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Capital Budgeting & Portfolio Theory

I. How to select projects?II. How to estimate cash flow?III. How to measure Risk?IV. How to integrate risk in the Capital Budgeting process?V. How to determine the cost of capital to be used in the

capital budgeting process?

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Capital Budgeting & Portfolio Theory

I. Capital Budgeting Techniques1- Payback No. of years to recover initial

investment. [We can use the discounted rather than the raw CF’s]

2- NPV = ∑ - CF0 (NPV > 0)

3- IRR = ∑ = 0 (IRR > WACC)

n

t=1

CFt

(1+r)t

n

t=0

CFt

(1+IRR)t

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4- MIRR = ∑ - CF0 (MIRR > WACC)

5- CAPM Expected Rate (ri) vs. Required Rate (ri)

• Using Market beta as a measure of risk (ri > ri)

[Refer to the hand-out case “Portfolio Selection” which applies to stocks and real assets]

n

t=1

TVIF(1+MIRR)t

^^

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II. Cash Flow Estimation

1- Relevant Cash Flows:a) Incremental Cash Flows; [Cash flows with the

project vs. cash flows without the project]b) Future Cash Flows; [including opportunity

cost and externalities]

2- Refer to the handout case on “Replacement Decisions”

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III. Measuring Risk

1- Stand alone Risk*Measured by σ or cv of NPV, IRR, or MIRR1- r = ∑ ri pi

2- σ = √ Variance = √ σ2

σ = √ ∑ (ri – r )2 Pi

3- CV = σ r

^ n

i=1

n

i=1

^

^

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* Another Interpretation:

Stand alone Risk = Market Risk + Diversifiable RiskCan not be eliminated Construct a Portfolio

σJ 2 = βJ

2 σ2n + σeJ

2

Where σej2 is the variance of stock J’s regression error

term.

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2- Corporate Risk

• Reflects the project’s effect on corporate earnings stability, and considers diversification within the firm.

• Measured by the project’s (σ) and its correlation (ρ) with returns on firm’s other assets.

• Could also be measured by the Project’s Corporate beta

rρ = wArA + (1-wA) rB

_________________________________________________

σρ = √ w2Aσ2

A + (1-wA)2σ2B + 2wA (1-wA)ρABσAσB

^ ^ ^

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3- Market Risk

• Reflects the project’s effect on a well diversified stock market portfolio.

• Depends on project’s σ and correlation with the stock market.

• Measured by the project’s market betaβi = Cov (ri, mi)

σm2

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IV. How to Integrate Risk in the Capital Budgeting Process?

1- Risk Adjusted Discount rate; Use higher discount rate for higher risk projects.

2- Certainty Equivalent Method; Discounting risk free CF by a risk free rate.

Determining the required rate of return (i.e the WACC, or the discount rate is a must in the

above two cases).

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3- Sensitivity Analysis4- Decision Tree5- Monte Carlo Simulation6- The Capital Asset Pricing Model (CAPM); using

β (for one factor).ri = rRF + (rm – rRF) β

7- The Arbitrage Pricing Theory (APT); using β (for more than one factor)

ri = rRF + (r1 – rRF) β1 + (r2 – rRF) β2 …….. + ………… +

(ri – rRF) βi

Use r and σnpv^

^

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8- Fama, French 3-factor Model; using β for 3 specific factors (i.e excess market return, excess return associated with size and excess return associated with book-to-market ratios.

ri = rRF + (rm – rRF) β1i + (rSMB )β2i …….. + (rHMB )β3i

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V. Cost of Capital

• Cost of Capital is the discount rate used in the capital budgeting process. It is the weighted average of the cost of the components of the optimal capital structure.

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1) Cost of debt (long term)– rdat = rdbt (1 – T)

– Where rdbt is determined by one of the following methods:

1- The coupon rate on new debt2- The yield on other bonds with a similar rating3- The yield on the company’s debt

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2) Cost of Preferred Stock

rps = Dps

Pn

= Dividends . Price – Flotation Cost

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3) Cost of Equity: (Three Methods) 1- Growth Model

rs = D1 + g = D0 (1 + 9) + g

P0 P0

2- CAPM Model (on a historical base)rs = rRF + ( rM – rRF ) ß (refer to handout case)

3- Own Bond Yield plus Risk Premiumrs = rd + Bond RP

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• Example:– The bond yield for a 15-year, 12% semiannual

bond which sells for $1,153.72

0 1 2 30

|----rd=?----|-------|-- - - ---------|

-1,153.72 60 60 60+1000