FIN 3320 Connect CH7

Suppose the real rate is 3.5 percent and the inflation rate is 5.1 percent. What rate would you expect to see on a Treasury bill? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Treasury bill rate 8.78 ± 1%

Explanation: The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is: (1 + R) = (1 + r)(1 + h) R = (1 + .035)(1 + .051) - 1 R = .0878, or 8.78%

Bourdon Software has 9.6 percent coupon bonds on the market with 20 years to maturity. The bonds make semiannual payments and currently sell for 107.6 percent of par. What is the current yield on the bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Current yield 8.92 What is the YTM? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) YTM 8.79 What is the effective annual yield? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual yield 8.98

Explanation: The current yield is: Current yield = Annual coupon payment / Price Current yield = $96 / $1,076 Current yield = .0892, or 8.92% The bond price equation for this bond is: P0 = $1,076 = $48(PVIFAR%,40) + $1,000(PVIFR%,40) Using a spreadsheet, financial calculator, or trial and error we find: R = 4.393% This is the semiannual interest rate, so the YTM is: YTM = 2 × 4.393% YTM = 8.79% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + .04393)2 - 1 Effective annual yield = .0898, or 8.98% Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Solve for I/Y. N = 40, PV = 1076, PMT = $96/2 = $48, FV = $1000, CPT I/Y = 4.393% x 2 = 8.79% YTM = 8.79% Solve for Effective Annual Yield ("EFF"). NOM = 8.79%, C/Y = 2, EFF = ? 8.79

You find a zero coupon bond with a par value of $10,000 and 14 years to maturity. The yield to maturity on this bond is 5.1 percent. Assume semiannual compounding periods. What is the price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price $ 4,940.85 ± .1%

Explanation: To find the price of a zero coupon bond, we need to find the value of the future cash flows. With a zero coupon bond, the only cash flow is the par value at maturity. We find the present value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent to the YTM of a coupon bond, so: P = $10,000(PVIF2.55%,28) P = $4,940.85 Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Solve for PV. N = 14 x 2 = 28, I/Y = 5.1% / 2 = 2.55%, FV = 10,000, PV = ? CPT PV = $4,940.85

The YTM on a bond is the interest rate you earn on your investment if interest rates don't change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). a. Suppose that today you buy a bond with an annual coupon of 10 percent for $1,050. The bond has 19 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected rate of return 9.42 ± 1% b1. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Bond price $ 1,139.69 ± 0.1% b2. What is the HPY on your investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) HPY 13.52 ± 1%

Explanation: a. The rate of return you expect to earn if you purchase a bond and hold it until maturity is the YTM. The bond price equation for this bond is: P0 = $1,050 = $100(PVIFAR%,19) + $1,000(PVIFR%,19) Using a spreadsheet, financial calculator, or trial and error we find: R = YTM = 9.42% b. To find our HPY, we need to find the price of the bond in two years. The price of the bond in two years, at the new interest rate, will be: P2 = $100(PVIFA8.42%,17) + $1,000(PVIF8.42%,17) P2 = $1,139.69 To calculate the HPY, we need to find the interest rate that equates the price we paid for the bond with the cash flows we received. The cash flows we received were $100 each year for two years and the price of the bond when we sold it. The equation to find our HPY is: P0 = $1,050 = $100(PVIFAR%,2) + $1,139.69(PVIFR%,2) Solving for R, we get: R = HPY = 13.52% The realized HPY is greater than the expected YTM when the bond was bought because interest rates dropped by 1 percent; bond prices rise when yields fall.