Laurence Booth Sean Cleary. LEARNING OBJECTIVES Cost of Capital 20 20.1 Explain how the three major...

Laurence Booth

Sean Cleary

LEARNING OBJECTIVES

Cost of Capital20

20.1 Explain how the three major problem areas in finance—valuation, cost of capital, and determining cash flows—are related.

20.2 Calculate the weighted average cost of capital (WACC) and explain its significance.

20.3 Estimate the cost of capital and its non-equity components.

20.4 Explain how operating and financial leverage affect a firm’s risk.

20.5 Apply the discounted cash flow model to estimate the equity cost and describe its advantages and disadvantages.

20.6 Estimate the cost of equity using risk-based models and describe the advantages and limitations of these models.

20.7 Explain how WACC interacts with the investment decision framework introduced in chapters 13 to 17.

© John Wiley & Sons Canada, Ltd.

Capital Structure • Table 20-1 illustrates the basic structure of a firm’s balance sheet

—a snapshot of a firm’s financial position at a point in time– Assets are things the firm owns– Liabilities are sources of financing obtained from lenders– Equity is the shareholders’ investment in the business plus any

retained earnings

Booth • Cleary – 3rd Edition 3

20.1 FINANCING SOURCES


• Financial structure is the whole right-hand side of the balance sheet, and includes both short and long term sources of financing

• Capital structure is how the firm finances its invested capital, such as bank loans, long-term debt, common stock and retained earnings. It excludes accruals and accounts payable (i.e., short term liabilities that are not strictly debt contracts which spontaneously change in response to the operations of the business)




• Balance sheets are prepared in accordance with International Financial Reporting Standards (IFRS) as well as generally accepted accounting principles (GAAP); they most often represent historical costs, which may not be relevant for current decision making purposes.

• An analysis of reported data should include ratios such as the debt-to-equity ratio. In Table 20-2, the firm has $50 of short-term debt, $650 of long-term debt, and $1,000 of shareholders’ equity. This gives a debt-to-equity ratio of ($50 + $650) / $1,000 = 0.7

• Book values can be converted into market values by multiplying the market-to-book (M/B) ratio by the book value

• Suppose that the market value of the shareholders’ equity $2,500 instead of the historical cost $1,000. Suppose also that the market values of the total debt is still $700. This makes the debt-to-equity ratio $700 / $2,500 = 0.28, which is much lower than the ratio when using the historical cost measure of the shareholders’ equity




Three Ways of Using the Valuation Equation• Equation 20-1 reprises what you learned in Chapter 5 about how to

determine the present value of an infinite stream of equal, periodic cash flows (i.e., a perpetuity)

• Equation 20-2 rearranges to solve for the required return and is also known as the earnings yield; Equation 20-3 rearranges to solve for the forecast earnings

• The earnings yield is not normally used as the investor’s required return because it simply measures the forecast earnings as a proportion of the current market price ignoring growth opportunities

where:S = the present value of the perpetuityX = the forecast annual earningsKe = the investor’s required return


SKXS

XK

K

XS ee

e



Deriving the Required Income Statement• Given market values and required rates of return, it is possible to establish

performance targets for management to sustain market values• For a firm financed by both debt and equity, the firm must plan to earn sufficient

returns to cover the interest cost on debt plus the required return for shareholders• Working back from these requirements, we can forecast the level of sales the firm

must earn in order to achieve these operating results which sets a performance target for management

• Suppose that the required return is 6% on debt and 12% on equity; Table 20-3 shows the forecast income statement that establishes a performance target for management




• Once sales performance targets are established, other targets can be determined through the application of ratios

• Since equity, in this case, is a perpetuity, we can express the price per share using Equation 20-4:

• Dividing both sides of Equation 20-4 by book value per share (BVPS) derives the market-to-book (M/B) ratio given in Equation 20-5:

• Notice that if the return on equity exceeds the investor’s required return, then the price of the stock will rise above book value.

• This is how a financial manager can add value


ee K

BVPSROE

K

EPSP

eK

ROE

BVPS

P



Determining the Weighted Average Cost of Capital (WACC)• The overall market value of the firm is the market value of its

debt plus the value of the equity: V = (D + S)• In our example, V = $3,200, EBIT = $442 and the tax rate is

40%. Therefore, after tax EBIT is $331.50.• We can represent EBIT as ROI × IC, and this allows us to use

Equation 20-6 to determine the value of the firm and Equation 20-7 to find the capital cost of an all equity firm:


%36.10200,3$

50.331$

V

ICROIK

K

ICROIV a

a

20.2 THE COST OF CAPITAL


• We can now substitute the component costs for both debt and equity to develop a general equation for the weighted average cost of capital (WACC) as the weighted average of the component costs, as in equations 20-8 and 20-9 (in Equation 20-9 we replace the term Kd(1 − T) with Ki)


