Question

Madsen Motors's bonds have 23 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 7.5%; and the yield to maturity is 13%. What is the bond's current market price? Round your answer to the nearest cent.

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Answer 1

Given the following information,

N = Number of years to maturity = 23

y = YTM = yield to maturity = 13% = 0.13

FV = face value = 1000

Number of coupon payments = paid annually = 1

Coupon rate = 7.5% = 0.075

So

CPN = (Coupon rate x face value)/ Number of Coupon payments per year

CPN = (0.075 x 1000)/ 1

CPN = 75

We know that the Price of a bond is given by the formula,

P = CPN x 1/y x (1- (1/(1+y)^N)) + FV/ (1+y)^N

Substituting the given values, we get

P = 75 x 1/0.13 x (1- (1/(1+0.13)^23)) + 1000/ (1+0.13)^23

P = 75 x 7.69 x (1- (1/(1.13)^23)) + 1000/ (1.13)^23

P = 75 x 7.69 x (1- (1/(16.63)) + 1000/ (16.63)

P = 75 x 7.69 x (1- (0.0601)) + 1000/ (16.63)

P = 75 x 7.69 x (0.9399) + 1000/ (16.63)

P = 542.22 + 60.14

P = 602.37

Therefore, Price of the bond = 602.37