公司金融8页练习答案详解
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1 Unless otherwise stated, assume that all cash flows occur at the end of the period. 1. An investment pays you annual stated rate (=nominal rate) of 9 percent interest, compounded annually. A second investment of equal risk, pays interest compounded quarterly. What nominal annual rate of interest would you have to receive on the second investment in order to make you indifferent between the two investments?
a) 2.18% b) 8.71% c) 9.00% d) 9.20% e) 9.31%
Effective annual rate: 1)41(%91)1(4nommnomimiEff
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%711.8)109.1(44nomi 2. You own two securities A and B. Security A pays you $100 a year every odd year in perpetuity (that is, it pays you $100 in year 1, year 3, year 5 etc, forever). Security B pays you $ 50 a year every even year in perpetuity (that is, it pays you $50 a year in year 2, year 4, year 6 etc, forever). Assume 10% is the annual interest rate. What is the present value of the cash flows from both securities combined (rounded off to the closest $10)
a) $720 b) $740 c) $760 d) $780 e) $800 Consider payments are made every period of two years. Considering that period, security A, as being made on year one, is (1+r) times a perpetuity that would start at year 2, like B. The 10% interest rate is a nominal annual interest rate. And we need to get the effective “every-two-years” rate. The nominal “every-two-years” rate is equal to the periodic rate (here, annual) multiplied by the number of periods (two). This is this rate that we’ll use in the equation for effective rate: 10%*2 = 20%
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91.761$21.0501.1100PV 3. You have $1,000 invested in an account which pays 16 percent, compounded annually, for 2 years. A commission agent (called a "finder") can locate for you an equally safe deposit which will pay 16 percent, compounded quarterly, also for 2 years. What is the maximum amount you should be willing to pay him now as a fee for locating the new account? 2
a) $10.92 b) $13.78 c) $16.14 d) $16.78 e) $21.13 16% = effective annual rate. A=1000*(1+0.16)^2=1345.6 B=1000*(1+0.16/4)^(2*4)=1368.58 B-A=22.96 Beware, we also need to calculate the present value of the difference! 22.96/(1+0.15/4)^8 = 16.78
4. Today is your birthday, and you decide to start saving for your college education. You will begin college on your 18th birthday and will need $4,000 per year at the end of each of the following 4 years. You will make a deposit 1 year from today in an account paying 12 percent annually and continue to make an identical deposit each year up to and including the year you begin college. If a deposit amount of $2,542.05 will allow you to reach your goal, what birthday are you celebrating today?
a) 13 b) 14 c) 15 d) 16 e) 17 Value of the college education at 18: N=4 PMT=4,000, ordinary annuity I/Y=12% FV=0 PV = $12,149.4 Number of years the $2542.05 payment must be made to arrive to $12,149.4 : FV=12149.4 PMT=$2542.05, ordinary annuity I/Y=12% PV=0 N=4 Birthday: N is the number of deposits between one year from your birthday and 18 (including the 18th year). So you make payments at 18, 17, 16 and 15, and you’re celebrating your 14th birthday.
5. Assume that you have $15,000 in a bank account that pays 5 percent annual interest. You plan to go back to school for a combination MBA/law degree 5 years from today. It will take you an additional 5 years to complete your graduate studies. You figure you will need a fixed annual income of $25,000 in today's dollars; that is, you will need $25,000 of today's dollars during your first year and each of the four subsequent years.
You will withdraw funds for your annual expenses at the beginning of each year. Inflation is expected to occur at the rate of 3 percent per year. How much must you save during each of the next 5 years in order to achieve your goal (rounded to the next $)? The first increment of savings will be deposited one year from today. (Hint: Calculate first the nominal annual income you need during the 5 years in school. Since this nominal income is constant, your real income will decline while you are in school because of inflation).
a) $20,242 b) $19,225
