Question

The Potomac Company’s bonds have a face value of $1,000, will mature in 20 years, and carry a coupon rate of 8 percent. Assume interest payments are made semiannually. (a) Determine the present value of the bond’s cash flows if the required rate of return is 15 percent. (b) Determine the present value of the bond’s cash flows if the required rate of return is 18 percent. (c) Is there a change in the present value in the above two examples? If yes, give a reason.

Answer 1

Present Value of cash flows is equal to the present value of coupon payments plus present value of redemption amount

(a) If required return is 15%

Semi-Annual Rate = 15%/2 = 7.5%

Number of periods = 20*2 = 40

Present Value = 1,000*8%*1/2*PVAF(7.5%, 40 periods) + 1,000*PVF(7.5%, 40 periods)

= 40*12.5944086 + 1,000*0.055419

= $559.20

(b)If rate is 18%

Semi-annual rate = 9%

Present Value = 1,000*8%*1/2*PVAF(9%, 40 periods) + 1,000*PVF(9%, 40 periods)

= 40*10.75736 +1,000*0.03183758

= $462.13

(c)Yes, present value has changed because the rate used for discounting has changed. Since investor has higher required return under (b), he will value bond less today