Bond J is a 7 percent coupon bond. Bond K is a 11 percent coupon bond. Both bond
ID: 2761199 • Letter: B
Question
Bond J is a 7 percent coupon bond. Bond K is a 11 percent coupon bond. Both bonds have 12 years to maturity and have a YTM of 8 percent. a. If interest rates suddenly rise by 1.6 percent, what is the percentage price change of these bonds? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Bond J % Bond K % b. If interest rates suddenly fall by 1.6 percent, what is the percentage price change of these bonds? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) Bond J % Bond K %
Explanation / Answer
The price of any bond is the PV of the interest payment, plus the PV of the par value . assuming
The par value of bond is $1,000
The formula to calculate the price of bond is
P = C(PVIFAR%,t) + $1,000(PVIFR%,t)
Where
C= coupon rate
R% = yield to maturity
T= time period
PVIFA= Present Value Interest Factor of an Annuity
PVIF = Present Value Interest Factor
Initially, at a YTM of 8 percent, the prices of the two bonds are
PJ = $70(PVIFA8%,12) + $1,000(PVIF8%,12) = $924.63
Pk = $110(PVIFA8%,12) + $1,000(PVIF8%,12) = $1226.07
If the YTM rises from 8 percent to 9.6 percent:
PJ = $70(PVIFA9.6%,12) + $1,000(PVIF9.6%,12) = $819.35
Pk = $110(PVIFA9.6%,12) + $1,000(PVIF9.6%,12) = $1097.32
The percentage change in price is calculated as:
Percentage change in price = (New price – Original price) / Original price
DPJ% = ($819.35 – 924.63) / $924.63 = –0.1138, or –11.38%
DPk% = ($1,097.32 – 1,226.07) / $1,226.07 = –0.1050, or –10.50%
If the YTM decreases from 8 percent to 6.4 percent:
PJ = $70(PVIFA6.4%,12) + $1,000(PVIF6.4%,12) = $1049.21
Pk = $110(PVIFA6.4%,12) + $1,000(PVIF6.4%,12) = $1377.33
The percentage change in price is calculated as:
Percentage change in price = (New price – Original price) / Original price
DPJ% = ($1049.21 – 924.63) / $924.63 = 0.1347, or 13.47%
DPk% = ($1,377.33 – 1,226.07) / $1,226.07 = 0.1234, or 12.34%