Chapter 13 ECON 2560 The Weighted-Average Cost of Capital ...
Chapter 13 ECON 2560 The Weighted-Average Cost of Capital & Company Valuation Capital Structure: A firm’s mix of debt & equity financing THE WEIGHTED-AVERAGE COST OF CAPITAL
The company cost of capital is defined as the opportunity cost of capital for the firm’s existing assets We use it to value new assets that have the same risk as the old ones Company’s cost of capital is the minimum acceptable rate of return when the firm expands by investing in average-risk projects When the firm invests rather than returns cash to shareholders, the shareholders lose the opportunity to invest in financial markets The expected rates of return on investments in financial markets determine the cost of capital for corporate investments The company cost of capital is the opp. Cost of capital for the company as a whole The weighted-average cost of capital formula adjusts for if company raises different types of debt & equity
Calculating Company Cost of Capital as a Weighted Average
Most companies issue debt as well as equity so their cost of capital depends on both the cost of debt & cost of equity In this case the company cost of capital is a weighted average of the returns demanded by the debt & equity investors.
Total Market Value (V) = Market Value Outstanding Debt (D) + Market Value Outstanding Equity (E) Company Cost of Capital = weighted average of debt & equity returns Debt holders need income of: (rdebt x D) Equity Investors need income of (requity X D) The total income that is needed is (rdebt x D) + (requity X D) To calculate the return needed on the assets, simply divide income by investments…. Rassets =
Total Income___ Value of Investment =
(rdebt x D) + (requity X D) = D V ( V x rdebt)
+
E ( V x requity)
Use Market Weights, Not Book Weights
Market values often differ from the values recorded by accountant in the company’s book If investors recognize company’s excellent prospects, the market value of equity may be much higher than book value and the debt ratio will be lower when measured in terms of market values rather than book values Financial managers use book debt-to-value ratios for various other purposes and sometimes they accidently look to the book ratios when calculating weights for the company cost of capital This is a mistake b/c the company cost of capital measures what investors want from the company and depends on how THEY value the companies securities and that value depends on future profits & cash flows not on accounting history Book values measure only cumulative historical outlays… they generally don’t measure market values accurately
Taxes & The Weighted-Average Cost of Capital
When you calculate a projects NPV, you need to discount the cash flows AFTER tax b/c the after-tax cash flows are the relevant project cash flows The interest payments on the debt companies are financed by are deducted from the income before tax is calculated Therefore the cost to the company of an interest payment is reduced by the amount of this tax saving After-tax cost of debt = (1 – tax rate) x pretax cost = (1 – Tc) x rdebt
The Weighted-average cost of capital: Expected rate of return on a portfolio of all the firm’s securities, adjusted for tax savings due to interest payments What if there are 2 or more sources of financing?
