Bond Wall-E is a 6 percent coupon bond. Bond EVE is a 12 percent coupon bond. Bo
ID: 2705648 • Letter: B
Question
Bond Wall-E is a 6 percent coupon bond. Bond EVE is a 12 percent coupon bond. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 9 percent.
If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16)))
What if rates suddenly fall by 2 percent instead? (Round your answers to 2 decimal places. (e.g., 32.16))
Bond Wall-E is a 6 percent coupon bond. Bond EVE is a 12 percent coupon bond. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 9 percent.
Explanation / Answer
All we have to do is recalculate their prices and then take the percent change. Bonds normally have a face value of $1,000, and the coupon rate is their annual payment (i.e. a 10% coupon is a $100 annual payment). The PV or price of a bond is found by the calculation: PMT * [(1 - (1 + i)) / i ] ^ -n, then add the value of the lump sum of $1,000 to be received at the bond's maturity date which is calculated by 1,000 / (1 + i) ^ n
Bond Wall-E's price is: 30 * [1 - (1 + 0.045) ^ -28] / 0.045 + 1,000 / (1 + 0.045) ^ 28= $763.86
NOTE: Tthe PMT and i must be halfed, and the n must be doubled because these are semiannual payments.
Bond EVE's price is: 60 * [1 - (1 +0.045) ^ -28] / 0.045 + 1,000 / (1 + 0.045) ^ 28 = $1,236.14
NOTE: We expect Wall-E to be below par ($1,000) because itspayment is lower than the yield (i.e. 3% < 4.5%), conversely, we expect EVE to be a premium bond (> $1,000) because its payment is above the yield (i.e. 6% > 4.5%).
If the YTM increases we expect both to decrease, If YTM decreases we expect both to increase. Let's see what happens:
YTM increases 2% (only change by 1% or 0.01 on a semiannual basis)
Wall-E: 30 * [1 - (1 + 0.055) ^ -28] / 0.055 + 1,000 / (1 + 0.055) ^ 28 = $646.96
EVE: 60 * [1 - (1 +0.055) ^ -28] / 0.055 + 1,000 / (1 + 0.055) ^ 28 = $1,070.61
YTM decreases 2%
Wall-E: 30 * [1 - (1 +0.035) ^ -28] / 0.035 + 1,000 / (1 + 0.035) ^ 28 = $911.66
EVE: 60 * [1 - (1 +0.035) ^ -28] / 0.035 + 1,000 / (1 + 0.035) ^ 28 = $1,441.68
To calculate the percentage change use: (new - old) / new
YTM increases 2%:
Wall-E: ($646.96 - $763.86) / $646.96 = -18.07%
EVE: ($1,070.61 - $1,236.14) / $1,070.61 = -15.46%
YTM decreases 2%
Wall-E: ($911.66- $763.86) / $911.66= 16.21%
EVE: ($1,441.68- $1,236.14) / $1,441.68= 14.26%
Hope that helps!