V

DK

V

PK

V

SKWACC

V

D)T1(K

V

SK

V

D)T1(KSK

V

ICROIK

iPe

dede

a



Estimating the Market Values• The total market value of equity (the market capitalization) is

the price per share multiplied by the number of shares outstanding, as in Equation 20-10:

• The market price for a preferred share is the annual preferred dividend divided by the preferred shareholder’s required return, as in Equation 20-11:

• The market capitalization of both common and preferred stock is determined using Equation 20-10.


nPS 0

P

PP k

DP



• The market value of bonds differs from book value only if the required rates of return in the market have changed since the bond’s original issue and do not currently equal the coupon rate.

• Knowing the term to maturity, the coupon rate and the bondholder’s required return, we can determine the market value of the bonds with Equation 20-12:

whereB = the bond priceI = interest (or coupon) paymentsKb = the bond discount rate (or market rate)n = the term-to-maturityF = the face (par) value of the bond

• Determine the total market value of debt by multiplying the market value of an individual bond by the number of bonds outstanding



• In order to calculate the market value weights required to calculate WACC (D/V, P/V and S/V), you will need to know the total market value of debt, preferred stock and common stockExample: Suppose a firm has 1 million common shares outstanding trading for $21.50 each and 4,000 long term bonds trading for $950 each. The firm has no preferred stock. Calculate the market value weights of each source of financing.

• These weights, D/V = 15.02% and S/V = 84.98%, can be used to calculate the weighted average cost of capital (WACC)

13

Type Market Price Number Outstanding

Total Market Value

Market Value Weight

Bonds $950.00 4,000 $3,800,000 15.02%

Common stock $21.50 1,000,000 $21,500,000 84.98%

Total $25,300,000 100.00%

Booth • Cleary – 3rd Edition



Flotation Costs and the Marginal Cost of Capital (MCC)• Issuing or flotation costs are incurred by a firm when it raises new capital

through the sale of securities in the primary market, and include:– Underwriting discounts paid to the investment dealer– Direct costs associated with the issue including legal and accounting costs

• The net proceeds of the sale of each security is therefore less than the price paid by each investor (this is called a financing wedge)

• Therefore, the component cost of capital exceeds the investor’s required return


20.3 ESTIMATING THE NON-EQUITY COMPONENT COSTS


• The marginal cost of capital (MCC) is the weighted average cost of the next dollar of financing to be raised

• At low levels of financing, WACC = MCC• But, as a firm raises more and more capital in a given

year, it will exhaust the supply of lower cost sources of capital and then have to access marginally higher cost sources of capital

• Therefore, MCC increases with the amount of capital to be raised




Debt• The cost of debt is a function of:

– The investor’s required rate of return– The tax-deductibility of interest expenses– The floatation costs incurred to issue new debt

• If you know the debt investor’s required rate of return, the corporate tax rate and the flotation cost percentage for debt, you can estimate the cost of debt as:

• Example: If the investor requires a 10% return, 40% is the corporate tax rate and there is a 3% flotation cost, then the firm’s cost of debt is:


d

d

f

TK

1

)1(Debt ofCost

%19.603.01

)4.01(1.0

1

)1(Debt ofCost

d

d

f

TK



• The bond valuation formula can also be adjusted, as in Equation 20-13, for the tax deductibility of interest expenses and the net proceeds the firm would receive on the sale of one bond after flotation costs

whereKi = the after-tax and after-floatation cost of debt

• Then, solve for the rate that causes the formula to equal the market price




Preferred Shares• If you know the preferred share investor’s required rate of return

and the floatation cost percentage for preferred share financing, you can estimate the cost of preferred shares as:

• Example: If an investor requires a 14% return and floatation costs are 5%, then the preferred shares cost is:

• Note that preferred share dividends are paid out of after-tax earnings, so there are no taxation effects on the preferred share component cost of capital


Pf

1

Return Required sInvestor'Equity Preferred ofCost

%74.1405.01

0.14Equity Preferred ofCost



• Alternatively, as in Equation 20-14, the component cost of preferred shares can be found by dividing the preferred share dividend by the net proceeds or the selling price of each preferred share less the floatation costs per share:


NP

DK PP



20.4 THE EFFECTS OF OPERATING AND FINANCIAL LEVERAGE

• Leverage is the increased volatility in operating income over time, created by the use of fixed costs

• Leverage multiplies both profits and losses• There are two types: operating leverage and financial

leverage• Both types of leverage have the same effect on

shareholders, but are accomplished in very different ways and for different strategic purposes



• Operating leverage is the increased volatility in operating income caused by fixed operating costs. This is commonly accomplished by a firm choosing to become more capital intensive and less labor intensive, thereby increasing operating leverage.

