Question

A bond you are evaluating has a 7 percent coupon rate (compounded semiannually), a $1,000 face value, and is 10 years from maturity. (LG 3-4) a. If the required rate of return on the bond is 6 percent, what is its fair present value? b. If the required rate of return on the bond is 8 percent, what is its fair present value? c. What do your answers to parts (a) and (b) say about the relation between required rates of return and fair values of bonds?

Answer 1

Solution

Fair present value of bond=Present value of coupon payments+Present value of face value

Fair present value of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Where n=number of periods=10*2=20 (Semi annual compounding)

r=rate of interest/return per period

Face value=1000

Semiannual coupon payment=Coupon rate/2*Face value=.07*1000/2=35

a Rate of return=6%

Putting values in above formula and r=.06

Fair value of bond=35*((1-(1/(1+.06)^20))/.06)+1000/(1+.06)^20

Fair present value of bond=713.252

b. Rate of return=8%

Putting values in above formula and r=.08

Fair value of bond=35*((1-(1/(1+.08)^20))/.08)+1000/(1+.08)^20

Fair present value of bond=558.183

c. The 2 values i.e @ 8% and @ 6% shows that as the required rates of return go up the Present values of bonds decreases ,thus rising intrests reduce present value of bonds

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