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1

The Cost

of Capital

March 14, 2012

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2

Learning Goals

Determining the value of K, the requiredrate of return for an investor

Sources of capital funding (Debt, Equity) Cost of each type of funding

Calculation of the weighted average cost of

capital funding (WACC) = K Construction and use of the marginal cost of

capital schedule (MCC) for decision making

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Cost of Capital

Capital is the term used by firms forfunds needed for investment

purposes, i.e., capital equipment(not for day to day operating needs)

This capital carries a cost because

each source of capital funding costsmoney to raise (i.e., issuing stockcosts a lot of money)

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Cost of Capital

To properly evaluate investmentdecisions, the firm must know how

much it will cost them to raise capitalfunds from all sources

WACC = K = hurdle rate

If it costs more to raise the capital (K)than you make on your investment,then you dont make the investment!

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Sources of Capital

Borrowing, such as Bonds, bank loans,

Issuing Preferred stock

Issuing Common stock Net Income (earnings)

Each of these sources carries a different

cost based on the required rate of returnof each provider (source) of these funds

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Optimal Capital

Structure The capital structure of a firm is how the

firm has elected to finance its assets

It is the level or percentage of totalassets financed by debt, preferred stockand common equity (common stock and

retained earnings) Each firm has an optimal level of debt

and equity at which it can operate most

efficiently and profitability (Draw curve)

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Compute the cost of each source ofcapital, i.e., debt, preferred stock,

common stock, retained earnings Determine percentage (weights) of each

source of capital in the firms optimal

capital structure Calculate Weighted Average Cost of

Capital (WACC)

Weighted Cost of Capital Model

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Required rate of return for creditors

e.g. Suppose that a company issues bonds witha before tax cost of 10%.

Since interest payments are tax deductible, thetrue cost of the debt is theAfter Tax cost (ATkd= Int Rate (1 T), where T is tax rate)

If the companys tax rate (state and federalcombined) is 40%, the after tax cost of debtATkd = 10%(1-.4) = 6% (show numerical example)

1. Compute Cost of Debt

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Flotation Costs cost of issuingsecurities to the general public

Accounting

Legal

Prospectus (pass out examples)

Underwriting (investment banker) Filing Fees (SEC)

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Dp = preferred stock dividend

Pp = Market price per share F = flotation costs per share

Flotation costs reduce the amount of money youget when you sell preferred stock

Cost to raise a dollar of preferred stock.

Dividend (Dp)

Market Price (PP) - F

Required rate kp =

2. Compute Cost Preferred Stock

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Cost of Preferred Stock

Example:You can issue preferredstock with a market price of $45, and

flotation costs of $3 per share, for anet price of $42 and if the preferredstock pays a $5 dividend,

The cost of preferred stock:

$5.00 =$42.00

kp = 11.9% (vs 11.1)

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Two Types of Common Equity Financing

Retained Earnings (internal common equity)

Issuing new shares of common stock(external common equity)

3. Compute Cost of Common Equity

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Cost of Common Equity (Retained Earnings) Management should retain earnings only

if they earn as much as stockholdersnext best investment opportunity of the

same risk.

Cost of Common Equity = opportunitycost of common stockholders funds.

Two methods to determineDividend Growth Model

Capital Asset Pricing Model


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Cost of Common Equity (Retained Earnings)Dividend Growth Model

D1

P0kS = + g


Ks = cost of internal common equity

D1 = the next dividend to be paidPo = the current market price of the stock

g = the projected rate of growth of the company

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Example:The market price (Po) of a share of commonstock is $60. The prior dividend paid (D0) was

$3, and the expected growth rate (g) is 10%.


Cost of Internal Common EquityDividend Growth Model

D1

P0kS = + g

If you are given D0, you must calculate D1D1 = D0 (1 + g)

D1 = 3.00 (1.10) = 3.30

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3.30

60

kS = + .10 =.055 + .10 = 15.5%

Example:The market price of a share of common stockis $60. The prior dividend (D0) is $3, and theexpected growth rate is 10%.


Cost of Internal Common Equity Dividend Growth Model

D1

P0kS = + g

(D1 = 3.00 x 1.10 = 3.30)

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Cost of New Common Stock Must adjust the Dividend Growth Model

equation for flotation (F) costs of the newcommon shares.


D1P0 - F

kn = + g

Kn = cost of sale of new common stockD1 is the next dividend to be paidPo is the current market price of shares outstandingF is the flotation costG is the rate of growth

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3.30

52.80kn = + .10 = .0625 + .10 = 16.25%

Example:If additional shares are issued, floatationcosts will be 12% of price per share. D0 =$3.00 and estimated growth is 10%, Price is$60 as before. Flotation cost = $60 x .12 =$7.20.

