Weighted Average Cost of Capital (WACC) Question with Expected Return Model

The management of a local corporation believes there will be 3 states of the economy in the next year, along with their probabilities and rates of return.

Economy	Probability	Return
Great	0.4	0.16
Average	0.5	0.08
Bad	0.1	-0.10

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The corp has 15,000,000 common shares outstanding currently trading at $3 per share on the Nasdaq. The company also has bonds with a face value of $30,000,000 yielding a market rate of 7% and trading at 99. Given this above information, calculate the WACC. Assume a tax rate of 40%

Bond Calculations

Stock Calculations

N =?
I/Y = 7% (Rd)
PV = 0.99 x 30,000,000 = 29,700,000 (D)
FV = -30,000,000

Re = Expected Return
Great -> 0.4 x 0.16 = 0.064
Average -> 0.5 x 0.08 = 0.04
Bad -> 0.1 x -0.10 = -0.1
Re = 0.064 + 0.04 + -0.1
Re = 0.094

Total Equity = $3 x 15,000,000
Total Equity = $45,000,000

(1-t) = (1 - 0.4) = 0.6

Weighted Average Cost of Capital (WACC) Formula

The formula for WACC is:

[Rd x D/V x (1-5)] + [Re x E/V]

Rd = Bond's yield to Maturity (I/Y in Calculator)
D = Market Value (Present Value) of Bonds
(1 - t) = 1 - tax rate = Interest tax shield deductibility of interest expense
Re = Shareholder's return requirement
V = Total value of all capital (Debt + Equity)

Summary of Important WACC Terms

Rd = 7% or 0.07
D = 29,700,000
(1-t) = 0.6
D / V = 29700 / 74,700 = 0.3976

Re = 0.094
E = 45,000,000
V = 74,700,000
E/V = 45000 / 74700 = 0.6024

WACC = [Rd x D/V x (1-t)] + [Re x E/V]
WACC = [0.07 x 0.3976 x 0.6] + [0.094 x 0.6024]
WACC = 0.0166992 + 0.0566256
WACC = 0.0733248 -> 7.33%

Interpretation of WACC

A WACC of 7.33% means the local corp must earn a return of 7.33% on all its assets and business operations in order to MAINTAIN the current stock price at $3 per share. If the Corp. wants its stock price to go higher, it must achieve a return rate greater than 7.33%