Problem 7-7 Interest rate sensitivity An investor purchased the following 5 bond
ID: 2647040 • Letter: P
Question
Problem 7-7
Interest rate sensitivity
An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell and each then had a new YTM of 7%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places.
Price @ 8% Price @ 7% Percentage Change 10-year, 10% annual coupon $ $ % 10-year zero $ $ % 5-year zero $ $ % 30-year zero $ $ % $100 perpetuity $ $ %Explanation / Answer
Bond price = PV of all coupon payments + PV of principal repayment
Zero coupn bond value = Face value / (1 + interest rate)T
Value of perpetual bond = Coupon rate / yield
So:
1) 10% 10-yr bond value = PV ($100, 10 years) + PV ($1000, 10 years) [discounted at 8%] = $ 7173.28 (at 8%)
10% 10-yr bond value = PV ($100, 10 years) + PV ($1000, 10 years) [discounted at 7%] = $ 7531.93 (at 7%)
So % change = (7531.93 - 7173.28) / 7173.28 = 4.99%
2) 10-yr ZCB = $463.19 (at 8%)
10-yr ZCB = $508.35 (at 7%)
So % change = (508.35 - 463.19) / 463.19 = 9.75%
3) 5-yr ZCB = $680.58 (at 8%)
5-yr ZCB = $712.99 (at 7%)
So % change = (712.99 - 680.58) / 680.58 = 4.76%
4) 30-yr ZCB = $99.38 (at 8%)
30-yr ZCB = $131.37 (at 7%)
So % change = (131.37 - 99.38) / 99.38 = 32.19%
5) $100 perpetuity = $100 / 0.08 = $1250 (at 8%)
$100 perpetuity = $100 / 0.07 = $1428.57 (at 7%)
So % change = (1428.57 - 1250) / 1250 = 14.29%