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Cost of CapitalWeek 12

FACULTY OF BUSINESS AND ACCOUNTANCY

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The cost of capital is the rate of return that a firm must earn on its project investments (required rate of return);

To maintain its market value To attract funds from the market suppliers of capital

If risk is held constant, projects with;

Rate of return > Cost of capital

Þ will increase the value of the firm

Introduction

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Since firms normally have a mixture of financing (debt or

equity or both), cost of capital should reflect the

interrelatedness of financing activities.

Thus, the relevant cost of capital is the overall cost of

capital or the weighted average cost of capital (WACC or r)

rather than the cost of specific source of funds used to

finance a given expenditure.

The cost of capital is measured on an after-tax basis

It is estimated at a given point in time

It should reflect the expected average future cost of funds

over the long run

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Rationale of using WACC

Example: a firm is currently faced with two investment opportunities.

Project A Project B

Life 20 years 20 years

Cost RM100,000 RM100,000

IRR 7% 14%

Cost of Capital (least available)

Debt – 6% Equity-15%

If select each investment based on separate r, then will only accept A.

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But do these actions are in the best interests of its owners?

~ recall that it accepted a project yielding a smaller return

(7%) & rejected the one with 14% return.

Better alternative is using a combined cost, WACC which ;

Reflects the interrelatedness of financing decisions

Provides better decisions over the long run

WACC is the weighted average, or composite cost of the

various types of funds a firm generally uses, regardless of the

specific financing used to fund a particular project.

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Assume that a 50-50 mix of debt & equity is targeted, WACC

would be;

.50 x 6% debt + .50 x 14% equity = 10%

The Decision

Separate cost WACC

Accept project A because;IRR (7%) > rdebt (6%)

Accept Project B because;IRR (14%) > rWACC (10%)

WACC is found by weighting the cost of each source of

financing by its target proportion in the firm’s capital

structure

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Sources of Capital

Four basic sources of long-term funds for business firms;

Balance Sheet

Current liabilities Long-term debt (bonds) Assets Stockholders’ equity Preferred stocks Common Stock Equity Common Stock Retained Earnings

The relevant cost is the after-tax cost of obtaining the financing

today, not the historically based cost reflected by the existing

financing on the firm’s book.

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Calculating the weighted average cost of capital

The w’s refer to the firm’s capital structure weights.

The r’s refer to the cost of each component.

WACC, ra = wdrd(1-T) + wprp + wsrr, or n

rd = cost of debt

rp = cost of preferred stock

rr or n = cost of common equity

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Should our analysis focus on before-tax or after-tax capital costs?

• Stockholders focus on A-T CFs. Therefore, we should

focus on A-T capital costs, i.e. use A-T costs of capital in

WACC. Only rd needs adjustment, because interest is tax

deductible.

Should our analysis focus on historical (embedded) costs or new (marginal) costs?

• The cost of capital is used primarily to make decisions

that involve raising new capital. So, focus on today’s

marginal costs (for WACC).

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How are the weights determined?

The weights must be in decimal form & the sum of all

weights must equal 1.0

Common stock equity weight, ws, is multiplied by either

the cost of retained earnings, rr, or the cost of new

common stock, rn.

WACC = wdrd(1-T) + wprp + wsrr or n

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1. The Cost of Long-Term Debt

COMPONENTS OF COST

Most corporate l-t debt are incurred through the sale of

bonds.

Net proceeds are the funds actually received from the sale

of a security.

Flotation costs are the total costs of issuing & selling a

security.Eg: A bond with a par value of RM1,000 sells at RM980. The

flotation costs are 2% of the par value;

Flotation costs = 2% x 1,000 = RM20

Net proceeds = RM980 - RM20 = RM960

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Before Tax Cost of Debt, rd

Can be obtained by;

1. Using cost quotations

a. When net proceeds equal its par value, rd would equal the coupon interest rate.

