corporate financial theory

CORPORATE FINANCIALTHEORYLecture 3

Interest Rate and Cash Flow - REALITY

rC

PV

Is not guaranteed

Has many different sources

Beta and the COC• Company cost of capital (COC) is based on the average beta of the assets

• The average beta of the assets is based on the % of funds in each asset• Assets = debt + equity

VE

VD

equitydebtassets βββ

0

20

0 0.2 0.8 1.2

Expected return (%)

Bdebt Bassets Bequity

Rdebt = 8

Rassets = 12.2Requity =

15

Beta and the COC

Company Cost of Capitalsimple approach

Company Cost of Capital (COC) is based on the average beta of the assets

The average Beta of the assets is based on the % of funds in each asset

Assets = Debt + Equity

equityequityDebtDebtassets rrr %%

COCCapital ofCost assetsr

IMPORTANT

E, D, and V are all market values of Equity, Debt and Total Firm Value

Company Cost of Capital

Shareper Price shares # Equity of ValueMarket

Debt of ValueMarket

Er

InterestD

EDV

debt

VE

equityVD

debtassets rrr

)(bondson YTM

fmfequity

debt

rrBrCAPMrr

Weighted Average Cost of Capital

VEr

VDrTrWACC EDcA 1

WACC is the traditional view of capital structure, risk and return.

Weighted Average Cost of Capitalwithout taxes & bankruptcy risk

r

DV

rD

rE

r

DV

rD

rE

WACC

Weighted Average Cost of Capitalwithout taxes & bankruptcy risk

DV

rD

rE

Includes Bankruptcy Risk

Weighted Average Cost of Capitalwithout taxes & bankruptcy risk

r

r

DV

rD

rE

Weighted Average Cost of Capitalwithout taxes & bankruptcy risk

Includes Bankruptcy Risk

r

DV

rD

rE

WACC

Weighted Average Cost of Capitalwithout taxes & bankruptcy risk

Includes Bankruptcy Risk

r

DV

WACCr*

D*

Weighted Average Cost of Capitalwithout taxes & bankruptcy risk

Includes Bankruptcy Risk

• Company cost of capital (COC) is based on average beta of assets• Average beta of assets is based on the % of funds in each asset

• Example1/3 new ventures β = 2.01/3 expand existing business β = 1.31/3 plant efficiency β = 0.6AVG β of assets = 1.3

Beta and the COC

• Company Cost of Capital

Beta and the COC

10%nologyknown tech t,improvemenCost COC)(Company 15%business existing ofExpansion

20%products New30% ventureseSpeculativ

RateDiscount Category

Project riskAllowing for Possible Bad Outcomes

ExampleProject Z will produce one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at 10% company COC:

100,909$1.1000,000,1

1PV 1

rC

Project riskAllowing for Possible Bad Outcomes

Example, continuedCompany’s engineers are behind schedule developing technology for project. There is a small chance that it will not work. Most likely outcome still $1 million, but some chance that project Z will generate zero cash flow next year:

Project riskAllowing for Possible Bad Outcomes

Example, continuedIf technological uncertainty introduces a 10% chance of zero cash flow, unbiased forecast could drop to $900,000:

000,818$1.1000,900PV

Risk, DCF and CEQ

Risk, Discounted Cash Flow (DCF), and Certainty Equivalents (CEQ)

tf

tt

t

rrC

)1(CEQ

)1(PV

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?

%12)8(75.6

)(

fmf rrBrr

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?

%12)8(75.6

)(

fmf rrBrr

240.2 PVTotal71.2100379.7100289.31001

12% @ PV FlowCashYearAProject

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?

%12)8(75.6

)(

fmf rrBrr

240.2 PVTotal71.2100379.7100289.31001

12% @ PV FlowCashYearAProject

Now assume that the cash flows change, but are RISK FREE. What is the new PV?

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

240.2 PVTotal71.284.8379.789.6289.394.61

6% @ PV FlowCashYearProject B

240.2 PVTotal71.2100379.7100289.31001

12% @ PV FlowCashYearAProject

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

240.2 PVTotal71.284.8379.789.6289.394.61

6% @ PV FlowCashYearProject B

240.2 PVTotal71.2100379.7100289.31001

12% @ PV FlowCashYearAProject

Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project? DEDUCTION FOR RISK

15.284.8100310.489.610025.494.61001

riskfor Deduction

CEQFlowCash Year

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

The difference between the 100 and the certainty equivalent (94.6) is 5.4%…this % can be considered the annual premium on a risky cash flow

flow cash equivalentcertainty 054.1

flow cashRisky

Risk,DCF and CEQExample

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

8.84054.1100 3Year

6.89054.1100 2Year

6.94054.1

100 1Year

3

2

Capital Budgeting & RiskInvest in highest NPV project

Need Discount rate to get NPV

Use CAPM to get discount rate

Modify CAPM (account for proper risk)

Modify Cash Flows

Capital Budgeting & RiskSensitivity Analysis - Analysis of the effects of

changes in sales, costs, etc. on a project.Scenario Analysis - Project analysis given a

particular combination of assumptions.Simulation Analysis (Monte Carlo) - Estimation of

the probabilities of different possible outcomes.Break Even Analysis - Analysis of the level of sales

(or other variable) at which the company breaks even.

Decision Trees – Binomial model in which outcomes are path dependent.

Real Options – The value of flexibility.

Sensitivity AnalysisExample

Given the expected cash flow forecasts for Otobai Company’s Motor Scooter project, listed on the next slide, determine the NPV of the project given changes in the cash flow components using a 10% cost of capital. Assume that all variables remain constant, except the one you are changing.

