Question

Titan Corp issued a 1,000 par value bond paying 8 percent interest with 15 years to maturity. Assume the current yield to maturity is 10 percent. What is the price (value) of the bond? Hint: use the present value annuity for yourncalculation

Answer 1

Price of the bond is the present value of the annual coupon payments and present value of the bond repayment at maturity. We will use the 10% rate of yield to maturity to calculate required present values. Price of the bond is given by:

Price = Present value of annual coupons + Present value of bond repayment at maturity

Annual coupons = 8% * par value = 8% * $1000 = $80

Since the coupon payments are annual, so it is an annuity. We will use the present value of annuity (PVA) of $1 table to calculate the present value of coupon payments. And for present value of bond repayment at maturity, we will use simple present value (PV) of $1 table, as per below:

Price = $80 * PVA (10%, 15 years) + $1000 * PV (10%, 15 years)

From the tables, the value of PVA at 10% for 15 years is 7.6061 and value of PV at 10% for 15 years is 0.239.

Now, putting these values in the above equation, we get,

Price = ($80 * 7.6061) + ($1000 * 0.239)

Price = $608.488 + $239

Price = $847.88

So, the price (value) of the bond is $847.88