Question

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?

Answer 1

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%.