Homework #1

RES 3200: Finance Fundamentals

Instructions:

1. Round all dollar amounts to the nearest cent and doesnt enter the dollar sign.

E.g. if the answer is $1,022.912, enter it as 1,022.91

Commas dont matter, hence you can also enter 1022.91

2. Round all percentages to the nearest basis point and dont enter the percent sign.

E.g. if the answer is 17.238 %, enter it as 17.24, not 0.1724.

1. What is the future value of $28,000 saved at i=7.82 %, compounded annually in 1 year?

2. What is the future value of $28,000 saved at i=7.82% compounded annually in 2 years?

3. What is the future value of $28,000 saved at i=7.82 %, compounded semi-annually in 2 years?

4. What is the future value of $28,000 saved at i=7.82 %, compounded quarterly in 2 years?

5. Suppose you save $12,000 per year in an ordinary annuity promising you an interest rate of i=5.25% compounded once per year. How much will you have after 35 years?

6. A risk-free bond will pay you $1000 in 1 year. The annual discount rate is i=18.5% compounded annually. What is the bonds present value?

7. A risk-free bond will pay you $1000 in 2 years and nothing in between. The annual discount rate is i=67.5% compounded annually. What is the bonds present value?

8. You buy a 30 year zero coupon bond which will pay you $10,000 in 30 years at an annual yield of i=1% compounded once per year. A few minutes later the annual yield rises to i=2% compounded once per year. What is the percent change in the value of the bond?

(Hint: recall the formula for percent change. The answer should be negative.)

9. You buy a 30 year zero coupon bond which will pay you $1000 in 30 years at an annual yield of i=16.5% compounded once per year. 25 years later it will be a 5-year zero-coupon bond. Suppose the interest rate on this bond will be 16.5%, what will the price of this bond be in 25 years?

10. You are offered an annuity that will pay you $200,000 once per year, at the end of the year, for 25 years. The first payment will arrive one year from now. The last payment will arrive twenty-five years from now. Suppose your annual discount rate is i=17.25 %, how much are you willing to pay for this annuity? (hint: this is the same as the present value of an annuity.)

11. An investment gives you an 18.35% nominal return over 1 year. There was 2.5% inflation over that year. What was your exact real return? (Dont use the Fisher Equation.)

12. An investment gives you an 8.35% nominal return over 1 year. There was 1.5% inflation over that year. According to the Fisher Equation, what was your real return?

13. You would like to develop an office building. Your analysts forecast that it will cost you $1,000,000 immediately (time 0), and it will cost you $500,000 in one year (time 1). The forecast you can sell the building for $2,400,000 in two years (time 2). If your discount rate is i=5 %, what is the net present value of this investment?

14. You would like to develop an office building. Your analysts forecast that it will cost you $1,000,000 immediately (time 0), and it will cost you $500,000 in one year (time 1). The forecast you can sell the building for $2,400,000 in two years (time 2). If your discount rate is i=11 %, what is the internal rate of return for this investment?

15. You would like to develop an office building. Your analysts forecast that it will cost you $1,000,000 immediately (time 0), and it will cost you $500,000 in one year (time 1). The forecast you can sell the building for $2,400,000 in two years (time 2). If your discount rate is i=63% should you invest in this building? Write 0 for no, and write 1 for yes.