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WACC1 wdrd(1 - T) wpsrps wcers WACC2

wdrd(1 - T) wpsrps wcere

CHAPTER 9 The Cost of Capital

- Cost of capital components
- Debt
- Preferred
- Common equity
- WACC
- MCC
- IOS

MINICASE, Chapter 9 (a-i), p. 340.(See DATA)

What sources of capital should be included in a

firms WACC?

- Long-term debt
- Preferred stock
- Common equity
- Retained earnings
- New common stock
- Short term debt?

Capital components are sources of funding that

come from investors. Accounts payable, accruals,

and deferred taxes are not sources of funding

that come from investors, so they are not

included in the calculation of the cost of

capital. We do adjust for these items when

calculating the cash flows of a project, but not

when calculating the cost of capital.

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.

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.

Should we focus on before-tax or after-tax

capital costs?

Only rd needs adjustment rd(1-T) rd - T x rd

where rd cost of debt, and T x rd Tax

savings due to using debt.

Should we focus on historical (embedded) costs or

new (marginal) costs?

The cost of capital is used primarily to make

decisions which involve raising new capital. So,

focus on todays marginal costs.

Cost of Debt

- Method 1 Ask an investment banker what the

coupon rate would be on new debt. - Method 2 Find the bond rating for the company

and use the yield on other bonds with a similar

rating. - Method 3 Find the yield on the companys debt,

if it has any. - Focus on method 3, to start.

Whats rd? Coupon 12 semi Price

1,153.72 15 years.

0

1

2

30

rd ?

60

60 1,000

60

-1,153.72

30 -1153.72 60 1000

5.0 x 2 rd 10 EAR ? Should we use it?

INPUTS

I/YR

N

PV

FV

PMT

OUTPUT

What should we do if this firm does not have an

outstanding bond?

- Use rate on bond of a comparable firm (method

2). - Ask investment bankers for their estimate

(method 1). - N.b. If the bond is callable, the YTC rather than

the YTM may be appropriate.

Component cost of debt

- Interest is tax deductible, so
- rd AT rd BT(1 - T)
- 10(1 - 0.40) 6.
- Use nominal rate. Why?
- Flotation costs small. Ignore, for now.
- May need to incorporate yield curve differences.

Whats the cost of preferred stock? Pps

113.10 10Q Par 100 F 2.

Use this formula

Dps PNet

0.25(100) 113.10 - 2.00

rps

0.025 2.25. Qtrly.

2.50 111.10

Picture of Preferred

ì

0

1

2

kps ?

2.50

2.50

-111.1

2.50

Dps rps

2.50 rPer

111.10 . rPer

2.25 rps(Nom) 2.25(4) 9.

2.50 111.10

Note

- Flotation costs for pfd. are significant, so are

reflected. Use net price. - Preferred dividends are not deductible, so no tax

adjustment. Just rps. - Nominal rps is used.
- Capital budgeting CFs are nominal.
- Use nominal values for component costs.

Is preferred stock more or less risky to

investors than debt? than equity?

- Risk Return

Debt

Preferred

Equity

Is preferred stock more or less risky to

investors than debt? than equity?

- Risk Return

Debt

Preferred

Equity

Is preferred stock more or less risky to

investors than debt? than equity?

- More risky company not required to pay preferred

dividend. - However, firms try to pay preferred dividends.

Otherwise, - Cannot pay common dividends.
- Difficult to raise new capital.
- Preferred stockholders may gain some control of

firm. - Therefore, does preferred have higher yield than

debt?

Illustration Preferred vs. debt for same company

or similar companies.

Recent data for RJR

rps 9.5 rd 11.4

Is this is as expected?.

Why is yield on preferred lower than kd?

- Corporations own most preferred stock, because

70 of preferred divi-dends are nontaxable to

corporations. - Therefore, preferred often has a lower B-T yield

than the B-T yield on debt. - But the A-T yield to an investor, and the A-T

cost to the issuer, are higher on preferred than

on debt. Consistent with higher risk of

preferred to investors.

Illustration Preferred vs. debt for same company

or similar companies.

Before tax for RJR

rps 9.5 rd 11.4

This looks strange!. Suppose T 40

rps, AT rps - rps (1 - 0.7)(T) 9.5 -

9.5(0.3)(0.4) 8.36 rd, AT 11.4 -

11.4(0.4) 6.84 A-T risk prem. on pfd.

