9 - 1

WACC1 = wd*rd(1 - T) + wpsrps + wcers

WACC2 = wd*rd(1 - T) + wpsrps + wcere

9 - 2

CHAPTER 9The Cost of Capital

Cost of capital componentsDebtPreferredCommon equity

WACCMCCIOS

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

9 - 3

What sources of capital should be included in a firm’s WACC?

Long-term debtPreferred stockCommon equity:

Retained earningsNew common stock

Short term debt?

9 - 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 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.

9 - 5

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.

9 - 6

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.

9 - 7

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

Only rd needs adjustment:rd(1-T) = rd - T x rd whererd = cost of debt, and T x rd = Tax savings due to using debt.

9 - 8

Should we focus on historical (embedded) costs or new (marginal)

costs?

The cost of capital is used primarilyto make decisions which involveraising new capital. So, focus ontoday’s marginal costs.

9 - 9

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 company’s debt, if it has any.

Focus on method 3, to start.

9 - 10

What’s rd? Coupon = 12% semi; Price = $1,153.72; 15 years.

60 60 + 1,00060

0 1 2 30rd = ?

30 -1153.72 60 1000

5.0% x 2 = rd = 10%

EAR =? Should we use it?

N I/YR PV FVPMT

-1,153.72

INPUTS

OUTPUT

9 - 11

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 banker’s for their estimate (method 1).

N.b. If the bond is callable, the YTC rather than the YTM may be appropriate.

9 - 12

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.

9 - 13

What’s the cost of preferred stock? Pps = $113.10; 10%Q; Par = $100; F = $2.

Use this formula:

rps = =

= = 0.025 = 2.25%.Qtrly.

0.25($100) $113.10 - $2.00

Dps

PNet

$2.50 $111.10

9 - 14

Picture of Preferred

2.50 2.50

0 1 2kps = ?

-111.1

ì

111.10 = = .

rPer = = 2.25; rps(Nom) = 2.25(4) = 9%.

Dps

rps

2.50rPer

2.50 111.10

2.50

9 - 15

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.

9 - 16

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

• Risk Return

Debt

Preferred

Equity

9 - 17

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

• Risk Return

Debt

Preferred

Equity

9 - 18

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?

9 - 19

`Illustration: Preferred vs. debt for

same company or similar companies.

rps = 9.5% rd = 11.4%

Is this is as expected?.

Recent data for RJR:

9 - 20

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.

9 - 21

Illustration: Preferred vs. debt for same company or similar companies.

rps = 9.5% rd = 11.4%

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 looks strange!. Suppose T = 40%

This is as expected.Riskier preferred has higher AT rate.

Before tax for RJR:

9 - 22

.

What are the two ways that companies can raise common equity?

9 - 23

Companies can issue new shares of common stock.

Companies can reinvest earnings.

What are the two ways that companies can raise common equity?

9 - 24

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.

9 - 25

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.

9 - 26

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-Yield-Plus-Risk Premium:

rs = rd + Bond RP.

9 - 27

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

rRF = 7%, RPM = 6%, β = 1.2.

rs = rRF + (rM - rRF ) .

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

9 - 28

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…

9 - 29

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.

9 - 30

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.

Explain the differences amonghistorical betas, adjusted betas,

and fundamental betas.

(More...)

9 - 31

Fundamental betas are adjusted further to include changes in a company’s 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.

9 - 32

Ex post datae.g., Ibottson and Assoc. provides this on an annual basis :RPM = 6.2% for 1926-1999.

Future estimates by financial analystsof market minus T-Bond. Could use IBES estimate of firm’s returns, building to rM.

How can RPM be measured?

9 - 33

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%.

9 - 34

Estimating the Growth Rate

Use the historical growth rate if you believe the future will be like the past.

Obtain analysts’ estimates: Value Line, Zack’s, Yahoo!.Finance.

Use the earnings retention model, illustrated on next slide.

9 - 35

Suppose the company has been earning 15% on equity (ROE = 15%) and retaining 35% (dividend payout = 65%), and this situation is expected to continue.

What’s the expected future g?

9 - 36

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. What’s g?

9 - 37

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

9 - 38

Non-Constant growth in Div’s

P0 = D1/(1+ks) + D2/(1+ks)2 + D3/(1+ks)3 +…+ Dn/(1+ks)n + [Dn+1/(ks-g)]/(1+ks)n

Dividend Stream:

D1 D2 D3 Dn Dn+1

Pn = Dn+1/(ks-g)PO

9 - 39

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

(rd = 10%, RP = 4%.)

This RP CAPM RPM.

Produces ballpark estimate of rs. Useful check.

rs = rd + RP

= 10.0% + 4.0% = 14.0%

9 - 40

What’s a reasonable final estimate of rs?

Method Estimate

CAPM 14.2%

DCF 13.8%

rd + RP 14.0%

Average 14.0%

9 - 41

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

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.

Three steps:

9 - 42

New common F = 15%:

re = + g

= + 5.0%

= + 5.0% = 15.4%.

But, re based solely on DCF method.