E.g.: A 10% coupon ir bond that net proceeds equal to bond’s RM1,000 par value would have a rd of 10%

b. Using yield to maturity (YTM) on a similar risk bond

E.g.: If a similar-risk bond has a YTM of 9.7%, then, can use this rate as rd

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2. Calculating the cost

rd is the IRR on the bond cash flows;

Bond’s price = interest pmt x PVIFAi,n + (par value x PVIFi%,n) annually

IRR or rd, can be calculated through either; a) F/C or b) Approximation

Eg: A bond of 20-years, 9% coupon annually & a par value of RM1,000. Sells at RM980 & the flotation costs are RM20

End of years Cash flows

0 RM960

1-20 -90

20 -1,000

20 -960 90 1000 comp

N PV PMT FV I/YR 9.45

rd

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3. Approximating the cost

rd = I + principal pmt - net proceeds n principal pmt + net proceeds 2

I = annual interest or coupon payments in RM

n = no. of years to bond’s maturity

rd = 90 + 1,000 - 960 20 1,000 + 960 2 = 90 + 2 = 9.3877% 980

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After-Tax Cost of Debt, ri

This is the relevant cost because interest on debt is tax

deductible & this will reduce the firm’s taxable income.

The interest deduction therefore reduces taxes by an amount

equal to the product of the deductible interest & the firm’s

tax rate (tax savings)

After-tax = interest rate - tax savings on debt cost of debt ri = rd - rdT = rd (1-T)

ri for the previous bond given a 40% tax rate;

ri = 9.4% (1 – 0.40) = 5.6%

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E.g.: A semiannual coupon bond at 12% coupon rate and 15 years to maturity. Current bond price = RM1,153.72. Tax rate = 40%

F/C;

30 -1,153.72 60 1000 comp P/Y = 1

N PV PMT FV I/YR% rd/2 = 5% rd = 10%

Component Cost of Debt; ri = 10% (1 – 0.40) = 6%

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2. The Cost of Preferred Stock, rp

Preferred stock represents a special type of ownership

interest in the firm.

It gives the owners the rights to receive their stated

dividends before any earnings can be distributed to

common s/holders

Preferred dividends are not tax-deductible, so no tax

adjustments necessary. Just use rp.

Nominal rp is used.

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What is the cost of preferred stock?

Cost of p.s. is the rate of return investors required on

the firm’s preferred stock.

Cost of preferred stock, rp is calculated as the preferred

dividend, Dp divided by the current price:

Tells the relationship between the cost of p.s. in the form

of its annual dividends, and the amount of funds provided

by the p.s. issue.

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Sometimes, net proceeds from the sale of the stock, Np is

used instead of current price

Net proceeds represent the amount of money to be

received minus any flotation costs

Because p.s. dividends are paid out of the firm’s after-tax

cash flows, a tax adjustment is not required.

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Preferred Stock Dividends, Dp

The dividends are stated in 2 ways;

1. As an RM amount ; RMx per year or RMx preferred stock

e.g. RM4 p.s. is expected to pay preferred s/h RM4 in

dividend per year on each share of p.s. owned.

2. As an annual percentage rate

- represents the percentage of the stock’s par or face

value that equals the annual dividend.

e.g. An 8% p.s. with a RM50 par value would be expected to

pay an annual dividend of RM4 per share (.08 x RM50 par

value = RM4)Note: any dividend stated as percentages, should be converted to

annual RM first to calculate rp

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Is preferred stock more or less risky to investors than debt?

More risky; company is not required to pay preferred

dividend.

However, firms try to pay preferred dividend. Otherwise,

(1) cannot pay common dividend, (2) difficult to raise

additional funds, (3) preferred stockholders may gain

control of firm.

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3. The Cost of Common Equity, rs

WACC = wdrd(1-T) + wprp + wsrs

New common equity can be raised in 2 ways;

Retaining some of the current year’s earnings

Issuing new common stocks

rr is the marginal cost

of common equity using retained earnings.

