Problem 15-12 Below is a list of prices for zero-coupon bonds of various maturities. Maturity (Years) Price of $1,000 Par Bond (Zero-Coupon) 1 $ 974.85 2 882.39 3 847.70 a. A 5.6% coupon $1,000 par bond pays an annual coupon and will mature in 3 years. What should the yield to maturity on the bond be? (Round your answer to 2 decimal places.) b. If at the end of the first year the yield curve flattens out at 6.5%, what will be the 1-year holding-period return on the coupon bond? (Round your answer to 2 decimal places.)

a. 5.63%

b. 5.72%

Explanation:

to calculate YTM of zero coupon bonds:

YTM = [ (face value / market value) ¹/ⁿ] - 1

YTM₁ = [ (1,000 / 974.85) ¹/ⁿ] - 1 = 2.58% YTM₂ = [ (1,000 / 882.39) ¹/ⁿ] - 1 = 6.46% YTM₃ = [ (1,000 / 847.70) ¹/ⁿ] - 1 = 5.66%

a. A 5.6% coupon $1,000 par bond pays an annual coupon and will mature in 3 years. What should the yield to maturity on the bond be?

the bond's current market price:

$1,000 / 1.0566³ = $847.75 $56/1.0258 + 56/1.0646² + 56/1.0566³ = $54.59 + $49.41 + $47.47 = $151.47 current market price = $999.22

YTM = [C + (FV - PV) / n] / [ (FV + PV) / 2] = [56 + (1,000 - 999.22) / 3] / [ (1,000 + 999.22) / 2] = (56 + 0.26) / 999.61 = 5.63%

b. If at the end of the first year the yield curve flattens out at 6.5%, what will be the 1-year holding-period return on the coupon bond?

the bond's current market price:

$1,000 / 1.065³ = $827.85 $56/1.0258 + 56/1.065² + 56/1.065³ = $54.59 + $49.37 + $46.36 = $150.32 current market price = $978.17

you invest $978.17 in purchasing the bond and you receive a coupon of $56, holding period return = $56 / $978.17 = 5.72%