$4.40 $42.50

D0(1 + g)

P0(1 - F)

$4.19(1.05) $50(1 - 0.15)

9 - 43

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%.

9 - 44

Comments about flotation costs:

See TableFlotation costs depend on the risk of

the firm, the size of the issue, and the type of capital being raised.

9 - 45

Why is re > rs?

Investors expect to earn rs.

If Company gets money as RE; it earns rs; everything’s 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.

9 - 46

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%.

9 - 47

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.

(More...)

9 - 48

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...)

9 - 49

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

9 - 50

What’s 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.

9 - 51

WACC Estimates for Some Large U. S. Corporations

Company WACC wd

Intel (INTC) 16.0 2.0%Dell Computer (DELL) 12.5 9.1%BellSouth (BLS) 10.3 39.8%Wal-Mart (WMT) 8.8 33.3%Walt Disney (DIS) 8.7 35.5%Coca-Cola (KO) 6.9 33.8%H.J. Heinz (HNZ) 6.5 74.9%Georgia-Pacific (GP) 5.9 69.9%

9 - 52

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%.

9 - 53

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?)

9 - 54

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?

9 - 55

How large will capital budget be before company must issue new CS?

Debt= 0.3 Capital raisedPreferred= 0.1 Capital raisedEquity = 0.6 Capital raised

= 1.0 Total capital

When only retained earnings are used for equity:Equity = RE = 0.6 Capital raised, soCapital raised(at BP) = RE/0.6.

Debt= 0.3 Capital raisedPreferred= 0.1 Capital raisedEquity = 0.6 Capital raised

= 1.0 Total capital

When only retained earnings are used for equity:Equity = RE = 0.6 Capital raised, soCapital raised(at BP) = RE/0.6.

9 - 56

Find retained earnings break point.

BPRE=

= = $500,000.

$500,000 total can be financed with RE, debt, and preferred.

Dollars of RE Fraction of equity

$300,0000.60

Alternative explanation:

9 - 57

0.3 0.1 0.6FundsRaised Debt kd Preferred kps Equity ks, ke WACC

100 30 0.1 10 0.09 60 0.14 0.111200 60 0.1 20 0.09 120 0.14 0.111300 90 0.1 30 0.09 180 0.14 0.111400 120 0.1 40 0.09 240 0.14 0.111500 150 0.1 50 0.09 300 0.156 0.121600 180 0.1 60 0.09 360 0.156 0.121700 210 0.1 70 0.09 420 0.156 0.121800 240 0.1 80 0.09 480 0.156 0.121900 270 0.1 90 0.09 540 0.156 0.121

1000 300 0.1 100 0.09 600 0.156 0.121

9 - 58WACC (%)

Dollars of New Capital(in thousands)

15

10

$500 $2,000

WACC1 = 11.1%WACC2 = 12.1%

How large should our capital budget be?

9 - 59

Investment Opportunities(Capital Budgeting Projects)

Which to accept?

A $ 700,000 17.0%

B 500,000 15.0%

C 800,000 11.5%

$2,000,000

9 - 60

A =17%B =15%

11.112.1

IOS

MCC

%

500 1,200 2,000 $

Cap. budgetC=11.5%

9 - 61

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%

9 - 62

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.

9 - 63

What factors influence a company’s WACC?

Market conditions, especially interest rates and tax rates.

The firm’s capital structure and dividend policy.

The firm’s investment policy. Firms with riskier projects generally have a higher WACC.

9 - 64

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.

What effect does depreciation haveon the MCC schedule?

9 - 65

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)

Would depreciation affect the acceptability of proposed capital

budgeting projects and the size of the total capital budget?

9 - 66

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, don’t subtract the current long-term T-bond rate from the historical average return on common stocks: rs= rRF + (rM - rRF )

(More ...)

9 - 67

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 ...)

9 - 68

3. Use the target capital structure to determine the weights.

If you don’t know the target weights, then use the current market value of equity, and never the book value of equity.

If you don’t know the market value of debt, then the book value of debt often is a reasonable approximation, especially for short-term debt. (More...)

WACC1 = wdrd(1 - T) + wpsrps + wcers

9 - 69

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.

9 - 70

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 project’s WACC should be adjusted to reflect the project’s risk.

See following case.

9 - 71

Risk and the Cost of Capital

Rate of Return(%)

WACC

Rejection Region

Acceptance Region

Risk

L

B

A

H12.0

8.0

10.010.5

9.5

0 RiskL RiskA RiskH

9 - 72

Divisional Cost of CapitalRate of Return

(%)WACC

Project H

Division H’s WACC

Risk

Project LComposite WACCfor Firm A

13.0

7.0

10.0

11.0

9.0

Division L’s WACC

0 RiskL RiskAverage RiskH

9 - 73

Division or Project Cost of Capital

9 - 74

Methods for estimating a division’s or a project’s beta

Pure play. Find several publicly traded companies exclusively in project’s business. Use average of their betas as proxy for project’s beta.

Hard to find such companies.

9 - 75

Accounting beta. Run regression between project’s ROA and S&P index ROA.

