Titan Corp issued a 1,000 par value bond paying 8 percent interest with 15 years to...

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

Solutions

Expert Solution

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

jeff jeffy answered 4 months ago

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