Solution to Handout #3
Part A
Value of Bond A:
PMT: 80
FV:1,000
N: 5
I/YR: 12%
PV: ?
The PV yields a value of $855.81 for Bond A
Value of Bond B:
PMT: 80
FV:1,000
N: 10
I/YR: 12%
PV: ?
The PV yields a value of $773.99 for Bond B
Value of Bond C:
PMT: 120
FV:1,000
N: 5
I/YR: 12%
PV: ?
The PV yields a value of $1,000.00 for Bond C
Part B
The total yield (yield to maturity) of a bond is comprised of the current yield (Interest/Price) and the capital gain yield:
For Bond A:
For Bond B:
For Bond C:
Part C
All three bonds need to be re-priced at the new interest rate of 8%. You should know that since the market rate of interest now equals the coupon rate of interest on Bonds A and B, their market prices should be the same as par.
Value of Bond A:
PMT: 80
FV:1,000
N: 5
I/YR: 8%
PV: ?
The PV at 8% yields a value of $1,000.00 for Bond A. Thus, the drop in interest rates from 12% to 8% caused the value of Bond A to increase from $855.81 to $1,000 or a gain of $144.19 on the bond. As a percentage of its initial value of $855.81 this amounts to a 16.85% increase in price
Value of Bond B:
PMT: 80
FV:1,000
N: 10
I/YR: 8%
PV: ?
The PV at 8% yields a value of $1,000.00 for Bond B. The drop in interest rates from 12% to 8% caused the value of Bond B to increase from $773.99 to $1,000 or a gain of $226.01 on the bond. As a percentage of its initial value of $773.99 this amounts to a 29.2% increase in price
Value of Bond C:
PMT: 120
FV:1,000
N: 5
I/YR: 8%
PV: ?
The PV at 8% yields a value of $1,159.71 for Bond C. The drop in interest rates from 12% to 8% caused the value of Bond C to increase from $1,000.00 to $1,159.71 or a gain of $159.71 on the bond. As a percentage of its initial value of $1,000.00 this amounts to a 15.97% increase in price
Thus, lower coupon and longer-lived bonds are more sensitive to changes in interest rates.