Finance

### FINANCIAL INSTITUTIONS MANAGEMENT

WRITTEN ASSIGNMENT # 2

Problem 1 (25 points)

TIME VALUE OF MONEY Answer the following questions:

1. Assuming a rate of 10% annually, find the FV of \$1,000 after 5 years.
2. What is the investment’s FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5 years?
3. Find the PV of \$1,000 due in 5 years if the discount rate is 10%.
4. What is the rate of return on a security that costs \$1,000 and returns \$2,000 after 5 years?
5. Suppose California’s population is 40 million people and its population is expected to grow by 2% annually. How long will it take for the population to double?
6. Find the PV of an ordinary annuity that pays \$1,000 each of the next 5 years if the interest rate is 15%. What is the annuity’s FV?
7. How will the PV and FV of the annuity in part f change if it is an annuity due?
8. What will the FV be for \$1,000 now in 5 years if the interest rate is 10%, semiannual compounding? What will the PV be for \$1,000 in 5 years if the interest rate is 10%, semiannual compounding?
9. What will the annual payments be for an ordinary annuity for 10 years with a PV of \$1,000 if the interest rate is 8%? What will the payments be if this is an annuity due?
10. Find the PV and the FV of an investment that pays 8% annually and makes the following end-of-year payments: Details
11. Five banks offer nominal rates of 6% on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. (1) What effective annual rate does each bank pay? If you deposit \$5,000 in each bank today, how much will you have in each bank at the end of 1 year? 2 years? (2) If all of the banks are insured by the government (the FDIC) and thus are equally risky, will they be equally able to attract funds? If not (and the TVM is the only consideration), what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A? (3) Suppose you don’t have the \$5,000 but need it at the end of 1 year. You plan to make a series of deposits—annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E—with payments beginning today. How large must the payments be to each bank? (4) Even if the five banks provided the same effective annual rate, would a rational investor be indifferent between the banks? Explain.
12. Suppose you borrow \$15,000. The loan’s annual interest rate is 8%, and it requires four equal end-of-year payments. Set up an amortization schedule that shows the annual payments, interest payments, principal repayments, and beginning and ending loan balances.

Problem 2 (25 points)

BOND VALUATION Clifford Clark is a recent retiree who is interested in investing some of his savings in corporate bonds. His financial planner has suggested the following bonds:

• Bond A has a 7% annual coupon, matures in 12 years, and has a \$1,000 face value.
• Bond B has a 9% annual coupon, matures in 12 years, and has a \$1,000 face value.
• Bond C has an 11% annual coupon, matures in 12 years, and has a \$1,000 face value.

Each bond has a yield to maturity of 9%.

1. Before calculating the prices of the bonds, indicate whether each bond is trading at a premium, at a discount, or at par.
2. Calculate the price of each of the three bonds.
3. Calculate the current yield for each of the three bonds. (Hint: Refer to footnote 6 for the definition of the current yield and to Table 7.1.)
4. If the yield to maturity for each bond remains at 9%, what will be the price of each bond 1 year from now? What is the expected capital gains yield for each bond? What is the expected total return for each bond?
5. Clark is considering another bond, Bond D. It has an 8% semiannual coupon and a \$1,000 face value (i.e., it pays a \$40 coupon every 6 months). Bond D is scheduled to mature in 9 years and has a price of \$1,150. It is also callable in 5 years at a call price of \$1,040. (1) What is the bond’s nominal yield to maturity? (2) What is the bond’s nominal yield to call? If Mr. Clark were to purchase this bond, would he be more likely to receive the yield to maturity or yield to call? Explain your answer.
6. Explain briefly the difference between price risk and reinvestment risk. Show the price change to each of the following bonds if market interest rates rise from 9% per year to 10% to year. Which has the most reinvestment risk and why?
• A 1-year bond with a 9% annual coupon
• A 5-year bond with a 9% annual coupon A 5-year bond with a zero coupon
• A 10-year bond with a 9% annual coupon
• A 10-year bond with a zero coupon
7. Calculate the price of each bond (A, B, and C) at the end of each year until maturity, assuming interest rates remain constant. Create a graph showing the time path of each bond’s value, similar to that shown in Figure 7.2. (1) What is the expected interest yield for each bond in each year? (2) What is the expected capital gains yield for each bond in each year? (3) What is the total return for each bond in each year?

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