Question

Below is a list of prices for zero-coupon bonds of various maturities. Maturity (Years) Price of $1,000 Par Bond (Zero-Coupon) 1 $ 949.20 2 866.42 3 817.77 a. An 8.6% 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 7.9%, what will be the 1-year holding-period return on the coupon bond? (Round your answer to 2 decimal places.)

Answer 1

Answer:

a. 6.91%

b. 8.46%

Explanation:

to calculate YTM of zero coupon bonds:

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

• YTM₁ =  [(1,000 / 949.20)¹/¹] - 1 = 5.35%
• YTM₂ =  [(1,000 / 886.42)¹/²] - 1 = 6.21%
• YTM₃ =  [(1,000 / 817.77)¹/³] - 1 = 6.94%

a. A 8.6% 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 / 1.0694³ = $817.67
• $86/1.0535 + 86/1.0621² + 86/1.0694³ = $81.63 + $76.24 + $70.32 = $228.19
• current market price = $1,045.86

YTM = [C + (FV - PV)/n] / [(FV + PV)/2] = [86 + (1,000 - 1,045.86)/3] / [(1,000 + 1,045.86)/2] = 70.71 / 1,022.93 = 6.91%

b. If at the end of the first year the yield curve flattens out at 7.9%, what will be the 1-year holding-period return on the coupon bond?

the bond's current market price:

$1,000 / 1.079³ = $796.04

$86/1.0535 + 86/1.079² + 86/1.079³ = $81.63 + $73.87 + $64.46 = $219.96

current market price = $1,016

you invest $1,016 in purchasing the bond and you receive a coupon of $86, holding period return = $86 / $1,016 = 8.46%