(Po F = $60.00 7.20 = $52.80)

(D1 = 3.00 x 1.10 = 3.30)

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Weighted Average Cost of Capital

Gallagher Corporation estimates the followingcosts for each component in its capital structure:

Gallaghers tax rate is 40%

Source of Capital Cost

Bonds (after tax) kd = 6.0%Preferred Stock kp = 11.9%

Common StockRetained Earnings ks = 15.5%New Shares kn = 16.25%

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If using retained earnings (Internal Equity) tofinance the equity portion:

WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)

WACC = weighted average cost of capital

WT = the weight, or percentage of each element of capital

(% of debt, preferred and common stock to total assetsATkd = after tax cost of debt

Kp = Cost of preferred stock

Ks

= Cost of equity (Internal retained earnings)

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If using retained earnings (internal equity) tofinance the common equity portion :


Assume that Gallaghers desired capital

structure is 40% debt, 10% preferred and50% common equity.

WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)

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WACC =Cost of Debt .40 x 6.0% = 2.40%+ Cost of Preferred .10 x 11.9% = 1.19%+ Cost of Int. Equity .50 x 15.5% = 7.75%

1.00 = 11.34%


If using retained earnings (Internal Equity) tofinance the equity portion:

Assume that Gallaghers desired capitalstructure is 40% debt, 10% preferred and50% common equity.

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WACC =Cost of Debt .40 x 6.0% = 2.40%+ Cost of Pref .10 x 11.9% = 1.19%+ Cost of Ext. Eq. .50 x 16.25% = 8.13%

= 11.72%

If using new common stock (External Equity) tofinance the common stock portion:


Then we must use the cost of stockadjusted for the Flotation costs

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Marginal Cost of Capital

Gallaghers weighted average cost willchange if one component cost of capital

changes. This may occur when a firm raises a

particularly large amount of capital suchthat investors think that the firm is riskier.

The WACC of the next dollar of capitalraised is called the marginal cost of capital.

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Spending Capital Money

The assumption is that the capitalmoney is spent in direct proportion tothe optimal capital structure.

So, if we spend $100,000, it would be inthe following proportions:

Capital Structure Spend

Debt 40% 40,000

Preferred 10% 10,000

Common 50% 50,000

(Buckets) Total 100,000

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Calculating the Breakpoint

Assume now that Gallagher Corporation has$100,000 in retained earnings with which to

finance its capital budget. We can calculate the point at which they will

need to issue new equity since we know thatGallaghers desired capital structure calls for

50% common equity.

Breakpoint = Available Retained EarningsEquity Percentage of Total

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Calculating the Breakpoint

Breakpoint = ($100,000)/.5 = $200,000 What this means is that once we spend

$200,000 in total on capital projects, wewill have used up our retained earningsof $100,000 (internal equity).

Therefore, if we spend over $200,000,we will need additional financing from the

issue of new shares of stock since 50% ofour spending must come from Equity.

The cost of issuing new shares is greaterthan internal equity due to flotation costs

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WeightedCostofCap

ital

TotalFinancing

10%

11%

12%

13%

0 100,000 200,000 300,000 400,000

Marginal weighted cost of capital curve:

Making Decisions Using

MCC

Using internalcommon equity

Usingnew

common equity

11.72%

11.34%

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Making Decisions UsingMCC Graph IRRs of potential projects

WeightedCostofCapital

TotalFinancing

9%

10%

11%

12%

0 100,000 200,000 300,000 400,000


Project 1IRR =12.4%

Project 2

IRR =12.1%

Project 3IRR =11.5%

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30WeightedCos

tofCapital

TotalFinancing

9%

10%

11%

12%

0 100,000 200,000 300,000 400,000


Project 1

IRR =12.4%

Project 2IRR =12.1%

Project 3IRR =11.5%

Making Decisions UsingMCC

Graph IRRs of potential projects

Graph MCC Curve

11.34%

11.72%

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31WeightedCos

tofCapital

TotalFinancing

9%

10%

11%

12%

0 100,000 200,000 300,000 400,000


Project 1

IRR =12.4%

Project 2IRR =12.1%

Project 3IRR =11.5%

Making Decisions Using MCC Graph IRRs of potential projects

Graph MCC Curve

Accept Projects #1 & #2

Choose projects whose IRR is above the weightedmarginal cost of capital

11.72%11.34%

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MCC and Capital BudgetingDecisons

See pages 250 256

Calculate the breakpoints

Calculate the new MCCs

Plot MCCs and Investment Projects

See Figures 9-5 and 9-6 for results

Do all the Self-test problems beforedoing the homework

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