Question

Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of,$1000, have 5 years remaining to maturity, and have a required rate of return of 10 percent

1. the bond has a 6 percent coupon rate.
2. the bond has a 8 percent coupon rate.
3. the bond has a 10 percent coupon rate.
4. what do your answers to parts (a) through (c) say about the relation between coupon rates and present values

Answer 1

Value of a bond is present value of future cash flows discounted at YTM

1)

When coupon = 6%

periodic coupons = 1000*6%/2 = $30

Number of periods = 5* 2 = 10

Required return = 10% / 2 = 5%

Present value= 30*PVIFA(r=5% ;n=10) +1000*PVF(r=5%;n=10)

Present value = 30*7.72173 + 1000*0.6139 = $845.57

2)

Here everything remains same except

Coupon = 1000*8%/2 = 40

Present value = 40*PVIFA(r = 5% ; n = 10)

+ 1000*PVF(r = 5% ; n = 10)

Present value = $922.78

3)

When coupon rate = required return , present value of bond will be par value

So present value of bond = $1000

conclusion:

when coupon rate increases present value of the bond increases