Question

Big Canyon Enterprises has bonds on the market making annual payments, with 12 years to maturity, a par value of $1,000, and a price of $1,030. At this price, the bonds yield 6.14 percent. What must the coupon rate be on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

The correct answer is 6.50%.

Explanation:

According to the scenario, the computation of the given data are as follows:

We can calculate the coupon rate by using following formula:

Coupon Rate = (Coupon Amount ÷ Face Value) × 100

Where Coupon amount can be calculated as

Price of bond = Coupon amount × PVIFA (n,i)+ Face value × PVIF (n,i)

Where n = time period, i = bonds yield

By putting the value, we get

$ 1,030 = Coupon amount × PVIFA (12 , 6.14%) + $1,000 × PVIF ( 12 ,6.14%)

By referring to PVIFA table

$ 1,030 = Coupon amount × 8.3199 + $1,000 × 0.4892

Coupon amount = ($1,030 - 489.2) ÷ 8.3199

= $65.00078126

By putting the value in the formula, we get

Coupon rate  = ($65.00078126 ÷ $1,000) × 100

= 6.50%