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%
