# WACC - two companies

I understand how to solve for WACC if there is only one company involved, but how do I solve for WACC when there are two companies involved? Question is shown below. Thanks in advance!

Q)

Utilitarian Co. is looking to expand its appliances division. It currently has a beta of 0.9, a D/E ratio of 2.5, a marginal tax rate of 30%, and its debt is currently yielding 7%. JF Black, Inc. is a publicly traded appliance firm with a beta of 0.7, a D/E ratio of 3, a marginal tax rate of 40%, and its debt is currently yielding 6.8%. The risk-free rate is currently 5% and the expected return on the market portfolio is 9%. Using this data, calculate Utilitarian’s weighted average cost of capital for this potential expansion.

A) 5.71%

This is all that βasset, βequity, deleverage/releverage junk.

Yuck!

Here goes:

JF Black’s asset beta:

βasset = βequity × (1 / (1 + ((1 – t)D/E)))

= 0.7 × (1 / (1 + 0.6(3)))

= 0.25

Utilitarian’s project beta, therefore, is:

βproject = βasset × (1 + ((1 – t)D/E))

= 0.25 × (1 + 0.7(2.5)))

= 0.6875

Thus, Utilitarian’s cost of equity for this project is:

rCE = 5% + 0.6875(9% – 5%) = 7.75%

and their WACC is:

(2.5/3.5)(7%)(1 – 30%) ) + (1/3.5)(7.75%)

= 5.71%.

It involves the concept of unlevering the beta and then levering the beta .we can solve it like this

JF Black’s asset beta:

βasset = βequity × (1 / (1 + ((1 – t)D/E)))

= 0.7 × (1 / (1 + 0.6(3)))

= 0.25

Utilitarian’s project beta, therefore, is:

βproject = βasset × (1 + ((1 – t)D/E))

= 0.25 × (1 + 0.7(2.5)))

= 0.6875

Thus, Utilitarian’s cost of equity for this project is:

rCE = 5% + 0.6875(9% – 5%) = 7.75%

and their WACC is:

(2.5/3.5)(7%)(1 – 30%) ) + (1/3.5)(7.75%)

= 5.71%.

Why did you simply copy and paste what I’d written?

Haha I liked your expression s2000 “YUCK” Thanks S2000magician, Kaplan should pay you to write the answer to these questions!

I am not sure if I will memorize this formula… haha

Not that hard to memorize. Just hink of it as the Dupont formula for beta (Note: the Equity mulitplier is Assets/equity or 1+D/E). Rememebr that ROE is the “Levered” version of ROA.

With ROE and ROA:

ROE = ROA x Equity Multiplier ==>

ROE = ROA x (1 + D/E)

vs. With Levered and Unlevered Beta:

Levered beta = Unlevered beta x [1+D/E(1-t)]

Since we’re talking about debt, there should be a tax adjustment. Hence the D/E is multiplied by “1-t”

c