In: Finance
Fingen's 15-year, $1,000 par value bonds pay 12 percent interest annually. The market price of the bonds is $1,100 and the market's required yield to maturity on a comparable-risk bond is 9 percent.
a. Compute the bond's yield to maturity.
b. Determine the value of the bond to you, given your required rate of return.
c. Should you purchase the bond?
a) | YTM is that discount rate which equates the cash flows from the | |
bond with the price of $1100 if it is held for 15 years, its maturity. | ||
The cash flows are the maturity value of $1000 at EOY 15 and | ||
the annual interest of $120 for 15 years. | ||
The relevant half yearly discount rate has to be found by trial and error, so that the PV of the expected cash flows equals the price of the bond. | ||
Discounting with 11%: | ||
Price = 1000/1.11^15+120*(1.11^15-1)/(0.11*1.11^15) = | $ 1,071.91 | |
Discounting with 10%: | ||
Price = 1000/1.10^15+120*(1.10^15-1)/(0.10*1.10^15) = | $ 1,152.12 | |
So, the YTM lies between 8% and 9%. | ||
By simple interpolation YTM = 10%+1%*(1152.12-1100)/(1152.12-1071.91) = | 10.65% | |
Using an online calculator, YTM = 10.64% | ||
b) | Value of the bond with 9% RRR = | |
= 1000/1.09^15+120*(1.09^15-1)/(0.09*1.09^15) = | $ 1,241.82 | |
c) | The bond can be purchased as it is underpriced in the market. If | |
purchased it will yield 10.65% and agains the required yield of 9%. |