Question

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.)

Answer 1

a. The yield to maturity on the bond should be 7.12%. b. The 1-year holding-period return on the coupon bond is 6.77%.

Step-by-step explanation:

a. To calculate the yield to maturity on the bond, we can use the formula:

YTM = ((Annual Interest Payment / Price) + ((Face Value - Price) / Maturity)) / ((Face Value + Price) / 2)

For the given bond, the annual interest payment is $1,000 * 5.6% = $56, the price is $847.70, the face value is $1,000, and the maturity is 3 years. Substituting these values into the formula, we get:

YTM = ((56 / 847.70) + ((1,000 - 847.70) / 3)) / ((1,000 + 847.70) / 2)

Simplifying this equation gives us a yield to maturity of 7.12% (rounded to 2 decimal places).

b. The 1-year holding-period return is the total return earned over the year, expressed as a percentage of the initial investment. In this case, the coupon payment for the first year is $1,000 * 5.6% = $56, and the bond price at the end of the year is $847.70. The holding-period return can be calculated using the formula:

Holding-Period Return = ((Coupon Payment + Ending Bond Price) / Starting Bond Price) - 1

Substituting the values into the formula, we get:

Holding-Period Return = ((56 + 847.70) / 847.70) - 1

Simplifying this equation gives us a 1-year holding-period return of 1.0677, or 6.77% (rounded to 2 decimal places).

Answer 2

a. 5.63%

b. 5.72%

Step-by-step 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%