Simply calculate the weighted-average after-tax return of each security type
WACC for a firm with common stock, bonds and preferred stocks…. WACC = [ D x (1 – Tc) rdebt] + [ P x rpreferred] + [ E x requity] V V V CALCULATING REQUIRED RATES OF RETURN The Expected Return on Bonds
As long as the company doesn’t go belly-up, the rate of return to investors in the yield to maturity offered on the bond If there is any chance firm won’t be able to repay the debt, the yield to maturity will be the most favorable outcome but the expected rate of return will be lower
The Expected Return on Common Stock Estimates Based on the Capital Asset Pricing Model Expected return on stock = risk free interest rate + [Stock’s beta x Expected market risk premium]
To implement CAPM you need the stock’s beta, the current risk-free interest rate and an estimate of the market risk premium
Estimates Based on the Dividend Discount Model P0 =
Whenever you’re given an estimate of the expected return on common stock, always look for ways to check whether it is reasonable One check is if the cost of equity is greater than the cost of debt b/c equity of firm is riskier than any of its debt Another check can be done using dividend discount model DIV1___ requity – g
P0 = current stock price DIV1 = the forecast dividend at the end of the year Requity = the expected return from the stock
The constant-growth dividend discount model is widely used in estimating expected rates of return on common stocks of public utilities Utility stocks gave a fairly stable growth pattern
Beware of False Precision
Don’t expect estimates of the cost of equity to be precise Estimates subject to error Sometimes accuracy can be improved by estimating the cost of equity or WACC for an industry or a group of comparable companies This cuts down the noise
The Expected Return on Preferred Stock Preferred stock that pays a fixed dividend can be valued from the perpetuity formula: Price of preferred = dividend__ rpreferred
rpreferred =
dividend______ price of preferred
CALCULATING THE WEIGHTED-AVERAGE COST OF CAPITAL Once you’ve worked out the company’s capital structure & estimated the cost of capital (required rate of return) of its securities…. Real Company WACC
One practical issue is the choice of risk-free security when implementing the CAPM Usually use treasury bill but often financial managers will use long-term government bond as a risk free security b/c they want a WACC to evaluate a long-term investment
INTERPRETING THE WEIGHTED-AVERAGE COST OF CAPITAL When You Can & Can’t Use WACC
A company’s WACC is the rate of return that the firm must expect to earn on its average risk investments in order to provide a fair expected return to all its security holders We use it to value new assets that have same risk as old ones & that supports the same ratio of debt Also used to calculate the company’s economic value added
Some Common Mistakes One danger w/ WACC formula is that it temps people to make logical errors
WACC = [D/V ( 1- Tc)rdebt + [P/V x rpreferred] + [E/V x requity] Read page 436 blurb How Changing Capital Structure Affects WACC When Corporate Tax Rate is 0
The required rate on the package f the debt & equity is unaffected by the change in capital structure when the corp. tax rate is 0 BUT it does effect the required returns on the individual securities The weighted average of the debt risk & equity risk must add up to the risk of the assets
ßassets = D x ßdebt + E x ßequity V V Stock’s beta = Expected return on stock – risk free rate Expected market risk premium
Debt’s Beta = Expected return on debt – risk free rate Expected market risk premium
What Happens if Capital Structure Changes & the Corp. Tax Rate Isn’t 0?
Adding corporate taxes complicates the picture Interest paid on the debt is tax-deductible and this increasing leverage reduces company’s tax bill and increases the company’s total cash flows
Unlevered Beta: Beta of the equity of a debt-free firm, reflecting the risk arising from the firm’s operating activities (ßu)
Unlevered beta measures the business risk, risk arising from operating activities NOT by its financing choices With leverage, the shareholders not only bear business risk but also added risk from financial leverage
Levered Equity Beta: Beta of equity of a firm that has debt reflecting both the risk arising from the firm’s operating activities and the risk created by the leverage ßlevered = ßu + (ßu - ßdebt)(1 – Tc) (D/E) If you can assume that debt is riskless, the debt beta is 0 and…. ßlevered = ßu x [1+ (1 – Tc) (D/E)] VALUEING ENTIRE BUSINESSES
Investors routinely buy and sell shares of common stock Companies often buy & sell entire businesses Discounted cash flow formulas work for entire businesses as loign as company’s debt ratio is expected to maintain fairly constant
Can treat company as 1 big project and discount the cash flows by the weighted-average cost of capital The operating cash flow – investment expenditures is the amount of cash that the business can pay out to investors after paying for all investment necessary for growth
Free Cash Flow: Cash flow that is not required for investment in fixed assets or working capital & is therefore available to investors WACC = [D/V ( 1- Tc)rdebt + [P/V x rpreferred] + [E/V x requity] Calculating the Value of the Concatenated Business
The value of the concatenated operation is equal to the discounted value of the free cash flows (FCFs) out to a horizon year plus the forecasted value of the business at the horizon, also discounted back to the present PV =
FCF1 + FCF2 + … + FCFH + PVH_____ 2 H 1 + WACC (1+ WACC) (1 + WACC) (1 + WACC)H
Horizon years are often chosen arbitrarily
*Page 442 for how to calculate horizon value
The company cost of capital is defined as the opportunity cost of capital for the firm’s existing assets We use it to value new assets that have the same risk as the old ones Company’s cost of capital is the minimum acceptable rate of return when the firm expands by investing in average-risk projects When the firm invests rather than returns cash to shareholders, the shareholders lose the opportunity to invest in financial markets The expected rates of return on investments in financial markets determine the cost of capital for corporate investments The company cost of capital is the opp. Cost of capital for the company as a whole The weighted-average cost of capital formula adjusts for if company raises different types of debt & equity
Calculating Company Cost of Capital as a Weighted Average
Most companies issue debt as well as equity so their cost of capital depends on both the cost of debt & cost of equity In this case the company cost of capital is a weighted average of the returns demanded by the debt & equity investors.
