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

The student's question pertains to finding the coupon rate of a bond given its selling price, yield to maturity, face value, and bond life. The coupon rate can be calculated by determining the annual coupon payments using the present value of annuities formula and then solving for the coupon payment amount.

Step-by-step explanation:

The student is asking how to calculate the coupon rate of a bond with a yield to maturity of 7.9%, a selling price of $1,006.27, a face value of $1,000, annual coupon payments, and a bond life of 9 years. To find the coupon rate, we need to determine the annual coupon payments that make the present value of the bond's cash flows equal to its current price.

The present value of annuities formula in financial mathematics is used to calculate these coupon payments. We use the yield to maturity as the discount rate for the present value calculations. The bond's current price is the sum of the present value of all future coupon payments and the present value of the face value repaid at maturity.

Let's assume the annual coupon payment is C, then the present value of the coupon payments PV(C) is calculated by:

PV(C) = C × [(1 - (1 + 0.079)⁻¹) / 0.079]

The present value of the face value PV(F) at maturity is calculated as:

PV(F) = $1,000 × (1 + 0.079)⁻¹

The equation becomes:

$1,006.27 = PV(C) + PV(F)

By solving this equation, we obtain the value of C, which can be then used to find the coupon rate by dividing C by the face value and multiplying by 100 to get a percentage.

Answer 2

The cuopon rate is 8%

Step-by-step 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

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000

time 9

rate 0.079

`(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 * (1-(1+r)^(-time) )/(rate) = PV\\`

then:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $501.83

time 9

rate 0.079

`501.83 * (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%