Cost of Capital

TIP If you do not understand

anything,

ask me!

The theoretical foundation for capital budgeting

By Donglin Li 2

From CAPM (single factor model) to Apt (multi-factor model)

The CAPM has not been verified completely.

Investors seem to be concerned with both market risk and other risk factors. Therefore, the SML may not produce a correct estimate of ki.

ki = kRF + (kM – kRF) βi + ???

By Donglin Li 3

Arbitrage Pricing Theory (Apt)

Alternative to CAPMAlternative to CAPM

Return = a + bfactor1(rfactor1) + bf2(rf2) +bf3(rf3)+…

By Donglin Li 4

Fama&French 3 factor model—a special case of APT

The required return is based on 3 factors.

In addition to the market factor, there are also a size factor and book-to-market factor., , ,( )t f t p m t f t p t p t tR R R R s SMB h HML

By Donglin Li 5

Usage I: Apply CAPM and portfolio theory in EQUITY valuation. i.e., deciding cost of EQUITY capital

So far, we have discussed portfolio theory and the relation between required returns and risk. What’s the usage?

In the dividend growth model, a stock whose dividends are expected to grow forever at a constant rate, g.

If g is constant, the dividend growth formula is:

What will determine Ks?g -k

D

g -kg)(1D

Ps

1

s

00

^

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Usage I: If kRF = 7%, kM = 12%, and β = 1.2, what is the required rate of return on the firm’s stock?

Use the SML (the CAPM equation) to calculate the required rate of return (ks):

ks = kRF + (kM – kRF)β

= 7% + (12% - 7%)1.2= 13%

By Donglin Li 7

Usage II: Apply CAPM and portfolio theory in capital budgeting

Another usage is to calculate the discount rate for a project in which a firm may be interested.

Now how can we approach this question?

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Usage II: The risk of a project

One simple approach to calculate the discount rate for a project is to ASSUME that the project has the same risk as the existing business or assets of the firm. Of course, if the new project has risk very different from existing business, one CANNOT do this.

We can estimate what is the required return on existing firm assets.

Then use this required return as the discount rate for the new project.

By Donglin Li 9

Usage II: Company Cost of Capital

Company Cost of Capital (COC) is defined as the cost of capital on the company’s assets. This is the required return on the existing firm assets.

The cost of capital on a firm’s assets is decided by the risk of assets ( or beta), which can be calculated by the portfolio theory.

By Donglin Li 10

Cost of Capital

Also called:Hurdle rateDiscount rateOpportunity cost of capitalRequired rate of return (if we ignore

flotation cost and tax.)

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Example:

Suppose the company 785.com has the following classes of assets:

2/3 Intangible, good will & New technology Beta=2.0

1/6 Machine & Plant Beta=1.31/6 Working assets Beta=0.6

Beta of firm assets =1.3*(2/3)+1.3/6+0.6/6=1.18

By Donglin Li 12

Same example

Suppose the same company is owned by stockholders (70% in value) and debt holders (30% in value).

Beta of stock=1.51, beta of debt=0.41Beta of the portfolio that contains all

stocks and debts =0.41*30%+1.51*70%=1.18

By Donglin Li 13

Company cost of capital

Certainly the risk of this portfolio is the same as the risk of the asset of the company. Why?

Now, we can calculate the risk of the asset of the company as the weighted average of the risk of equity and debt.

The required return on the asset of the company is thus the weighted average of the required return on equity and required return on debt.

By Donglin Li 14

Cost of capital (continue)

equitydebtasset

portfolioasset

rED

Er

ED

DR

RRCOC

First way (I prefer this),

Second way,

)( fmassetfasset

equitydebtasset

portfolioasset

rRrRED

E

ED

D

IMPORTANT

E and D are all market values

By Donglin Li 15

Of course there is a third way…

Cost of capital is also equal to the weighted average of all company assets’ (intangible, machinery, working assets) required returns.

But this approach is more difficult to follow and thus it is not very useful, why?

By Donglin Li 16

Capital Structure

Capital Structure refers to the mix of debt and equity within a company

We may use CAPM to calculate the cost of equity and the cost of debt respectively as follows:

)(

)(

fmdebtfdebt

fmequityfequity

rRrr

rRrr

By Donglin Li 17

Example

100 valueFirmAssets Total

70ueEquity val

30Debt value100Assets

%75.12%157030

70%5.7

7030

30

assets

equitydebtassets

R

requitydebt

equityr

equitydebt

debtR

%5.7%,15 debtequity rr

By Donglin Li 18

Cost of capital with tax benefit

When tax benefit of debt financing is considered, the company cost of capital is calculated as:

Tc is tax rate.

equitycdebt rED

ETr

ED

DWACC

)1(

By Donglin Li 19

Question:

The CEO (who is a sfsu MBA) of 785.com is thinking about whether to invest in a project that will return a sure 7% with no risk. The company can borrow from bank at a rate of 5%. Risk free rate is 4.5%. Seems a good deal. However, the CFO (who is a Stanford MBA) is fiercely against the project. The weighted average cost of capital of the company is 11%.“This is definitely a negative NPV project because the project return,7%, is lower than the cost of capital, 11%.” Please help our CEO & alumni clarify the confusion.

By Donglin Li 20

The risk of this new project risk is very different from that of existing assets in the firm.

We should decide the discount rate based on the risk level of new project.

The correct discount rate in the above example is ___. Should you take the project? Yes___ No____.