Question

• ABC Corp. wants to issue FCB. The firm has estimated that its cost of debt is 8%. It has decided to issue 30 year FCBs. However, it is deciding on the coupon rate (annual). The choices are (a) 5%, (b) 8%, and (c) 11%

• The Price of the bonds under the three alternatives?

a. Coupon of 5%: PV=?

b. Coupon of 8%: PV=?

c. Coupon of 11%: PV=?

CAN YOU PLEASE GIVE DETAIL STEPS IN HOW YOU ACHIEVE ANSWER, NO EXCEL , NO CALCULATOR I would like to learn the steps in finding the answer

Answer 1

a)

Assuming face value to be $1000

Coupon = 5% of 1000 = 50

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 50 * [1 - 1 / (1 + 0.08)³⁰] / 0.08 + 1000 / (1 + 0.08)³⁰

Price = 50 * [1 - 0.099377] / 0.08 + 99.377333

Price = 50 * 11.257788 + 99.377333

Price = $662.27

b)

Price = $1,000

When cost of debt is equal to coupon rate, price will always be equal to the face value. Here the cost of debt of 8% is equal to coupon rate of 8%. Therefore, the price will be equal to face value of $1000.

c)

Assuming face value to be $1000

Coupon = 11% of 1000 = 110

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 110 * [1 - 1 / (1 + 0.08)³⁰] / 0.08 + 1000 / (1 + 0.08)³⁰

Price = 110 * [1 - 0.099377] / 0.08 + 99.377333

Price = 110 * 11.257788 + 99.377333

Price = $1,337.73