1.52.

This is as expected.

Riskier preferred has higher AT rate.

What are the two ways that companies can raise

common equity?

- .

What are the two ways that companies can raise

common equity?

- Companies can issue new shares of common stock.
- Companies can reinvest earnings.

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. - Thus, there is an opportunity cost if earnings

are retained.

- 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

ks. So, rs is the cost of retained earnings.

Three ways to determine the cost of equity, rs

1. CAPM rs rRF (rM - rRF)? rRF

(RPM) ? 2. DCF rs D1/P0 g. 3. Own-Bond-Yiel

d-Plus-Risk Premium rs rd Bond RP.

Whats the cost of equity based on the CAPM? rRF

7, RPM 6, ß 1.2.

rs rRF (rM - rRF ) ? .

7.0 (6.0)1.2 14.2.

Issues in Using CAPM

- Most analysts use the rate on a long-term (10 to

20 years) government bond as an estimate of rRF.

For a current estimate, go to www.bloomberg.com,

select U.S. Treasuries from the section on the

left under the heading Market.

More

Issues in Using CAPM (Continued)

- Most analysts use a rate of 5 to 6.5 for the

market risk premium (RPM) - Estimates of beta vary, and estimates are noisy

(they have a wide confidence interval). For an

estimate of beta, go to www.bloomberg.com and

enter the ticker symbol for STOCK QUOTES.

Explain the differences among historical betas,

adjusted betas, and fundamental betas.

- Historical betas are found by running a linear

regression between past returns on a stock versus

a market index. - Adjusted betas are historical betas adjusted for

tendency to move towards 1.0 over

time.

(More...)

- Fundamental betas are adjusted further to include

changes in a companys fundamental factors over

time such as leverage, sales volatility, etc.

E.g. Adj. ? 0.33(Hist. b) 0.67(1.0) Fund.

? f(Hist. b, 1.0, leverage, etc.) - Both attempt to overcome the problem that

historical betas measure past market risk while

investors are interested in future market risk.

How can RPM be measured?

- Ex post data e.g., Ibottson and Assoc. provides

this on an annual basis RPM 6.2 for

1926-1999. - Future estimates by financial analysts of market

minus T-Bond. Could use IBES estimate of firms

returns, building to rM.

Whats the DCF cost of equity, rs? Given D0

4.19P0 50 g 5.

Estimating the Growth Rate

- Use the historical growth rate if you believe the

future will be like the past. - Obtain analysts estimates Value Line, Zacks,

Yahoo!.Finance. - Use the earnings retention model, illustrated on

next slide.

Suppose the company has been earning 15 on

equity (ROE 15) and retaining 35 (dividend

payout 65), and this situation is expected to

continue. Whats the expected future g?

Retention growth model g b(ROE) 0.35(15)

5.25. Here b Fraction retained. Close to g

5 given earlier. Intuitive notion Think of

bank account paying 10 with b 0, b 1.0, and

b 0.5. Whats g?

Could DCF methodology be applied if g is not

constant?

- YES, nonconstant g stocks are expected to have

constant g at some point, generally in 5 to 10

years. - But calculations get a little complicated yet

still just the PV of all future dividends. See

FM11 ch.9 Tool Kit.xls

Non-Constant growth in Divs

- P0 D1/(1ks) D2/(1ks)2 D3/(1ks)3

Dn/(1ks)n Dn1/(ks-g)/(1ks)n - Dividend Stream

D1 D2 D3

Dn Dn1

Pn Dn1/(ks-g)

PO

Find ks using the own-bond-yield-plus-risk-premium

method. (rd 10, RP 4.)

rs rd RP 10.0 4.0 14.0

- This RP ¹ CAPM RPM.
- Produces ballpark estimate of rs. Useful check.

Whats a reasonable final estimate of rs?

Method

Estimate

CAPM

14.2

DCF

13.8

rd

RP

14.0

Average

14.0

How do we find the cost of new common stock, re?

Three steps

Use DCF formula, but adjust P0 for flotation

cost. Compare DCF re with DCF rs to determine

flotation adjustment. Apply flotation adjustment

to final rs estimate.

New common F 15 re

g 5.0

5.0 15.4. But, re based solely on

DCF method.

