Question

A public company is offering bonds with a face value of $4,500 and a coupon rate of 14%, paid annually,

if you want a yield to maturity of 10%, what is the maximum price you will pay for it? Assume that the

bond will mature in 10 years and the first payment will be received in one year.

Answer 1

The Price that he will be willing to pay is the net present value(NPV) of all future receiving.

Here he receives 4500 at the end of 10th year and 14% of 4500 = 0.14*4500 = 630.

Present value(PV) of Periodic payment is given by :

PV = (P/r)(1 - 1/(1 + r)ⁿ)

Present value(PV") of amount after n years is given by :

PV" = A/(1 + r)ⁿ

where A = amount after n years = 4500, r = yield to maturity = 10% = 0.10, n = time period and P = annual receiving = 630

Thus Net Present Value(NPV) = PV + PV" = (P/r)(1 - 1/(1 + r)ⁿ) + A/(1 + r)ⁿ

=> NPV = (630/0.10)(1 - 1/(1 + 0.10)¹⁰) + 4500/(1 + 0.10)¹⁰ = 5606.02

Thus, Price that he will be willing to pay is the net present value(NPV) = $5606.02

Hence, Price that he will be willing to pay for this Bond = $5606.02