Question

. Suppose you buy a five-year zero-coupon Treasury bond for $800 per $1000 face value. Answer the following questions: (a) What is the yield to maturity (annual compounding) on the bond? (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. (c) Assume yields to maturity on comparable bonds remain at 7%, calculate your annual return if you sell the bond after two years. (d) Suppose after 3 years, the yield to maturity

Answer 1

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%