Question

"Suppose that General Motors Acceptance Corporation issued a bond with 10 years until​ maturity, a face value of $ 1 comma 000​, and a coupon rate of 7.4 % ​(annual payments). The yield to maturity on this bond when it was issued was 6.4 %. What was the price of this bond when it was​ issued?"

Answer 1

$1,072.22

Step-by-step explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. Both of these cash flows discounted and added to calculate the value of the bond.

According to given data

Face value of the bond is $1,000

Coupon payment = C = $1,000 x 7.4% = $74 annually

Number of periods = n = 10 years

Market Rate = 6.4% annually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond = $74 x [ ( 1 - ( 1 + 1.064% )^-10 ) / 1.064% ] + [ $1,000 / ( 1 + 1.064% )^10 ]

Price of the Bond = $534.47 + $537.75 = $1072.22

Price of the Bond = $5,627.25

Answer 2

$ 1,072.23

Step-by-step explanation:

Price of the Bond is the Present Value of the Bond.

Thus, Calculate the Present Value of this Bond

N= 10

PMT = $1,000×7.4% = $ 74

YTM = 6.4%

FV = $1,000

P/YR = 1

PV = ?

Using a Financial Calculator PV is $ 1,072.23