Leyland Enterprises has R5,000,000 in bonds outstanding.The bonds each have a maturity value of R1,000, an annual coupon of 12 percent, and 15 years left until maturity.The bonds can be called at any time at a call price of R1,100 per bond.If the bonds are called, the company must pay flotation costs of R50,000 (R10 for every R1,000 of bonds outstanding).Ignore tax considerations.Assume that the tax rate is zero.The company's decision whether to call the bonds depends critically on the current interest rate it would pay on new bonds issued.What is the breakeven interest rate, below which it is profitable to call in the bonds?

Question

Quizplus · Accepted Answer

To calculate the breakeven interest rate, we need to find the present value of the bond both with and without the call option and compare the two values. The present value of the bond without the call option is:

PV = 120/(1 + r) + 120/(1 + r)² + ... + 120/(1 + r)^15 + 1,000/(1 + r)^15
PV = 1,000PVIFA(12%, 15) = 1,000(7.4694) = R7,469.4

Where r is the current interest rate.

The present value of the bond with the call option is:

PV = max(1,000, 1,100/(1 + r))PVIFA(12%, 15) - flotation costs
PV = max(1,000, 1,100/(1 + r))(1 − 1/(1 + r)^15)/0.12 − 50,000
PV = max(1,000, 1,100/(1 + r))PVIFA(12%, 15) − 50,000

The call option is exercised only if the current interest rate is lower than the breakeven interest rate, which we need to calculate. We need to find the rate that makes the present value of the bond with the call option equal to the present value of the bond without the call option.

1,000PVIFA(12%, 15) = max(1,000, 1,100/(1 + r))PVIFA(12%, 15) − 50,000
1,000(7.4694) = max(1,000, 1,100/(1 + r))(7.4694) − 50,000
7,469.4 = max(1,000, 1,100/(1 + r)) − 6,690.6
max(1,000, 1,100/(1 + r)) = 14,160
1,100/(1 + r) = 1,000
1 + r = 1.1
r = 10%

Therefore, the breakeven interest rate is 10%. If the company can issue new bonds at an interest rate lower than 10%, it is profitable to call in the old bonds.

Leyland Enterprises Has R5,000,000 in Bonds Outstanding