Question

Suppose that General Motors Acceptance Corporation issued a bond with 10 years until​ maturity, a face value of $1,000​ and a coupon rate of 7.5%

​(annual payments). The yield to maturity on this bond when it was issued was 6.5%. Assuming the yield to maturity remains​ constant, what is the price of the bond immediately before it makes its first coupon​ payment?

Answer 1

Price of the bond is the present value of annual coupon payments and present value of principal payment at maturity.

Price of the bond = Present value of annual coupon payments + Present value of principal payment at maturity

Now, Formula for Present value of annual coupon payments is:

P * (1 - (1+r)^-n / r

where, P is the annual coupon payments, r is rate of interest and n is the time period

and formula for Present value of principal payment at maturity is:

C / (1+r)ⁿ

where, C is principal payment at maturity, r is the rate of interest and n is the time period

Annual coupons = 7.5% * $1000 = $75

We will use yield to maturity of 6.5% as "r" in the above formula. So, now, price of the bond is given by:

Bond price = P * (1 - (1+r)^-n / r + C / (1+r)ⁿ

Bond price = $75 * (1- (1+0.065)^-10 / 0.065 + $1000 / (1+0.065)¹⁰

Bond price = $75 * (1- (1.065)^-10 / 0.065 + $1000 / (1.065)¹⁰

Bond price = $75 * (1- 0.53272603552) / 0.065 + $1000 / 1.87713746527

Bond price = $75 * (0.46727396448 / 0.065) + $532.726

Bond price = $75 * 7.18883 + $532.726

Bond price = $539.1622 + $532.726

Bond price = $1071.89