Question

Maxcorp’s bonds sell for $1,006.27. The bond life is 9 years, and the yield to maturity is 7.9%. What is the coupon rate on the bonds? (Assume a face value of $1,000 and annual coupon payments.) (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Answer:

The cuopon rate is 8%

Explanation:

We are given with the data and need to solve for the rate of the cuopon:

Market value: 1,006.27

Market value = cuopon payment + maturity

$\frac{Maturity}{(1 + rate)^{time} } = PV$

Maturity 1,000

time 9

rate 0.079

$\frac{1000}{(1 + 0.079)^{9} } = PV$

PV  504.4371 = Maturity value

Market value = cuopon payment + maturity

1,006.27        =  cuopon payment + 504.44

1,006.27 - 504.44 = 501.83

The present value of the cuopon payment Using the annuity formula we solve for cuota:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

then:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $501.83

time 9

rate 0.079

$501.83 \times \frac{1-(1+0.079)^{-9} }{0.079} = C$

C -$ 80.00

We know that Cuopon payment is equal to:

Face value x bonds interest = C

1,000 x r = 80

r = 80/1,000 = 0.08 = 8%