Bond J has a coupon rate of 5.4 percent. Bond S has a coupon rate of 15.4 percen
ID: 2660377 • Letter: B
Question
Bond J has a coupon rate of 5.4 percent. Bond S has a coupon rate of 15.4 percent. Both bonds have twelve years to maturity, make semiannual payments, and have a YTM of 11.8 percent.
If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).)
If interest rates suddenly fall by 2 percent instead, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)
Bond J has a coupon rate of 5.4 percent. Bond S has a coupon rate of 15.4 percent. Both bonds have twelve years to maturity, make semiannual payments, and have a YTM of 11.8 percent.
Explanation / Answer
Bond J has a coupon rate of 5.4 percent. Bond S has a coupon rate of 15.4 percent. Both bonds have twelve years to maturity, make semiannual payments, and have a YTM of 11.8 percent.
1: Initially, at a YTM of 11.8 percent, the prices of the two bonds are
: PJ = $27.0(PVIFA5.9%,24) + $1,000(PVIF5.9%,24) = $594.65
PS = $77.0(PVIFA5.9%,24) + $1,000(PVIF5.9%,24) = $1,228.01
If the YTM rises from 11.8 percent to 13.8 percent:
PJ = $27.0(PVIFA6.9%,24) + $1,000(PVIF6.9%,24) = $514.03
PS = $77.0(PVIFA6.9%,24) + $1,000(PVIF6.9%,24) = $1,092.57
The percentage change in price is calculated as: Percentage change in price = (New price Original price) / Original price PJ% = ($514.03 594.65) / $594.65 = 0.1356 or 13.56%
PS% = ($1,092.57 1,228.01) / $1,228.01 = 0.1103 or 11.03%
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2: If the YTM declines from 11.8 percent to 9.8 percent:
PJ = $27.0(PVIFA4.9%,24) + $1,000(PVIF4.9%,24) = $693.45 PS $77.0(PVIFA4.9%,24) = + $1,000(PVIF4.9%,24) = $1,390.15
PJ% = ($693.45 594.65) / $594.65 = 0.1662 or +16.62% PS% = ($1,390.15 1,228.01) / $1,228.01 = 0.1320 or +13.20%
PJ% = ($514.03 594.65) / $594.65 = 13.56% PS% = ($1,092.57 1,228.01) / $1,228.01 = 11.03%
If the YTM declines from 11.8 percent to 9.8 percent
: PJ% = ($693.45 594.65) / $594.65 = +16.62% PS% = ($1,390.15 1,228.01) / $1,228.01 = +13.20%
All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates