Weighted Average Cost of Capital.
WACC
Topics Covered
-Understanding and calculating a firm’s capital structure. -Estimate the required rates of return on the securities issued by A firm. - Calculate and interpret the WACC
COC by CAPM
-When a firm is entirely financed by equity, the market value of All the firms business assets belongs to the shareholders.
-When this is the case, the CAPM provides us with the Expected return on the one relevant security, common stock.
-This expected return is then the firms COC. -When the capital structure includes more than equity the CAPM provides us with the Cost of Equity.
Dropping the assumption that the firm is all equity financed. The value and risk of the firms business is represented by the entire Portfolio of its securities: debt & equity. Total ownership of the business would entail owning every security A portfolio of debt and equity. The cost of capital for the firm is then the expected ROR on this Portfolio.
Value of business = Value of portfolio of all the firm’s debt & equity.
Risk of business = Risk of portfolio. ROR on business = ROR on portfolio. Investors’ Required = Investors’ required ROR ROR (COC) on portfolio.
Cost of Capital
-Opportunity cost of capital. -Used to value new assets. -Minimum ROR on new assets. -Op Cost and management responsibility. When a firm invests they could have returned cash to Shareholders or retired debt. If a firm is acting in shareholders best Interests it will invest only if the project will give a ROR at least Equal to what investors could have earned elsewhere in the market. Thus, the opportunity cost of capital is determined by the market value of assets with similar risk.
Calculating the Capital Structure
-We must determine the current market value of the company, The current market value of the firms capital structure. MRKT Val Equity = (#shares * Current Market Price)
Market Value of Debt. Example: Corporate bonds (5 year, 7% coupon) Book Value = $1200 Book value is based on the original terms of the Debt.
84 PV 1.07
1
84 1.07
2
1284 ... 1.07
5
1200
The Market value depends upon current prevailing interest rates.
84 PV 1.08
1
84 1.08
2
1284 ... 1.08
5
1190.97
Basic Balance Sheet
Assets MRKT Value of Firm’s business $3590.97 Liabilities and Shareholder Equity MRKT Value of Debt (8%, 5 Year, $84 Coup) $1190.97(33%) MRKT Value of Equity $2400 (67%) Total Value $3590.97 (100%)
Total Value
$3590.97
Capital Structure: The particular mix of a firm’s financing; bank debt, Corporate bonds, common stock, preferred stock.
Calculating WACC
(Ignoring Taxes)
E r r assets
D rd V
E re
D rd V
E re V
Weighted average of expected returns by debt and equity investors.
D: Mrkt Val of Debt E: Mrkt Val of Equity
rd : Expected return on debt re : Expected return on equity
The expected return on equity is estimated from the CAPM rf = 3% Mrkt Prem = 7% Beta = 1.57
re = 3% + 1.57 (7%) = 14%
WACC (ignoring taxes)
WACC .33 .08 .67 .14 .12
D/V = .33 E/V = .67 rd = 8% re = 14%
Taxes
Interest payments are tax deductible. These interest payments create a “tax shield” for the firm. It is as if the government is subsidizing the firms interest payments by the amount of the tax write off.
Debt cost (interest) = D rd Tax shield = t D rd t : tax rate
Net cost of debt = D rd - t D rd = D rd (1-t) = D (1-t) rd
WACC (w/Taxes)
WACC
Tax rate 35%
D V
1
rd
E re V
WACC .33 1 .35 .08 .67 .14 .11
Interpreting WACC
-WACC is the rate of return that the firm must expect to earn on Its average risk investments. -WACC is the appropriate discount rate for a project that is a Carbon copy of the firms existing business. -WACC is the return the company needs to earn after tax in order To provide the expected return to all its security holders. -WACC assumes that proportions of debt and equity used to finance The project are identical to those of the capital structure.
WACC assumes that the capital structure of the project is identical To the firms capital structure.
WACC .33 1 .35 .08 .67 .14 .11
Example:
Project Cost: 50
Annual Required Expected Return
Debt: 16.5 (33%) Equity: 33.5 (67%)
16.5 * 8% = 1.32 33.5 * 14% = 4.69
WACC minimum return required to satisfy the expected return to all Securities holders. After tax cash flow (not including interest) = 5.551
IRR = 5.551 / 50 = 11%
WACC = 11%
NPV = 0
WACC minimum return required to satisfy the expected return to all Securities holders.
Revenue (Operating expenses) Operating Cash Flow before tax and interest (Interest, .08 x 16.5) Pretax Cash Flow (Tax 35%) After Tax (and interest) Cash Flow
Annual Required Expected Return
14.54 -6 8.54 -1.32 7.22 -2.527 4.69
Debt: 16.5 (33%) Equity: 33.5 (67%)
16.5 * 8% = 1.32 33.5 * 14% = 4.69
Financing Irrelevance
-A change in the financing mix that constitutes the capital structure should have no effect on the WACC.
-The WACC is the discount rate for valuation of the earnings of the firm It accounts for the risk inherent in those earnings. Since this overall risk Has not changed, the WACC must remain the same.
Ignoring Taxes.
Assets MRKT Value of Firms business $3590.97 Liabilities and Shareholder Equity MRKT Value of Debt $1190.97(33%)
Total Value
MRKT Value of Equity $2400 (67%) $3590.97 Total Value $3590.97 (100%)
Firm restructures by issuing $1200 in debt to buy back shares Assets MRKT Value of Firms business $3590.97 Liabilities and Shareholder Equity MRKT Value of Debt $2390.97(66.6%)
Total Value
MRKT Value of Equity $1200 (33.4%) $3590.97 Total Value $3590.97 (100%)
Prior to restructuring
WACC .33 .08 .67 .14 .12
After restructuring
WACC .666 .08 .334 .14 .10
The Firms earnings are the same, the risk of the business is still the Same. How could a lower discount rate be appropriate? - Answer: It couldn’t.
There are two costs to debt, implicit and explicit. In the previous Example we only accounted for the explicit cost of debt, the rate of Interest required on debt.
The implicit cost of debt financing is that borrowing makes debt and Equity more risky increasing their required rates of return Respectively. - Default risk - Financial leverage Levered Beta
L
u
1 1
D E
Initial case, ignoring taxes.
WACC .33 .08 .67 .14 .12
Financing irrelevance.
WACC .666 .10 .334 .16 .12
While the restructuring will influence the required rates of return On the components of the WACC. But the package of debt and equity is unaffected. Therefore the WACC remains the same
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