Notes

The Cost of Capital


Cost of Capital, Discounts Rates, and the required Rate of Return



We know how to do capital budgeting problems, but what about the discount rate?



We also know that the discount rate will depend on the risk of the project:

Investors will require a higher required rate of return for riskier projects
Investors will look at projects as portfolios and therefore the systematic risk is the correct measure of risk. Any unsystematic risk can be diversified away, and no compensation for this is necessary.


Required rate of return, appropriate discount rate, and cost of capital are different names for the same concept.


The cost of capital depends on the risk, and hence primarily on the use of the funds, not the source.


Firm's overall cost of capital reflects the required rate of return on the firm's assets as a whole. This overall cost of capital is called the weighted average cost of capital, and reflects the costs of debt, equity, and preferred stock.


The weighted average cost of capital (WACC)

Assume the firm has a target capital structure (mix of debt and equity)

Capital structure weights:

Value of the Firm = Value of Equity + Value of Preferred + Value of Debt

V = E + P + D

wE = E / (E +P + D) = E / V

wD = D / (E + P + D) = D / V

wP = P / (E + P + D) = P / V




Weighted Average Cost of Capital:

WACC = RWACC = wE ( RE + wP ( RP + wD ( RD ( (1 ( Tc)


Focus on before-tax or after-tax capital costs?

Shareholders are concerned with cash flows available to them

after corporate taxes have been paid

Therefore, use After-Tax WACC.

Only rD needs adjustment.



Why adjust rD ?

The cost of debt is tax deductible to the issuing firm.

Costs of preferred and common are not deductible.



What is marginal cost?

Decisions are being made regarding new capital investment.

Therefore, the cost of the next dollar of capital is the relevant question
(marginal cost).


Market or Book Values?

Cost of capital measures marginal cost of issuing new securities to finance projects. These securities are issued at market value.

Weights assigned to debt and equity in calculating WACC should be based on market value.


The Cost of Debt

Example: Calculate the return on debt if you know the following information:
Coupon = 10% semiannual;
Face = $1,000
Price = $1,081.44;
Maturity = 15 years

















Example:
Pharmacia has bonds outstanding with the following specifications. These are 30-year, 7% annual coupon bonds, and selling at 96% of their face value ($1,000). What is the cost of debt for Pharmacia?













What if Debt isnt Publicly Traded?

Note: Since the bond pays a coupon semi-annually, and earns 4.5% in six months, we coiuld also calculate the effective annual rate (EAR).

EAR = (1.045) 2 - 1 = ________%


However, nominal rates are generally used for the cost of debt.

Reason:







Flotation cost - Total costs of issuing and selling a security reduce the net proceeds from the sale

These costs are typically small on public debt issues.


Most debt is privately placed directly with large investors. So flotation costs are almost nonexistent.


Flotation Cost Approaches

Incorporate into component costs of capital

bond price = par value = $1,000
flotation costs = 1% of issue = $10
net proceeds = $990

Treat flotation costs as investment outlay of new project

cost of capital theoretically depends on risk of use of funds, not source

increase initial cost to account for flotation costs

The Cost of Preferred Equity

Example: Calculate the return on preferred stock if you know the following information:
Price =$112.5;
Dividend Yield = 9%;
Par=$100;














Preferred dividends are not tax deductible, so no tax adjustment.
Just rP.

Nominal rP is used.

Preferred stock tends to be a small part of a firms capital structure, and in practice is often ignored.




Is Preferred stock more or less risky than debt?

Corporations own most preferred stock, because 70% of preferred dividends are nontaxable to corporations.
Therefore, preferred often has a lower B-T yield than debt.
The A-T yield to an investor, and the A-T cost to the issuer, are higher on preferred than on debt.




The Cost of Equity

Equity consists of two components: retained earnings and new equity issues

Why is there a cost for retained earnings?

Earnings can be reinvested or paid out as dividends.

Investors could use dividends to buy other securities and earn a return.

Thus, there is an opportunity cost if earnings are retained.

Opportunity cost is the return stockholders could earn on alternative investments of equal risk.


They could buy similar stocks and earn RE, or the company could repurchase its own stock and earn RE. So RE is the cost of retained earnings.


Cost of Retained Earnings

Model I: The Security Market Line (SML) Approach

Remember, the required rate of return on a risky assets depends on:

the risk free rate, Rf
the market risk premium, E(RM) ( Rf
the systematic risk of the asset, relative to the average, (


The SML, or CAPM tells us that the expected return on the firm's equity is:

E(RE) = Rf + (E ( [E(RM) ( Rf]

And, if we drop the expectations:

RE = Rf + (E ( [RM ( Rf]


Example:

rRF = risk free rate = 7.0%
current rate on government security
RPM = (rM - rRF) = 5.0%
bS = 1.25




Example:
Pharmacia has an equity beta of 1.6, the risk free rate for return is equal to 5%, and the return on a well-diversified market portfolio is 15%. What is the cost of equity capital for Pharmacia?





The Risk-Free rate: T-bonds vs. T-bills

Embodies long-term inflation expectations.


Is influenced less by Federal Reserve actions, currency flows, etc.


Is the more logical investment alternative to stocks since they have similar investment horizons.



How do we calculate the risk premium on the market?

Ex post data (Historical)
e.g. Ibottson and Assoc. provides this on an annual basis :
RPM = 7.3% for 1926-1996.


Future estimates by financial analysts
of market minus T-bond





Model II: The Dividend Growth (or Discounted Cash Flow) Model


P0 = (D0 ( [1 + g]) / (RE ( g) = D1 / (RE ( g) ( RE = (D1 / P0)+ g



Example:


What is the DCF (discounted cash flow) cost of retained earnings?
Given: D0 = $5.00;P0 = $76; g = 6%?













Pharmacia has just paid a $9 dividend. The dividends are expected to grow at 12% per year. Pharmacia currently sells for $112 per share. What is the cost of equity capital for Pharmacia?














Disadvantages of Discounted Cash Flow Method

Model is simple to use, but there are many disadvantages and problems:

You need a firm that pays dividends

You need very constant growing dividends

You need a very accurate estimate of the growth rate



Can Discounted Cash Flow Method be used if g is not constant?





New Common Stock versus Retained Earnings

New Common stock incurs flotation costs

Some books suggest increasing the discount rate to reflect flotation costs.

End up with a cost of new equity greater than the cost of retained earnings


But required return should reflect risk of investment (use of funds, not source of funds)


Example:











The Weighted Average Cost of Capital

Book value debt = $3 million
Preferred stock is selling for $100/share and there are 10,000 shares out
Common stock is selling for $20/share and there are 300,000 shares out

Target capital structure (market value)
B = 30%
P = 10%
S = 60%

Return on debt = 9%
Return on Preferred = 8%
Return on Equity = 13.1%
Tax rate = 40%
Pharmacia has $200 million worth of equity and $600 million worth of debt on its balance sheet. The market value of the equity is $650 million, and the market value of the debt is $975 million. The corporate tax rate is 34%. What is the WACC for Pharmacia?







We can use the WACC as the discount rate in capital budgeting only if the project has a similar risk as the firm as a whole.

If the project has a risk that is different from the firm as a whole, the SML approach is needed.

Pure Play Approach: if there is no beta for the project available, use the WACC or beta from a company that has similar risk as the project.

Example: Giant Eagle is considering an expansion in the pharmaceutical business. The problem that they are facing is that they do not have a beta for this project available, and they realize that the risk involved with the pharmaceutical business is quite different from being in the grocery store business. What discount rate could Giant Eagle use?