Sensitivity AnalysisExample - continued

Possible Outcomes

bil 2bil 3bil 4Cost Fixed275,000300,000360,000CostVar Unit 380,000375,000350,000priceUnit

.16.1.04ShareMarket mil 1.1mil 1.0mil .9SizeMarket

OptimisticExpectedcPessimistiVariableRange

Sensitivity AnalysisExample - continued

NPV Possibilities (Billions Yen)

6.53.40.4Cost Fixed11.13.415.0-CostVar Unit 5.03.44.2-priceUnit

17.33.410.4-ShareMarket 5.73.41.1SizeMarket

OptimisticExpectedcPessimistiVariableRange

Sensitivity Analysis

315- FlowCashNet 3.0flow cash Operating1.5after taxProfit 1.550% @ .Taxes3profitPretax 1.5onDepreciati3Costs Fixed

30Costs Variable37.5Sales

15-Investment10-1 Years0Year

NPV= 3.43 billion Yen

Sensitivity AnalysisExample - continued

Possible Outcomes

bil 2bil 3bil 4Cost Fixed275,000300,000360,000CostVar Unit 380,000375,000350,000priceUnit

.16.1.04ShareMarket mil 1.1mil 1.0mil .9SizeMarket

OptimisticExpectedcPessimistiVariableRange

Sensitivity AnalysisNPV Calculations for Optimistic Market Size Scenario

NPV= +5.77 bil yen

3.3815- FlowCashNet 3.38flow cash Operating1.88after taxProfit 1.8850% @ .Taxes3.75profitPretax 1.5onDepreciati3Costs Fixed

33Costs Variable41.25Sales

15-Investment10-1 Years0Year

Sensitivity AnalysisExample - continued

NPV Possibilities (Billions Yen)

6.53.40.4Cost Fixed11.13.415.0-CostVar Unit 5.03.44.2-priceUnit

17.33.410.4-ShareMarket 5.73.41.1SizeMarket

OptimisticExpectedcPessimistiVariableRange

Break Even AnalysisAccounting break-even does not consider time value of money Otobai Motors has accounting break-even point of 60,000 units sold

60 200

Sales, thousands

Accounting revenue and

costs (Yen)Billions

60

40

20

Break -evenProfit =0

Revenues

Costs

Break Even AnalysisPoint at which NPV=0 is break-even pointOtobai Motors has a break-even point of 85,000 units sold

Sales, thousands

PV (Yen)Billions

400

200

19.6

85 200

Break-evenNPV = 0

PV inflows

PV Outflows

Monte Carlo Simulation

Step 1: Modeling the Project Step 2: Specifying Probabilities Step 3: Simulate the Cash Flows Step 4: Calculate NPV

Modeling Process

Monte Carlo Simulation

Decision Trees

NPV=0

Don’t test

Test (Invest $200,000)

Success

Failure

Pursue project NPV=$2million

Stop project

NPV=0

Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

+150(.6)

+30(.4)

+100(.6)

+50(.4)

-550

NPV= ?

-250

NPV= ?

-150

0or

Turboprop

Piston

Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

+150(.6)

+30(.4)

+100(.6)

+50(.4)

-550

NPV= ?

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NPV= ?

-150

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812

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Decision Trees960 (.8)

220(.2)

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100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

+150(.6)

+30(.4)

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NPV= ?

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Decision Trees960 (.8)

220(.2)

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100(.6)

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NPV= ?

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812

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+150(.6)

+30(.4)

+100(.6)

+50(.4)

NPV=444.55

NPV=888.18

NPV=550.00

NPV=184.55

*450

331

18.88815010.1

812

Turboprop

Piston

Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

812

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+150(.6)

710.73

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403.82

+50(.4)

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0

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or

NPV=444.55

NPV=888.18

NPV=550.00

NPV=184.55

-550

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40.55.44460.18.888

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Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

812

456

660

364

148

+150(.6)

710.73

+30(.4)

+100(.6)

403.82

+50(.4)

-550

NPV=96.12

-250

NPV=117.00

-150

0

*450

331

or

NPV=444.55

NPV=888.18

NPV=550.00

NPV=184.55

12.9655010.1

73.710

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Piston

Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

-550

NPV= ?

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+150(.6)

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Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

812

456

660

364

148

+150(.6)

710.73

+30(.4)

+100(.6)

403.82

+50(.4)

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NPV=96.12

-250

NPV=117.00

-150

0

*450

331

or

NPV=444.55

NPV=888.18

NPV=550.00

NPV=184.55

Turboprop

Piston

Flexibility & Real OptionsDecision Trees - Diagram of sequential

decisions and possible outcomes. Decision trees help companies determine

their Options by showing the various choices and outcomes.

The Option to avoid a loss or produce extra profit has value.

The ability to create an Option thus has value that can be bought or sold.

Corporate Real Options1. Option to expand (make follow up investment)

2. Option to abandon3. Timing option (wait and invest later)4. Flexible production facilities

Value = NPV with option - NPV w/o option

Value = Black Scholes approach

Corporate Real OptionsExample - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for

$150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Use a discount rate of 10%

Corporate Real OptionsExample - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for

$150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Year 0 Year 1 Year 2

120 (.6) 100 (.6) 90 (.4)NPV = 145 70 (.6) 50 (.4)

40 (.4)

Corporate Real OptionsExample - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for

$150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Year 0 Year 1 Year 2

120 (.6) 100 (.6) 90 (.4)NPV = 162 150 (.4) Option Value =

162 - 145 =$17 mil

Corporate Real OptionsReality

• Decision trees for valuing “real options” in a corporate setting can not be practically done by hand.

• We must introduce binomial theory & B-S models