D0(1 g) P0(1 - F)

4.19(1.05) 50(1 - 0.15)

4.40 42.50

Flotation adjustment re(DCF) - rs(DCF)

15.4 - 13.8 1.6 . Add the 1.6 flotation

adjustment to final rs 14 to find final

ke re rs Float adjustment 14

1.6 15.6.

Comments about flotation costs

- See Table
- Flotation costs depend on the risk of the firm,

the size of the issue, and the type of capital

being raised.

Why is re rs?

- Investors expect to earn rs.
- If Company gets money as RE it earns rs

everythings Cool! - But when investors buy new stock F pulled out

so must earn rs on funds company receives to

provide rs on money investors put up.

Example

1. rs 10 F 20. 2. Investors put up 100,

expect to earn 0.1(100) 10. 3. But, after F,

company nets only 80. (Who gets the

20?) 4 Company needs to earn 12.5 on the 80 to

pay 10 to investors. 5. i.e. Need to earn re

10/0.8 12.5. 6. Conclusion re 12.5 rs

10.0.

Estimating Weights for the Capital Structure

- If you dont know the targets, it is better to

estimate the weights using current market values

than current book values. - If you dont 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.

(More...)

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.

(More...)

- 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

Whats the WACC1?

WACC1 wdrd(1 - T) wpsrps wcers

0.3(10)(0.6) 0.1(9) 0.6(14) 1.8 0.9

8.4 11.1.

Cost per dollar until Retained earnings are used

up.

WACC Estimates for Some Large U. S. Corporations

WACC with new CommonStock

WACC2 wdrd(1 - T) wpsrps wcere

0.3(10)(0.6) 0.1(9) 0.6(15.6) 1.8

0.9 9.4 12.1.

Summary to this point

re or rs WACC Debt Pfd RE

14.0 11.1 Debt Pfd NCS 15.6 12.1 WACC

rises because equity cost increases. (WHY?)

Define the MCC schedule.

- MCC shows cost of each dollar raised.
- Each dollar consists of 0.30 of debt, 0.10 of

Pfd, and 0.60 of equity (RE or new CS). - First dollars cost WACC1 11.1, then WACC2

12.1. - Where does the WACC change?

How large will capital budget be before company

must issue new CS?

Debt 0.3 Capital raised Preferred 0.1

Capital raised Equity 0.6 Capital raised

1.0 Total capital When only retained

earnings are used for equity Equity RE 0.6

Capital raised, so Capital raised(at BP) RE/0.6.

Find retained earnings break point.

Dollars of RE Fraction of equity

BPRE 500,000.

300,000 0.60

500,000 total can be financed with RE, debt, and

preferred.

Alternative explanation

(No Transcript)

WACC ()

WACC1 11.1

15

WACC2 12.1

10

500 2,000

Dollars of New Capital (in thousands)

How large should our capital budget be?

Investment Opportunities (Capital Budgeting

Projects)

A 700,000 17.0 B 500,000 15.0 C

800,000 11.5 2,000,000

Which to accept?

A 17

B 15

MCC

12.1

11.1

IOS

C11.5

Cap. budget

500

1,200

2,000

- Projects A and B would be accepted (IRR exceeds

the MCC). - Project C would be rejected (IRR is less than the

MCC). - Capital budget 1.2 million.
- WACC 12.1

Would the MCC (slide 60) remain constant beyond

the RE breakpoint?

- No. WACC would eventually rise above 12.1.
- Cost of debt, preferred stock would rise.
- Large increases in capital budget may also

increase the perceived risk of the firm,

increasing WACC.

What factors influence a companys WACC?

- Market conditions, especially interest rates and

tax rates. - The firms capital structure and dividend policy.
- The firms investment policy. Firms with riskier

projects generally have a higher WACC.

What effect does depreciation have on the MCC

schedule?

- Depreciation is a noncash expense.
- Depreciation cash flow is available for dividends

or retained earnings, e.g., could repurchase debt

or stock. - These funds therefore have an opportunity cost

equal to the WACC using retained earnings, 11.1. - This will shift the MCC schedule outward by the

of depreciation.

Would depreciation affect the acceptability of

proposed capital budgeting projects and the size

of the total capital budget?

Possibly. If the lower cost MCC is shifted to

the right, the cost of capital used to evaluate

projects may be lower. (Slide 49, again)

Four Mistakes to Avoid

1. When estimating the cost of debt, use the

current interest rate on new debt, not the coupon

rate on existing debt. 2. When estimating the

risk premium for the CAPM approach, dont

subtract the current long-term T-bond rate from

the historical average return on common stocks

rs rRF (rM - rRF )?

