Question

What is the cost of capital for a bond issued a 30-year bond 6 years ago so N=___    Tax 35% 5.9% semi-annual coupon   Current price $1080 Par $1000   Reminder-think of this now as a cost so the firm is paying the dividend and paying the $1000 par. Also take into account semi-annual payment changes to N, PMT, and I.

If the company has $5 million in bond debt and $5 million in equity for the capital structure for the above, what is their WACC?

How would their WACC change if they took on another $2 million in long term debt at the stated rate of 6%?

Answer 1

Solution:

Par Value = $ 1000

Current Price = $1080

Coupon rate = 5.9% semi annual

Coupon Amount = $ 59 semi annual

The remaining life of Bond today (N) = 30 - 6 = 24 Years

in order to calculate the cost of capital, the coupon rate and remaining life should be consistent.

Since coupon rate is given semi-annually, the period should also be converted as = 24 years * 2 = 48 years

hence,

Cost of Capital of the Bond = [ Coupon * (1-tax rate) + (Maturity Value - Bond Price) / n ] / (Maturity Value + Bond Price)/2

= [ $ 59 * (1-35%) + ( $ 1000-$1080)/48)] / ($1000+1080)/2

= 3.53%

Thus, the Cost of Capital of the Bond is 3.53%

Calculation of WACC

WACC is the weighted aggregate of cost of debt and cost of equity.

	US $ in million	Weight	Cost of capital	WACC = (Cost of Capital *Weight)
Bond	5	50%	3.53%	1.76%
Equity	5	50%	-
Total	10	100%		1.76%

Since no information is given about Equity dividend or price, we cannot estimate the cost of equity.

Hence the Weighted cost of debt will be the WACC in this case.

Calculation of Revised WACC with the additional debt of $ 2 million will be

Cost of Long Term Debt = Interest * (1-tax)

= 6% * (1-35%)

= 3.90%

Revised WACC

	US $ in million	Weight	Cost of capital	WACC = (Cost of Capital *Weight)
Bond	5	41.67%	3.53%	1.47%
Long Term Debt	2	16.66%	3.90%%	0.65%
Equity	5	41.67%	-	-
Total	12	100%		2.12%

Again, as no information is given about Equity dividend or market price, we cannot estimate the cost of equity.

Hence the Weighted cost of both the debt will be the WACC in this case which is 2.12%.