Total Market Value (V) = Market Value Outstanding Debt (D) + Market Value Outstanding Equity (E) Company Cost of Capital = weighted average of debt & equity returns Debt holders need income of: (rdebt x D) Equity Investors need income of (requity X D) The total income that is needed is (rdebt x D) + (requity X D) To calculate the return needed on the assets, simply divide income by investments…. Rassets =
Total Income___ Value of Investment =
(rdebt x D) + (requity X D) = D V ( V x rdebt)
+
E ( V x requity)
Use Market Weights, Not Book Weights
Market values often differ from the values recorded by accountant in the company’s book If investors recognize company’s excellent prospects, the market value of equity may be much higher than book value and the debt ratio will be lower when measured in terms of market values rather than book values Financial managers use book debt-to-value ratios for various other purposes and sometimes they accidently look to the book ratios when calculating weights for the company cost of capital This is a mistake b/c the company cost of capital measures what investors want from the company and depends on how THEY value the companies securities and that value depends on future profits & cash flows not on accounting history Book values measure only cumulative historical outlays… they generally don’t measure market values accurately
Taxes & The Weighted-Average Cost of Capital
When you calculate a projects NPV, you need to discount the cash flows AFTER tax b/c the after-tax cash flows are the relevant project cash flows The interest payments on the debt companies are financed by are deducted from the income before tax is calculated Therefore the cost to the company of an interest payment is reduced by the amount of this tax saving After-tax cost of debt = (1 – tax rate) x pretax cost = (1 – Tc) x rdebt
The Weighted-average cost of capital: Expected rate of return on a portfolio of all the firm’s securities, adjusted for tax savings due to interest payments What if there are 2 or more sources of financing?
Simply calculate the weighted-average after-tax return of each security type
WACC for a firm with common stock, bonds and preferred stocks…. WACC = [ D x (1 – Tc) rdebt] + [ P x rpreferred] + [ E x requity] V V V CALCULATING REQUIRED RATES OF RETURN The Expected Return on Bonds
As long as the company doesn’t go belly-up, the rate of return to investors in the yield to maturity offered on the bond If there is any chance firm won’t be able to repay the debt, the yield to maturity will be the most favorable outcome but the expected rate of return will be lower
The Expected Return on Common Stock Estimates Based on the Capital Asset Pricing Model Expected return on stock = risk free interest rate + [Stock’s beta x Expected market risk premium]
To implement CAPM you need the stock’s beta, the current risk-free interest rate and an estimate of the market risk premium
Estimates Based on the Dividend Discount Model P0 =
Whenever you’re given an estimate of the expected return on common stock, always look for ways to check whether it is reasonable One check is if the cost of equity is greater than the cost of debt b/c equity of firm is riskier than any of its debt Another check can be done using dividend discount model DIV1___ requity – g
P0 = current stock price DIV1 = the forecast dividend at the end of the year Requity = the expected return from the stock
The constant-growth dividend discount model is widely used in estimating expected rates of return on common stocks of public utilities Utility stocks gave a fairly stable growth pattern
Beware of False Precision
Don’t expect estimates of the cost of equity to be precise Estimates subject to error Sometimes accuracy can be improved by estimating the cost of equity or WACC for an industry or a group of comparable companies This cuts down the noise
