# You want to have $2 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 10 percent and the inflation rate is 3.8 percent. What real amount must you deposit each year to achieve your goal?

Problem 1:

**Interpreting Bond Yields.** Is the yield to maturity on a bond the same thing as the required return? Is the YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate of the bond then? The YTM?

Problem 3:

**Valuing Bonds**. Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual €1,000, 25 years to maturity, and a coupon rate of 6.4 percent paid annually. If the yield to maturity is 7.5 percent, what is the current price of the bond?

Problem 8:

**Coupon Rates.** Ponzi Corporation has bonds on the market with 14.5 years to maturity, a YTM of 6.1 percent, and a current price of 1,038. The bonds make semiannual payments. What must the coupon rte be on these bonds?

Problem 10:

**Inflation and Nominal Returns.** Suppose the real rate is 2.5 percent and the inflation rate is 4.1 percent. What rate would you expect to see on a Treasury bill?

Problem 12:

**Nominal versus Real Returns.** Say you own an asset that had a total return last year of 10.7 percent. If the inflation rate last year was 3.7 percent, what was the real return?

Problem 14:

**Using Treasury Quotes.** Is this a premium or discount bond? What is the current yield? What is it’s yielded to maturity? What is the bid-ask spread?

Maturity: August 2029

Coupon: 6.125

Bid: 123:13

Asked: 123:15

Change: -58

Asked Yield: 4.2790

Problem 17:

**Interest Rate Risk.** Bond J is a 3 percent coupon bond. Bond K is a 9 percent coupon bond. Both bonds have 15 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

Problem 18:

**Bond Yields**. Martin Software has 9.2 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. What is the current yield on the bonds? They YTM? The effective annual yield?

Problem 26:

**Zero Coupon Bonds.** Suppose your company needs to raise $45 million and you want to issue 30-year bonds for this purpose. Assume the required return on your bond issue will be 6 percent, and you’re evaluating two issue alternatives: a 6 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 35 percent.

a. How many of the coupon bonds would you need to issue to raise the $45 million? How many of the zeros would you need to issue?

b. In 30 years, will your company’s repayment be if you issue the coupon bonds? What if you issue the zeroes?

c. Based on your answers in (a) and (b), why would you ever want to issue the zeroes? To answer, calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. Assume the IRS amortization rules apply for the zero coupon bonds.

Problem 28:

**Real Cash Flows.** You want to have $2 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 10 percent and the inflation rate is 3.8 percent. What real amount must you deposit each year to achieve your goal?