• Financial leverage is the increased volatility in operating income caused by fixed financial costs and can be increased by taking on financial obligations with fixed annual claims on cash flow (e.g., bonds or preferred stock), or using the proceeds from the debt to retire equity

• Shareholders bear the added risks associated with the use of leverage

• The higher the use of leverage, the higher the risk to the shareholder




Operating Leverage

22

Advantages Disadvantages

• Magnification of profits to shareholders• Operating efficiencies, such as faster production, fewer errors and higher quality, usually result in increasing productivity

• Magnification of losses to shareholders• Higher break even point• High capital cost of equipment• Equipment can be illiquid

Advantages Disadvantages

• Magnification of profits to shareholders• Lower cost of capital at low to moderate levels of financial leverage because interest expense is tax deductible

• Magnification of losses to shareholders• Higher break even point• At higher levels of financial leverage, the low after-tax cost of debt is offset by other effects such as bankruptcy and agency costs

Financial Leverage

Booth • Cleary – 3rd Edition


The Constant Growth Model• The constant growth model, referred to as the Gordon model, assumes

constant growth in the stream of dividends, as in Equation 20-15

• The price per share today equals the next expected dividend divided by the shareholder’s required return less the long-run constant growth rate

• Equation 20-15 can be rearranged into Equation 20-16 to solve for the investor’s required rate of return:

• This shows that the investor’s required rate of return consists of two components: expected dividend yield and the long-run growth rate

• This is known as the cost of internal equity, or the cost of retained earnings where the firm does not need to incur floatation costs


gP

DK

0

1e

20.5 GROWTH MODELS AND THE COST OF COMMON EQUITY

gK

DP

e

10


• The constant growth model can be modified to solve for the cost of new equity by using the net proceeds (NP) the firm receives for each new share sold after floatation costs, as in Equation 20-17:

• The constant growth model can only be used in cases where it is reasonable to assume that the growth rate can be sustained in the very long term, which usually means for large, mature companies that already pay a significant dividend

• But, the constant growth model should not be used for smaller, more rapidly growth firms where higher current growth rates are experienced which are not expected to be sustained in the long term


gNP

DK 1

ne



Growth and ROE• Equation 20-18 shows one way to estimate the constant growth rate is the

sustainable growth method: multiplying the firm’s retention ratio by the forecast return on equity:

• Substituting the sustainable growth rate into the Gordon model gives Equation 20-19:

• We can rewrite this as Equation 20-20 by recognizing that the expected dividend is the expected earnings per share (X) multiplied by the dividend payout ratio (which is one minus the retention ratio):


ROEbg

ROEbK

DP

e 1

0

ROEbK

bXP

e

)1(1

0



• Conclusion:– A firm’s share price is determined by:

• Forecast earnings per share• Dividend payout• Return on equity• Shareholders’ required return

– The higher the growth rate, the higher the share price because larger future dividends and earnings are forecast

– We can rearrange Equation 20-20 into Equation 20-21 by substituting in alternative expressions for the dividend and growth rate:


ROEbP

bXg

P

DK e

0

1

0

1 )1(



• Table 20-8 shows the use of Equation 20-21 to estimate the cost of internal equity for three different growth scenarios

• Notice that sustainable growth rate increases with return on equity, but that expected dividend yield falls




• Table 20-09 demonstrates that the cost of capital is a hurdle rate, or the return on an investment required to create value; below this value an investment will destroy value

• When a firm retains earnings and reinvests them at lower rates than what shareholders require, the value of the firm falls

• The key to share price growth is the reinvest earnings at rates greater than the cost of capital




• Growing firms reinvest in projects that offer rates equal to its cost of capital (ROE = Ke)

• Growth firms reinvest earnings at rates higher than the cost of capital (ROE > Ke)

• This is the reason that earnings yield is not an appropriate estimate of the firm’s cost of capital

• What is relevant is not whether dividends or earnings are growing, but rather whether the firm is investing at rates of return greater than the cost of capital

• This means the firm should be investing in projects with positive NPVs (IRRs > cost of capital)




Multi-Stage Growth Models • Multi-stage growth models, such as the multi-stage dividend discount

model (DDM), account for different levels of growth in earnings and dividends over time

• Since there is no limit to the number of growth stages one can forecast for a given company, this is a very flexible model

• Equation 20-22 shows a two-stage growth model that breaks price into two components:– Present value of existing opportunities (PVEO)– Present value of growth opportunities (PVGO)


