## Sunday, July 21, 2013

### Weighted Average Cost of Capital with Expected Return

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

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

 [Rd x D/V x (1-T)] + [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

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