会使得该债券更具
公司理财复习题答案
公司理财复习题答案 第一章公司理财概述四名词解释 1公司理财 是指有关公司资金的筹集、投放与使用、分配的管理活动。2资金 就是公司财产物资价值的货币表现。 3财务活动 是指资金的筹集、运用、耗费、收回及分配等一系列行为。五简答题 1简述以股东财富最大化作为公司理财目标的原因 考虑到了货币时间价值和风险价值，也体现了对公司资产保值增值的要求，有利于克服公司经营上的短期行为，促使公司理财当局从长远战略角度进行财务决策，不断增加公司财富。 2简述公司理财具体内容 1）筹资决策 2）投资决策
3）股利分配决策 第二章财务报表分析四名词解释 1资产负债表 是反映公司在某一特定时期（月末、季末、年末）财务状况的会计报表。 2资产 是指过去的交易、事项形成并由企业拥有或控制的资源，该资源预期会给公司带来经济利益。 3负债 是指过去的交易、事项形成的现时义务，履行该义务预期会导致经济利益流出公司。 4所有者权益 是指所有者在公司资产中享有的经济利益，其金额为资产减去负债后的余额。 5利润表 是反映公司在一定期间（月份、季度、年度）经营成果实现情况的报表。
6利润 是公司在一定期间的经营成果。 7现金流量表 是反映公司在一定期间内（年度）现金流入和现金流出情况的报表，它反映的是一定会计期间内的数据，属于动态的年度报表。 8现金等价物 指公司持有的期限短、流动性强、易于转换为已知金额现金、价值变动风险很小的投资。 五简答题 简述资产的含义及特征 资产是指过去的交易、事项形成并由企业拥有或控制的资源，该资源预期会给公司带来经济利益。 1）资产的实质是经济资源，这些资源能为公司带来未来的经济利益。 2）资产必须为公司所拥有或控制。 3）资产必须能以货币计量。 4）资产可以是有形的，也可以是无形的。 2简述负债的含义及特征
23题：This question is asking for the present value of an annuity, but the interest rate changes during the life of the annuity. We need to find the present value of the cash flows for the last eight years first. The PV of these cash flows is: PVA2 = $1,500 [{1 – 1 / [1 + (.09/12)]⌒96} / (.09/12)] = $102,387.66 Note that this is the PV of this annuity exactly seven years from today. Now, we can discount this lump sum to today. The value of this cash flow today is: PV = $102,387.66 / [1 + (.13/12)]⌒84 = $41,415.70 Now, we need to find the PV of the annuity for the first seven years. The value of these cash flows today is: PVA1 = $1,500 [{1 – 1 / [1 + (.13/12)]⌒84} / (.13/12)] = $82,453.99 The value of the cash flows today is the sum of these two cash flows, so: PV = $82,453.99 + 41,415.70 = $123,869.99 24题The monthly interest rate is the annual interest rate divided by 12, or: Monthly interest rate = .104 / 12 Monthly interest rate = .00867 Now we can set the present value of the lease payments equal to the cost of the equipment, or $3,500. The lease payments are in the form of an annuity due, so: PV Adue = (1 + r) C({1 – [1/(1 + r)]⌒t } / r ) $3,500 = (1 + .00867) C({1 – [1/(1 + .00867)]⌒24 } / .00867 ) C = $160.76 25题Here, we need to compare to options. In order to do so, we must get the value of the two cash flow streams to the same time, so we will find the value of each today. We must also make sure to use the aftertax cash flows, since it is more relevant. For Option A, the aftertax cash flows are: Aftertax cash flows = Pretax cash flows(1 – tax rate) Aftertax cash flows = $175,000(1 – .28) Aftertax cash flows = $126,000 The aftertax cash flows from Option A are in the form of an annuity due, so the present value of the cash flow today is: PV Adue = (1 + r) C({1 – [1/(1 + r)]⌒t } / r ) PV Adue = (1 + .10)$126,000({1 – [1/(1 + .10)]⌒31 } / .10 ) PV Adue = $1,313,791.22 For Option B, the aftertax cash flows are: Aftertax cash flows = Pretax cash flows(1 – tax rate) Aftertax cash flows = $125,000(1 – .28) Aftertax cash flows = $90,000 The aftertax cash flows from Option B are an ordinary annuity, plus the cash flow today, so the present value: PV = C({1 – [1/(1 + r)]⌒t } / r ) + CF0 PV = $90,000{1 – [1/(1 + .10)]⌒30 } / .10 ) + $530,000 PV = $1,378,422.30 26题The cash flows for this problem occur monthly, and the interest rate given is the EAR. Since the cash flows occur monthly, we must get the effective monthly rate. One way to do this is to find the APR based on monthly compounding, and then divide by 12. So, the pre-retirement APR is: EAR = .11 = [1 + (APR / 12)]⌒12– 1; APR = 12[(1.11)1/12 – 1] = 10.48% And the post-retirement APR is: