A bond with 10 years to maturity has a face value of $1,000. The bond pays an 8%
ID: 2740871 • Letter: A
Question
A bond with 10 years to maturity has a face value of $1,000. The bond pays an 8% semiannual coupon, and the bond has a 9% nominal yield to maturity.
a.) Draw a timeline showing the expected cash flows to the bondholder. Make sure you clearly identify the period and the associated cash flow.
b.) What is the current price for this bond?
c.) Assume two years have passed and the nominal yield to maturity for this bond is/will be 6%. What is/will be the new price for the bond?
d.) What is the percentage change in the price of each bond assuming you bought it at the price found in part b and sold it at the price in part c?
e.) What is the total return earned by an investor who bought the bond at the price found in part b and sold it at the price in part c? [Hint it is not the same as part d]
Explanation / Answer
Rate on interest = 8 / 2 = 4 % Or 0.04 (Semi-annually), Time Period = 10 * 2 = 20 Semi-annual Periods.
Yield to Maturity = 9 / 2 = 4.5 % (Semi-annually).
b) Current Price of Bond = 1000 * 4 % * Cumulative Present Value Factors for 20 Years @ 4.5 % + 1000 * Present Value Factor for 20TH Year @ 4.5 %
= 40 * 13.0079 + 1000 * 0.4146
= $ 934.92 (approx)
Conclusion:- Current Price of Bond = $ 934.92 (approx)
c) Assume two years have passed and the nominal yield to maturity for this bond is 6%.
Rate on interest = 8 / 2 = 4 % Or 0.04 (Semi-annually), Time Period = 8 * 2 = 16 Semi-annual Periods.
Yield to Maturity = 6 / 2 = 3 %. (Semi-annually).
The new price of Bond = 1000 * 4 % * Cumulative Present Value Factors for 16 Years @ 3% + 1000 * Present Value Factor for 16TH Year @ 3 %
= 40 * 12.5611 + 1000 * 0.6232
= $ 1125.64 (approx)
Conclusion:- The new price of Bond = $ 1125.64
c) The percentage change in the price of each bond = 1125.64 - 934.92 / 934.92 = 0.2040 = 20.40 % (approx)
d) The total return earned by an investor who bought the bond at the price calculated in part (b) and sold it at the price computed in part (c) = 1125.64 - 934.92 = $ 190.72
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