Cost of capital

What types of long-term capital do firms use?

Long-term debtPreferred stockCommon equityTerm loansRetained earnings

What is the “Cost” of Capital?

• When we talk about the “cost” of capital, we are talking about the required rate of return on invested funds

• It is also referred to as a “hurdle” rate because this is the minimum acceptable rate of return

• Any investment which does not cover the firm’s cost of funds will reduce shareholder wealth (just as if you borrowed money at 10% to make an investment which earned 7% would reduce your wealth)

Importance of Cost of Capital

more wealth created to shareholders.

more projects end up with NPV > 0

NPV increases

If financing cost is reduced

Weighted Average Cost of Capital (overview)

• A firm’s overall cost of capital must reflect the required return on the firm’s assets as a whole

• If a firm uses both debt and equity financing, the cost of capital must include the cost of each, weighted to proportion of each (debt and equity) in the firm’s capital structure

• This is called the Weighted Average Cost of Capital (WACC)

Should we focus on before-tax or after-tax capital costs?

Tax effects associated with financing can be incorporated either in capital budgeting cash flows or in cost of capital.

Most firms incorporate tax effects in the cost of capital. Therefore, focus on after-tax costs.

Only cost of debt is affected.

Cost of Debt– Cost of debt is the discount rate which equates the net proceeds

from issue of debentures to the expected cash outflows in the form of interest and principal

– Kd = I(1-t) + (F-P) (1-t)

n F + P 2

This is derived from the formula– P = Σ I(-t) + F

(1+kd)t (1+kd)n

F= redemption valueP= Issue priceT – tax rate , I = interest

Cost of term loans

• Will be simply equal to the interest rate multiplied by (1-tax rate)

• The interest rate used here will be the interest rate applicable to the new term loan

• Kt = I (1-t)

Cost of preference capital• It is that discount rate which equates the proceeds from

preference capital issue to the payments associated like dividend and principal repayment etc

• It is derived from P = Σ D + F (1+Kp)t (1+Kp)n

Approximating this we get,

Kp = D + ((F-P)/n)

(F+P)/2

Cost of equity

• It is that discount rate that equates the inflow of funds with that of the expected rate of return for the equity holders

• Measuring the rate of return by equity holders is difficult and complex

• Some holders prefer dividend stream, some prefer terminal value and some both

• Thus there are three main approaches for valuing equity

Warning: Most people misunderstand “Expected.”

Time

Profit

“Expected”

“Risk”

Time

Profit

Expected

Risk

Risk

What many people mean What the formula means

• This may explain high required-return hurdles.

Three ways to determine the cost of equity, Ke:

1. Capital Asset Pricing Model:

Ke= rRF + (rM - rRF)b

= rRF + (RPM)b.

2. Discounted Cash flow: Ke= D1/P0 + g.

3. Own-Bond-Yield-Plus-Risk Premium:

Ke = Kd + RP.

What’s the cost of equity based on the CAPM?

rRF = 7%, RPM = 6%, b = 1.2.

rs = rRF + (rM - rRF )b.

= 7.0% + (6.0%)1.2 = 14.2%.

What’s the DCF cost of equity, rs?Given: D0 = $4.19;P0 = $50; g = 5%.

g

P

gDg

P

Drs

0

0

0

1 1

$4. .

$50.

. .

.

19 1050 05

0 088 0 05

13 8%.

• Earnings can be reinvested or paid out as dividends.

• Investors could buy other securities, earn a return.

• Thus, there is an opportunity cost if earnings are reinvested.

Why is there a cost for reinvested earnings?

• Opportunity cost: The return stockholders could earn on alternative investments of equal risk.

• They could buy similar stocks and earn rs, or company could repurchase its own stock and earn rs. So, rs, is the cost of reinvested earnings and it is the cost of equity.

Finding the Weights

• The weights that we use to calculate the WACC will obviously affect the result

• Therefore, the obvious question is: “where do the weights come from?”

• There are two possibilities:– Book-value weights– Market-value weights

Book-value Weights

• One potential source of these weights is the firm’s balance sheet, since it lists the total amount of long-term debt, preferred equity, and common equity

• We can calculate the weights by simply determining the proportion that each source of capital is of the total capital

Book-value Weights (cont.)

Source Total Book Value % of Total Long-term Debt Rs4,00,000 40% Preferred Equity Rs1,00,000 10% Common Equity Rs5,00,000 50% Grand Totals Rs 10,00,000 100%

The following table shows the calculation of the book-value weights

Market-value Weights

• The problem with book-value weights is that the book values are historical, not current, values

• The market recalculates the values of each type of capital on a continuous basis. Therefore, market values are more appropriate

• Calculation of market-value weights is very similar to the calculation of the book-value weights

• The main difference is that we need to first calculate the total market value (price times quantity) of each type of capital

Calculating the Market-value Weights

Source Price per Unit

Units Total Market Value

% of Total

Debt Rs905 400 Rs3,62,000 31.15% Preferred Rs100 1,000 Rs1,00,000 8.61% Common Rs 70 10,000 Rs7,00,000 60.24% Totals Rs1,162,000 100.00%

The following table shows the current market prices:

WACC 0 3115 0 07 0 0861 010 0 6024 012 01027 10 27%. . . . . . . .

Market vs Book Values

• It is important to note that market-values is always preferred over book-value

• The reason is that book-values represent the historical amount of securities sold, whereas market-values represent the current amount of securities outstanding

• For some companies, the difference can be much more dramatic

Estimating Weights for the Capital Structure

• If you don’t know the targets, it is better to estimate the weights using current market values than current book values.

• If you don’t know the market value of debt, then it is usually reasonable to use the book values of debt, especially if the debt is short-term.

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Estimating Weights (Continued)

• Suppose the stock price is $50, there are 3 million shares of stock, the firm has $25 million of preferred stock, and $75 million of debt.

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• Vce = $50 (3 million) = $150 million.

• Vps = $25 million.

• Vd = $75 million.

• Total value = $150 + $25 + $75 = $250 million.

• wce = $150/$250 = 0.6

• wps = $25/$250 = 0.1

• wd = $75/$250 = 0.3

What’s the WACC?

WACC = wdrd(1 - T) + wpsrps + wcers

= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)

= 1.8% + 0.9% + 8.4% = 11.1%.

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Extended Example – WACC - I• Equity Information– 50 million shares– $80 per share– Beta = 1.15– Market risk premium

= 9%– Risk-free rate = 5%

• Debt Information– $1 billion in outstanding debt (face value)– Current quote = 110– Coupon rate = 9%, semiannual coupons– 15 years to maturity

• Tax rate = 40%

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Extended Example – WACC - II

• What is the cost of equity?– RE = 5 + 1.15(9) = 15.35%

• What is the cost of debt?– N = 30; PV = -1100; PMT = 45; FV = 1000; CPT I/Y =

3.9268– RD = 3.927(2) = 7.854%

• What is the after-tax cost of debt?– RD(1-TC) = 7.854(1-.4) = 4.712%

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Extended Example – WACC - III

• What are the capital structure weights?– E = 50 million (80) = 4 billion– D = 1 billion (1.10) = 1.1 billion– V = 4 + 1.1 = 5.1 billion– wE = E/V = 4 / 5.1 = .7843

– wD = D/V = 1.1 / 5.1 = .2157

• What is the WACC?– WACC = .7843(15.35%) + .2157(4.712%) = 13.06%