The Expected Return on Preferred Stock Preferred stock that pays a fixed dividend can be valued from the perpetuity formula: Price of preferred = dividend__ rpreferred
rpreferred =
dividend______ price of preferred
CALCULATING THE WEIGHTED-AVERAGE COST OF CAPITAL Once you’ve worked out the company’s capital structure & estimated the cost of capital (required rate of return) of its securities…. Real Company WACC
One practical issue is the choice of risk-free security when implementing the CAPM Usually use treasury bill but often financial managers will use long-term government bond as a risk free security b/c they want a WACC to evaluate a long-term investment
INTERPRETING THE WEIGHTED-AVERAGE COST OF CAPITAL When You Can & Can’t Use WACC
A company’s WACC is the rate of return that the firm must expect to earn on its average risk investments in order to provide a fair expected return to all its security holders We use it to value new assets that have same risk as old ones & that supports the same ratio of debt Also used to calculate the company’s economic value added
Some Common Mistakes One danger w/ WACC formula is that it temps people to make logical errors
WACC = [D/V ( 1- Tc)rdebt + [P/V x rpreferred] + [E/V x requity] Read page 436 blurb How Changing Capital Structure Affects WACC When Corporate Tax Rate is 0
The required rate on the package f the debt & equity is unaffected by the change in capital structure when the corp. tax rate is 0 BUT it does effect the required returns on the individual securities The weighted average of the debt risk & equity risk must add up to the risk of the assets
ßassets = D x ßdebt + E x ßequity V V Stock’s beta = Expected return on stock – risk free rate Expected market risk premium
Debt’s Beta = Expected return on debt – risk free rate Expected market risk premium
What Happens if Capital Structure Changes & the Corp. Tax Rate Isn’t 0?
Adding corporate taxes complicates the picture Interest paid on the debt is tax-deductible and this increasing leverage reduces company’s tax bill and increases the company’s total cash flows
Unlevered Beta: Beta of the equity of a debt-free firm, reflecting the risk arising from the firm’s operating activities (ßu)
Unlevered beta measures the business risk, risk arising from operating activities NOT by its financing choices With leverage, the shareholders not only bear business risk but also added risk from financial leverage
Levered Equity Beta: Beta of equity of a firm that has debt reflecting both the risk arising from the firm’s operating activities and the risk created by the leverage ßlevered = ßu + (ßu - ßdebt)(1 – Tc) (D/E) If you can assume that debt is riskless, the debt beta is 0 and…. ßlevered = ßu x [1+ (1 – Tc) (D/E)] VALUEING ENTIRE BUSINESSES
Investors routinely buy and sell shares of common stock Companies often buy & sell entire businesses Discounted cash flow formulas work for entire businesses as loign as company’s debt ratio is expected to maintain fairly constant
Can treat company as 1 big project and discount the cash flows by the weighted-average cost of capital The operating cash flow – investment expenditures is the amount of cash that the business can pay out to investors after paying for all investment necessary for growth
Free Cash Flow: Cash flow that is not required for investment in fixed assets or working capital & is therefore available to investors WACC = [D/V ( 1- Tc)rdebt + [P/V x rpreferred] + [E/V x requity] Calculating the Value of the Concatenated Business
The value of the concatenated operation is equal to the discounted value of the free cash flows (FCFs) out to a horizon year plus the forecasted value of the business at the horizon, also discounted back to the present PV =
FCF1 + FCF2 + … + FCFH + PVH_____ 2 H 1 + WACC (1+ WACC) (1 + WACC) (1 + WACC)H
Horizon years are often chosen arbitrarily
*Page 442 for how to calculate horizon value
