Question

The Frush Corporation has two different bonds currently outstanding. Bond M has a face value of $30,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $800 every six months over the subsequent eight years, and finally pays $1,000 every six months over the last six years. Bond N also has a face value of $30,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required return on both these bonds is 6.4 percent compounded semiannually, what is the current price of Bond M? Of Bond N?

Answer 1

The price of any bond is the PV of the future cash flows. Even though bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for bond M is:

P_M = $800(PVIFA_4%,16)(PVIF_4%,12) +$1000(PVIFA_4%,12)(PVIF_4%,28) +$20,000(PVIF_4%,40) = $13,117.33

Notice that for the coupon payments of $800, we found the PVA for the coupon payments, and then discounted the lump sum back today.

Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the PV of the par or

P_N = $20,000(PVIF_4%,40) = $4165.78