Answer:
(a) What is the yield to maturity (annual compounding) on the bond?
Yield to maturity (YTM) = (face value / market price)¹/ⁿ - 1
- face value = $1,000
- market price = $800
- n = 5
YTM = ($1,000 / $800)⁰°² - 1 = 0.0456 or 4.56%
(b) Assume the yield to maturity on comparable zeros increases to 7% immediately after purchasing the bond and remains there. Calculate your annual return (holding period yield) if you sell the bond after one year.
holding period yield = (end of period value - initial value) / initial value
initial value = $800
end of period value = ?
to determine the end of period value we must solve:
7% = ($1,000 / ?)⁰°²⁵ - 1
1.07 = ($1,000 / ?)⁰°²⁵
1.07⁴ = $1,000 / ?
? = $1,000 / 1.3108 = $762.90
holding period yield = ($762.90 - $800) / $800 = -4.64%
(c) Assume yields to maturity on comparable bonds remain at 7%, calculate your annual return if you sell the bond after two years.
1.07³ = $1,000 / ?
? = $1,000 / 1.225 = $816.30
holding period yield = ($816.30 - $800) / $800 = 2.04%
annualized return = (1 + total return)¹/ⁿ - 1 = (1 + 0.0204)¹/² - 1 = 1.01%
(d) Suppose after 3 years, the yield to maturity on similar zeros declines to 3%. Calculate the annual return if you sell the bond at that time.
1.03² = $1,000 / ?
? = $1,000 / 1.0609 = $942.60
holding period yield = ($942.60 - $800) / $800 = 17.83%
annualized return = (1 + total return)¹/ⁿ - 1 = (1 + 0.1783)¹/³ - 1 = 5.62%