PVGOPVEOP

K

KROE

K1

Inv

K

BVPSROEP

0

e

e2

ee

10



• PVGO is discounted to the present by one year because it represents an incremental investment decision today that will not result in the first cash flow until one year from now

• PVGO adds a perpetual amount represented by the difference between the ROE2 and the cost of equity– If ROE2 = Ke then the future investment adds nothing to the

value of the firm– If ROE2 > Ke then the future investment adds value to the firm


PVGOPVEOP

K

KROE

K1

Inv

K

BVPSROEP

0

e

e2

ee

10



• Figure 20-1 shows four scenarios:Star: high PVEO and high PVGOCash cow: high PVEO and low PVGOTurnaround: low PVEO and high PVGODog: low PVEO and low PVGO




The Fed Model • The Fed Model is used by the U.S. Federal Reserve to estimate whether

the stock market is over or under valued and is given in Equation 20-23:

• Aggregate valuation across the entire market is easier because unsystematic risk attached to individual stocks is eliminated as a factor

• The Fed’s estimate of the market value is the expected EPS on the S&P 500 index divided by the yield on long-term U.S. Treasury bonds less 1%

• We can rearrange Equation 20-23 into Equation 20-24:


%)0.1/()(

TBond

actual

Fed

actual

KEPSExp

V

V

V

%0.1

)(

TBondFed K

EPSExpV



• All of the data required for this model is readily available, so this estimate of value is easy to produce and track over time, as shown in Figure 20-3:




• Equation 20-25 is a variation of the Fed model that can be used to determine if the market is fairly valued:

• When the earnings yield on the S&P 500 (the market proxy) is equal to the long-term Treasury bond yield less 1% the market is fairly valued

• The earnings yield is the appropriate discount rate for the no-growth (perpetual) case, whereas we would expect the market as a whole to grow at the nominal GDP growth rate

• The required return on the market as a whole is, then, the long-term Treasury yield plus an approximately 4% risk premium (5% nominal GDP less 1%), and can serve as a useful benchmark for financial managers as they attempt to estimate their own firm’s cost of capital


%0.1K%0.1P

XTBond

500P&S



20.6 RISK-BASED MODELS AND THE COST OF COMMON EQUITY

• The capital asset pricing model (CAPM) can be used to estimate the return required by common shareholders, particularly in situations where discounted cash flow methods will perform poorly (i.e., growth firms)

• CAPM estimates a market determined estimate, because the risk-free rate (RF) is the benchmark return and is measured directly, and the market risk premium (MRP) is taken from current market estimates

• Equation 20-26 shows the CAPM is a single-factor model, so we estimate the required return on equity based on an estimate of the systematic risk of the firm as measured by the firm’s beta coefficient:

• The yield on 91-day treasury bills is often used for RF• But MRP is harder to forecast: one common approach is to use an

estimate of the current expected MRP based on a long-run averageBooth • Cleary – 3rd Edition 36

eFe MRPRK


• Table 20-13 shows TD Economics’ long-run forecasts for the returns on different asset classes




• Figure 20-4 shows that the estimated betas for the major sub-indices of the S&P/TSX have varied significantly over time




• Table 20-14 shows the data charted in Figure 20-4




• Figure 20-3 and Table 20-14 show the following:– The IT sub index shows rapidly increasing betas while other sub-

indices show relatively constant betas– The weighted average of all betas is, by definition, the market

beta of 1.0– If one sub index is changing, that change alone affects all others

in the opposite direction– During the internet bubble of the late 1990s, rapid growth in the

IT sector caused its beta to change– When betas are measured over the period of a sector bubble or

crash, it is necessary to adjust the beta estimates of firms in other sectors by taking the industry grouping as a major input to develop estimates of equity capital cost using the range of company betas prior to the bubble or crash




• Figure 20-5 shows Nortel’s stock price (1987–2005), and illustrates the IT bubble




• Figure 20-6 shows Tim Horton’s stock price vs. the S&P/TSX Composite Index during the 2008 financial crisis. Notice how the value of the index crashes while Tim Horton’s stock holds its value. How would this affect Tim Horton’s beta?




• Equation 20-27 shows we can scale our estimate of the equity holder’s required return when accessing new equity and incurring flotation costs:


NP

PxKK 0

ene



20.7 THE COST OF CAPITAL AND INVESTMENT

• The investment opportunity schedule (IOS) is the ranking of a firm’s investment opportunities from highest to lowest profitability according to expected internal rate of return (IRR)

• When superimposed on a marginal cost of capital (MCC) curve, the firm can identify projects that will increase the value of the firm by looking at the portion of the IOS that lies above the WACC line. Projects represented by the portion of the IOS below WACC should be rejected


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