The rate of return investors require on the firm’s

common equity using new equity is rn.

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To solve rs then, we can either find the expected rates of return

or rs itself.

In equilibrium, expected & required rates of return on stocks

should be equal;

rs = rs

Finding the required rates of return, rs

1. CAPM Approach2. Bond-Yield-Plus-Risk-Premium Approach3. Discounted Cash Flow (DCF) Approach

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1. The CAPM Approach

Capital asset Pricing Model (CAPM) is used to estimate the

cost of common equity.

The steps;

1. Estimate the risk-free rate, rRF

- taken from government bills or bonds

2. Estimate the stock’s beta coefficient, bi

- the extent of which the returns on a given stock move with the stock market

3. Estimate the required rate of return on the market, rm

CAPM: rs = rRF + (rM – rRF) bi

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E.g.: If the rRF = 7%, RPM = 6%, and the firm’s beta is 1.2, what’s

the cost of common equity based upon the CAPM?

rs = rRF + (rM – rRF) β

= 7.0% + (6.0%) 1.2

= 14.2%

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Own-Bond-Yield-Plus-Risk Premium:

rs = rd + RP

2. Bond-yield-plus-risk-premium Approach

Add a judgmental risk premium of 3 to 5 percentage points

to the interest rate on the firm’s own long-term debt.

For example, if Firm J has bonds that yielded 8% annually, its

cost of equity might be estimated as follows;

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If rd = 10% and RP = 4%, what is ks using the own-bond-yield-plus-risk-premium method?

• This RP is not the same as the CAPM RPM.• This method produces a ballpark estimate of

rs, and can serve as a useful check.

rs = rd + RP

rs = 10.0% + 4.0% = 14.0%

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3. Discounted Cash Flow (DCF) Approach

Po = current price of the stock

D1 = dividend expected to be paid at the end of next

year, or Year 1

g = constant rate of growth in dividends

Implies that investors expect to receive dividend yield, D1 /

P0 , plus a capital gain, g.

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E.g. If D0 = RM4.19, P0 = RM50, and g = 5%, what’s the cost of common equity based upon the DCF approach?

D1 = D0 (1 + g)

D1 = RM4.19 (1 + .05)

D1 = RM4.3995

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What is the expected future growth rate?

The firm has been earning 15% on equity (ROE = 15%) and retaining 35% of its earnings (dividend payout = 65%). This situation is expected to continue.

g = ( 1 – Payout ) (ROE)= (0.35) (15%)= 5.25%

Very close to the g that was given before.

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Can DCF methodology be applied if growth is not constant?

Yes, non-constant growth stocks are expected to

attain constant growth at some point, generally in

5 to 10 years.

Will be complicated to compute.

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What is a reasonable final estimate of ks?

Method Estimate

CAPM 14.2%

DCF 13.8%

rd + RP 14.0%

Average 14.0%

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Why is there a cost for retained earnings?

Earnings can be reinvested or paid out as dividends.

Investors could buy other securities, earn a return.

If earnings are retained, there is an opportunity cost (the

return that stockholders could earn on alternative

investments of equal risk).

– Investors could buy similar stocks and earn rs.

– Firm could repurchase its own stock and earn rs.

– Therefore, rs is the cost of retained earnings.

Cost of Retained Earnings, rr

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Why is the cost of retained earnings cheaper than the cost of issuing new common stock?

When a company issues new common stock they

also have to pay flotation costs to the underwriter.

Issuing new common stock may send a negative

signal to the capital markets, which may depress the

stock price.

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Cost of New Common Stock, rn

In issuing new common stock, firms incur flotation costs

(underwriting & selling costs).

Therefore, cost of new common stock should reflect both; the

required return paid to investors & the flotation fees paid to

issue it.

DFC approach can be adapted to account for flotation costs

when calculating rn

rn = D1 + g P0 (1 - F)

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E.g. If issuing new common stock incurs a flotation cost of

15% of the proceeds, what is rn?

