Question

Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?

Answer 1

Answer:

Ans. The price of the bond immediately after it makes its first coupon payment is $1,068.02

Explanation:

Hi, we have to bring to present value the remaining cash flows, that is 9 coupons and its face value, so we need to use the following equation.

$Price=\frac{Coupon((1+YTM)^{n}-1) }{YTM(1+YTM)^{n} } +\frac{FaceValue}{(1+YTM)^{n} }$

Where:

Coupon = 0.07*$1,000=$70

YTM = Yield to maturity, in our case 6% or 0.06

n = 9 (since the bond is paying every year and there are 9 years left until maturity)

Face Value= $1,000.

Everything should look like this

$Price=\frac{70((1+0.06)^{9}-1) }{0.06(1+0.06)^{9} } +\frac{1,000}{(1+0.06)^{9} }$

Therefore:

$Price=476.12+591.90=1,068.02$

So, the price of this bond right after paying its first coupon is $1,068.02

Best of luck.