valuing bonds

 25. Valuing Bonds – The Morgan Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 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 $20,000 and a maturity of 20 year; it makes no coupon payments over the life of the bond. If the required return on both these bond is 8 percent compounded semiannually, what is the current price of Bond M? Of Bond N?

Answer:

The price of any bond ( or financial instrument) 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)

P_M = $ 13,117.88

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) = $4,165.78

Reference:  Chapter 8, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.