Question

A corporation issues a 9 percent coupon bond with 13 years maturity and $1,000 face (par) value. If the current market price of this bond is $1000, find its yield to maturity.

a. 6.43%

b. 6.04%

c. 9.00%

d. 10.07%

e. none of the answers is correct

Answer 1

First step would be to compute the approximate YTM using the following formula -

where, I = Interest, RV = redeemable value (par), MP = Current market price, n = number of years to maturity

or 9%

Now, YTM is rate at which the present value of inflows, i.e., present value of interest and redeemable value is equal to the initial outflows, i.e., current market price. So, we can use 9% to see if PV of inflows is equal to initial outflow.

PV of cash Inflows = Interest per year for 13 years x PVFA (9%, 13) + RV x PVF (9%, 13)

where, PVFA = Present value factor annuity (rate, year), PVF = Present value factor

PV of cash Inflows = $90 x 7.48690392324 + $1000 x 0.32617864685 = $999.999 or $1000

So, PV of cash Inflows = PV of cash outflows @9%.

YTM = 9% (option c)