(More ...)

- For example, if the historical rM has been about

12.7 and inflation drives the current rRF up to

10, the current market risk premium is not 12.7

- 10 2.7!

(More ...)

WACC1 wdrd(1 - T) wpsrps wcers

3. Use the target capital structure to determine

the weights. If you dont know the target

weights, then use the current market value of

equity, and never the book value of equity. If

you dont know the market value of debt, then the

book value of debt often is a reasonable

approximation, especially for short-term debt.

(More...)

4. Capital components are sources of funding that

come from investors. Accounts payable, accruals,

and deferred taxes are not sources of funding

that come from investors, so they are not

included in the calculation of the WACC. We do

adjust for these items when calculating the cash

flows of the project, but not when calculating

the WACC.

Should the company use the composite WACC as the

hurdle rate for each of its projects?

- NO! The composite WACC reflects the risk of an

average project undertaken by the firm.

Therefore, the WACC only represents the hurdle

rate for a typical project with average risk. - Different projects have different risks. The

projects WACC should be adjusted to reflect the

projects risk. - See following case.

Risk and the Cost of Capital

Divisional Cost of Capital

Division or Project Cost of Capital

Methods for estimating a divisions or a

projects beta

- Pure play. Find several publicly traded

companies exclusively in projects business. Use

average of their betas as proxy for projects

beta. Hard to find such companies.

- Accounting beta. Run regression between

projects ROA and SP index ROA. Accounting

betas are correlated (0.5-0.6) with market

betas. But normally cant get data on new

projects ROAs before the capital budgeting

decision has been made.

Should the company use the composite WACC as the

hurdle rate for each of its divisions?

- NO! The composite WACC reflects the risk of an

average project undertaken by the firm. - Different divisions may have different risks.

The divisions WACC should be adjusted to reflect

the divisions risk and capital structure.

What procedures are used to determine the

risk-adjusted cost of capital for a particular

division?

- Estimate the cost of capital that the division

would have if it were a stand-alone firm. - This requires estimating the divisions beta,

cost of debt, and capital structure.

Methods for Estimating Beta for a Division or a

Project

- 1. Pure play. Find several publicly traded

companies exclusively in projects business. - Use average of their betas as proxy for

projects beta. - Hard to find such companies.

- 2. Accounting beta. Run regression between

projects ROA and SP index ROA. - Accounting betas are correlated (0.5 0.6) with

market betas. - But normally cant get data on new projects

ROAs before the capital budgeting decision has

been made.

Find the divisions market risk and cost of

capital based on the CAPM, given these inputs

- Target debt ratio 10.
- rd 12.
- rRF 7.
- Tax rate 40.
- betaDivision 1.7.
- Market risk premium 6.

- Beta 1.7, so division has more market risk than

average. - Divisions required return on equity
- rs rRF (rM rRF)bDiv.
- 7 (6)1.7 17.2.
- WACCDiv. wdrd(1 T) wcrs
- 0.1(12)(0.6) 0.9(17.2)
- 16.2.

How does the divisions WACC compare with the

firms overall WACC?

- Division WACC1 16.2 versus company WACC1

11.1. - Typical projects within this division would be

accepted if their returns are above 16.2.

Divisional Risk and the Cost of Capital

Recall what are the three types of project risk?

- Stand-alone risk
- Corporate risk
- Market risk

How is each type of risk used?

- Stand-alone risk is easiest to calculate.
- Market risk is theoretically best in most

situations. - However, creditors, customers, suppliers, and

employees are more affected by corporate risk. - Therefore, corporate risk is also relevant.

A Project-Specific, Risk-Adjusted Cost of Capital

- Start by calculating a divisional cost of

capital. - Estimate the risk of the project using the

techniques in Chapter 11. - Use judgment to scale up or down the cost of

capital for an individual project relative to the

divisional cost of capital.

Why is the cost of internal equity from

reinvested earnings cheaper than the cost of

issuing new common stock?

1. When a company issues new common stock they

also have to pay flotation costs to the

underwriter. 2. Issuing new common stock may send

a negative signal to the capital markets, which

may depress stock price.

Estimate the cost of new common equity P050,

D04.19, g5, and F15.