Accounting betas are correlated (0.5-0.6) with market betas.

But normally can’t get data on new projects’ ROAs before the capital budgeting decision has been made.

9 - 76

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 division’s WACC should be adjusted to reflect the division’s risk and capital structure.

9 - 77

Estimate the cost of capital that the division would have if it were a stand-alone firm.

This requires estimating the division’s beta, cost of debt, and capital structure.

What procedures are used to determine the risk-adjusted cost of capital for a

particular division?

9 - 78

Methods for Estimating Beta for a Division or a Project

1. Pure play. Find several publicly traded companies exclusively in project’s business.

Use average of their betas as proxy for project’s beta.

Hard to find such companies.

9 - 79

2. Accounting beta. Run regression between project’s ROA and S&P index ROA.

Accounting betas are correlated (0.5 – 0.6) with market betas.

But normally can’t get data on new projects’ ROAs before the capital budgeting decision has been made.

9 - 80

Find the division’s 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%.

9 - 81

Beta = 1.7, so division has more market risk than average.

Division’s 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%.

9 - 82

How does the division’s WACC compare with the firm’s 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%.

9 - 83

Divisional Risk and the Cost of Capital

Rate of Return (%)

WACC

Rejection Region

Acceptance Region

Risk

L

B

A

H WACCH

WACCL

WACCA

0 RiskL RiskA RiskH

9 - 84

Recall what are the three types of project risk?

Stand-alone riskCorporate riskMarket risk

9 - 85

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.

9 - 86

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.

9 - 87

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.

Why is the cost of internal equity from reinvested earnings cheaper than the cost of issuing new common stock?

9 - 88

Estimate the cost of new common equity: P0=$50, D0=$4.19, g=5%, and

F=15%.

gFP

gDre

)1(

)1(

0

0

%.4.15%0.550.42$

40.4$

%0.515.0150$05.119.4$

9 - 89

Estimate the cost of new 30-year debt: Par=$1,000, Coupon=10%paid annually,

and F=2%.

Using a financial calculator:N = 30PV = 1000(1-.02) = 980PMT = -(.10)(1000)(1-.4) = -60FV = -1000

Solving for I: 6.15%

9 - 90

Part 2: The Optimal Capital Budget: Chapter 11, appendix

We’ve 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.

9 - 91

HANDOUT on Optimal Capital Budget

BLUM Industries

9 - 92

Blum Industries has 5 potential projects

Projects B & B* are mutually exclusive, the others are independent. Neither B nor B* will be repeated.

Project Cost CF Life (N) IRR

A $400,000 $119,326 5 15%B 200,000 56,863 5 13B* 200,000 35,397 10 12C 100,000 27,057 5 11D 300,000 79,139 5 10

9 - 93

Additional information

For differential project risk, add or sub-tract 2% to WACC.

Interest rate on new debt 8.0%Tax rate 40.0%Debt ratio 60.0%Current stock price, P0 $20.00Last dividend, D0 $2.00Expected growth rate, g 6.0%Flotation cost on CS, F 19.0%Expected addition to RE $200,000 (NI = $500,000, Payout = 60%.)

9 - 94

Calculate WACC, then plot IOS and MCC schedules.

Step 1: Estimate the cost of equity

rs = + g = + 6% = 16.6%.

re = + g = + 6%

= + 6% = 19.1%.

D0(1 + g)P0

$2(1.06)$20

D1

P0(1 - F) $2(1.06) $20(1 - 0.19)

$2.12$16.2

Which method should we use?

9 - 95

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%.

9 - 96

Each dollar up to $500,000 has $0.40of RE at cost of 16.6%, then WACC rises.

BPRE=

= = $500,000.

Retained earningsEquity fraction

$200,0000.4

Step 3: Estimate the RE break point

9 - 97

500 700

%

New Capital (000s)

FIGURE 1

B

A

WACC1 = 9.5%

C

D

B*WACC2 = 10.5%

MCCIOS

7

8

9

10

11

12

13

14

15

16

9 - 98

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.

9 - 99

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%.

9 - 100

If all 5 projects are average risk, what’s 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*.

9 - 101

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?.

minics11.xls

9 - 102

Suppose you aren’t 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 = -35,397Indifference r = IRR = 10.52%

9 - 103

Including Depreciation

Suppose that you discovered that $400 of depreciation existed, that you hadn’t considered before. Now what would your decision be? (Return to slide 75 to see picture)

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Project r = 10.5% ± 2%

The risk-adjusted rates are as follows:

Project Risk Project Req. ret.Low: C, D 8.5%Average: B, B* 10.5High: A 12.5

Adjusting for RISK:

Suppose

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Now the optimal capital budget consists of A, B (or B*), C, and D, for a total of $1,000,000.

one

IRR Project k

A 15% 12.5% AcceptB 13 10.5 AcceptB* 12 10.5 AcceptC 11 8.5 AcceptD 10 8.5 Accept

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(f) Divisional Hurdle rates

Companies often have so many projects that you can’t plot a IOS. Then what?

Suppose the company has three divisions: L, A and H for low risk, average risk and high risk

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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

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