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 7.8% ​(annual payments). The yield to maturity on this bond when it was issued was 5.5%. What was the price of this bond when it was​ issued?

Answer 1

Bond price is the present discounted value of future cash stream generated by a bond. It refers to the sum of the present values of coupon payments and the present value of the par value at maturity.

Price of Bond = Coupon payment * PVAF(_r,n) + (Face value / (1 +r)ⁿ)

where C= coupon payment

r= discount rate/ YTM

F= Face value

n=number of periods

Here,

Coupon payment = 7.8% * $1,000 = $78

r or YTM = 5.5%

n= 10 years

PVAF_(r,n) = 1- (1+r)^-n / r

= 1-(1+5.5%)^-10 / 5.5%

= 7.53

Price of bond = $78 * 7.53 + $1000/ (1+ 0.055)¹⁰

Price of bond = $587.34 + 1000/1.708

Price of bond = $587.34 + $585.48 = $1,172.82