Estimate the cost of new 30-year debt

Par1,000, Coupon10paid annually, and F2.

- Using a financial calculator
- N 30
- PV 1000(1-.02) 980
- PMT -(.10)(1000)(1-.4) -60
- FV -1000
- Solving for I 6.15

Part 2 The Optimal Capital Budget Chapter 11,

appendix

- Weve seen how to evaluate projects.
- We need cost of capital for evaluation.
- But corporate cost of capital depends on size of

capital budget. - Must combine MCC and IOS schedules to get

corporate cost of capital.

HANDOUT on Optimal Capital Budget

- BLUM Industries

Blum Industries has 5 potential projects

Project Cost CF Life (N) IRR

A 400,000 119,326 5 15 B 200,000 56,863 5 13

B 200,000 35,397 10 12 C 100,000 27,057 5 11 D

300,000 79,139 5 10

Projects B B are mutually exclusive, the

others are independent. Neither B nor B will be

repeated.

Additional information

Interest rate on new debt 8.0 Tax

rate 40.0 Debt ratio 60.0 Current stock

price, P0 20.00 Last dividend, D0 2.00 Expected

growth rate, g 6.0 Flotation cost on CS,

F 19.0 Expected addition to RE

200,000 (NI 500,000, Payout 60.)

For differential project risk, add or sub-tract

2 to WACC.

Calculate WACC, then plot IOS and MCC schedules.

Step 1 Estimate the cost of equity

Which method should we use?

D0(1 g) P0

2(1.06) 20

rs g 6

16.6. re g

6 6 19.1.

D1 P0(1 - F)

2(1.06) 20(1 - 0.19)

2.12 16.2

Step 2 Estimate the WACCs

WACC1 wdrd(1 - T) wcers (0.6)(8)(0.6)

0.4(16.6) 9.5. WACC2 wdrd(1 - T)

wcere (0.6)(8)(0.6) 0.4(19.1) 10.5.

Step 3 Estimate the RE break point

Retained earnings Equity fraction

BPRE 500,000.

200,000 0.4

Each dollar up to 500,000 has 0.40 of RE at

cost of 16.6, then WACC rises.

FIGURE 1

16

A

15

14

B

13

B

12

WACC2 10.5

C

11

MCC

WACC1 9.5

10

IOS

D

9

8

7

700

500

New Capital (000s)

- The IOS schedule plots projects in descending

order of IRR. - Two potential IOS schedules--one with A, B, C,

and D and another with A, B, C, and D. - The WACC has a break point at 500,000 of new

capital.

What corporate cost of capital do we use for

capital budgeting, i.e., for calculating NPV?

- Corporate r WACC that exists where IOS and MCC

schedules intersect. In this case, Corporate r

10.5.

If all 5 projects are average risk, whats the

optimal capital budget?

- Corporate r 10.5.
- IRR and NPV lead to same decisions for

independent projects. Thus, all independent

projects with IRRs above 10.5 should be

accepted. - Therefore, accept A and C, reject D, and accept B

or B.

- NPV and IRR can conflict for mutually exclusive

projects. - NPV method is better, so choose between B and B

based on NPV at WACC 10.5. - NPVB 12,905 NPVB 12,830, so choose B

over B?.

Suppose you arent sure of Corporate k. At what

k would B and B have the same NPV?

Get differences CF0 200,000 - 2000,000

0 CF1- 5 56,863 - 35,397 21,466 CF6-10 0

- 35,397 -35,397 Indifference r IRR

10.52

Including Depreciation

- Suppose that you discovered that 400 of

depreciation existed, that you hadnt considered

before. Now what would your decision be?

(Return to slide 75 to see picture)

Adjusting for RISK

The risk-adjusted rates are as follows

Project r 10.5 2

Suppose

Project Risk

Project Req. ret.

Low C, D

8.5

Average B, B

10.5

High A

12.5

Now the optimal capital budget consists of A, B

(or B), C, and D, for a total of 1,000,000.

(f) Divisional Hurdle rates

- Companies often have so many projects that you

cant plot a IOS. Then what? - Suppose the company has three divisions L, A and

H for low risk, average risk and high risk

- Division Proj. Risk Proj k
- Low 6.5
- Average 8.5
- High 10.5
- Low 8.5
- Average 10.5
- High 12.5
- Low 12.5
- Average 14.5
- High 16.5

Low

Average

High

ENOUGH!