15.4%

0.05 RM42.50RM4.3995

0.05 0.15)-RM50(1

5)RM4.19(1.0

g F)-(1Pg)(1D

k0

0e

rn

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Retained Earnings Breakpoint

The amount of capital raised beyond which new common stock must be issued

The total amount of financing that can be raised before the firm is forced to sell new common stock

Retained earnings = addition to retained earnings break point equity fraction from capital struc.

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E.g: Firm A’s addition to retained earnings in 2006 is expected to be RM68 mil. Its capital structure consists of 45% debt, 2% p.s. & 53% equity.

Retained earnings = addition to retained earnings break point equity fraction from capital struc. = RM68 / 0.53 = RM128.3

Means that the firm’s financing comes from; Debt : 0.45 (128.3) = RM57.74 P.s. : 0.02 (128.3) = RM2.57 Ret. E : 0.53 (128.3) = RM67.9

If A’s capital budget exceed RM128.3m, the amount of equity required will exceed the available r.e.. So must obtain it from issuance of new stock.

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Calculating the weighted average cost of capital

WACC = wdrd(1-T) + wprp + wsrs

Eg; Facts: 30% l-t debt 10% P.S. 60% Common Equity

Target capital structure

rd = 10% ; rp = 9%; rs = 14% ; T = 60%

WACC = wdrd(1-T) + wprp + wsrs

= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%) = 1.8% + 0.9% + 8.4% = 11.1%

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The Weighted Marginal Cost of Capital (WMCC)

Firm should only invest in projects where the expected return is more than WACC.

WACC varies depending on the volume of financing the

firms want to raise. Why?

As the volume of financing increases, the costs of the

various types of financing will increase, raising WACC

WMCC is the firm’s WACC associated with its next RM of total new investment.

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Breaking Points for Each Components

Before calculating WMCC, must calculate BP which reflect the level of total new financing at which the cost of one of the financing components rises.

BPj = AFj / wj

Breaking pointsfor financingsource j

Amount of fundsavailable fromfinancing source jat a given cost

Capital structure weights

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Eg; Firm B exhausts its RM300k of available retained earnings (rr = 13%). It must use the more expensive issuance of new common stock (rn = 14%). Furthermore, the firm expects that it can borrow only RM400k of debt at 5.6% cost, any additional debt will have an after-tax cost of 8.4%. Find the WMCC at each level of financing and construct its schedule.

Steps to calculate & construct WMCC schedule;1. Determine the BP points2. Calculate the WACC over the range of total new

financing btw BPs a. Find WACC between zero & the first BP b. Find BP btw first BP and the second one & so

on.

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The breaking points; (the total financing)

1. When the RM300k of r.e. costing 13% will be exhausted

BPs = RM300k / 0.50 = RM600,000

2. When the RM400k of l-term debt costing 5.6% will be exhausted

BPd = RM400k / 0.40 = RM1,000,000

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WACC for Ranges of Total Financing for Firm BRange of total new financing

Source of

Capital (1)

Weight (2) Cost

(3)

Weighted Cost (4) = (2) x (3)

RM0 – RM600 k DebtP.S.R.Earnings

.40

.10

.50

5.6%10.6%13.0%

2.2%1.1%6.5%

WACC = 9.8%

RM600 k – RM1 m

DebtP.S.C. Stocks

.40

.10

.50

5.6%10.6%14.0%

2.2%1.1%7.0%

WACC = 10.3%

RM1,000,000and above

DebtP.S.C.Stocks

.40

.10

.50

8.4%10.6%14.0%

3.4%1.1%7.0%

WACC = 11.5%

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DB

C

A

WMCC Schedule

WACC (%)

11.5

11.0

10.5

10.0

9.59.8%

10.3%

11.5%

500k 1 m 1.5 m

Total new financing (‘000)

Rates of return