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%.|