6.5 - Discussion

MBAA 518 Cost and Capital and WACC notes/explanation (Module 6)

A project (or firm) will be financed through a combination of equity and debt.

Q: What is equity?

Q: What is debt?

The value of a firm or project can be thought of as:

V = B + S (eq. 1)

Where,

V = value, B = market value of debt, S = market value of equity

(recall if firms obtain debt financing in the financial markets, they issue bondshence the B for

debt, you could also have loans etc.)

Example:

You start a project. You and your classmates invest $1,000,000 ($1M) of your own funds

into the project and you obtain $9,000,000 ($9M) of debt financing (this mix of debt and equity is the

capital structure.).

Q: What is the value of the project?

V= $1M +$ 9M =$ 10M

Assume a nearly identical project across the street from yours sells for $15M the day after you arrange

the financing above. (this is a gross simplification for illustrative purposes)

Q: What is the value of debt? Equity? And total value?

If the project is nearly identical than it appears the market is pricing the

project at $15M, so V = $15M

Value of debt (B) is what?

Debt holders are the ones who have a claim against your project via interest paid on the loan. The

bond/debt holders are the ones who can force you into bankruptcy and hold a higher priority of

claim (they get paid first). Debt holders do not partake in the increase in the value of equity so the value.

Therefore, the value of B is:

$ 9 m

Who gets the increase in value, the equity holders. You and your classmates now have equity of $6M.

MBAA 518 - Managerial Finance

May 2015 1

Does financing all have to come from external sources?

No, can use retained earnings.

The use of the capital is not free, there is a cost (cost of capital). Do you go to the market to purchase

groceries? Do people go to the financial markets to purchase capital? Is there a cost when you buy

groceries? Do you think there is also a cost of capital? The answer is yes.

Determining (estimating) the cost of capital is important in the evaluation of projects. The cost of

capital is the r we have been using in our analysis. Another term for r is the weighted average cost

of capital (WACC), to estimate the cost of capital the estimate must:

Consider all sources of capital*

Be computed on an after tax basis

Use nominal rates of return

(*For this course we will assume there is equity (S) and debt (B) only. There can be other financial

instruments used to finance a firm.)

Formula for estimating WACC

Recall equation 1 form above:

V = B + S

If you divided both sides of the equation by V the result is:

1 = B/V + S/V (eq. 2)

Note, that B/V and S/V represent the weights of each component of the firms financing. The total

value is V, B divided by V and S divided by V would give the percentage of each type of financing of the

capital structure.

After taxes also needs to be considered. Recall EBIT. The I is for interest which is an expense that

reduces taxable income. Therefore, debt actually costs is less than the stated interest rate.

For example:

Company XYZ has a corporate tax rate (Tc) of 39 percent with expected earnings

before interest and taxes (EBIT) of $2 million dollars each year. All earnings are

paid out as dividends.

MBAA 518 - Managerial Finance

May 2015 2

Two alternative capital structures are under consideration. For Plan I, XYZ will have

no debt and under Plan II, XYZ would have $8,000,000(B) in debt and the cost of

the debt is 10 percent (rb). What would the cash flows for XYZ look like under the

two plans?

Plan I Plan II

EBIT 2,000,000 2,000,000

Interest on debt 0 800,000

EBT 2,000,000 1,200,000

Taxes 780,000 468,000

Earnings After Tax 1,220,000 732,000

Total Cash Flows to Investors1 1,220,000 1,532,000

(1: interest + earnings, interest is paid out to investors who provided debt and in this example all earnings

are paid out as dividends to shareholders)

What is of most interest to us?

Total cash flows to investors which includes interest paid to debt holders and earnings

paid to shareholders. The difference in the two plan is:

1,532,000 1,220,000 = 312,000

This difference is due to the change in the amount of taxes paid:

780,000 468,000 = 312,000

Interest escapes corporate taxation while earnings do not.

This reduction in taxes is equal to:

Tc x rb x B (eq. 3)

= 0.39 x 0.10 x 8,000,000 = $312,000

The real cost of the debt (interest paid less the decrease in taxes) =

(800,000312,000)/8,000,000 = 0.061

Or an after tax cost of debt of 6.1 percent

Another way of calculating the cost of debt is:

(1 Tc)(rb) (eq. 4)

(10.39)(0.10) = 0.061 (or 6.1 pct)

MBAA 518 - Managerial Finance

May 2015 3

The financing arrangements are referred to as capital structure. (Just like you may have a structure (i.e.

your house) framed from wood, you can have a project built in all equity, all debt (may be unlikely) or a

combination of debt and equity).

We still are missing the cost of equity financing which is the opportunity cost of equity financing. This is

a complex question which requires a discussion of risk, return, some statistical properties of stock

market returns relative to the return of a given stock and the derivation of models to estimate the cost

of capital. Numbers that are required are the risk free rate, market risk premium and beta. (you have

studied this in the previous modules). The cost of equity should be the market cost of equity for a

similar project/firm. For this example, we will use a cost of equity of 10 percent.

We now have the components to calculate the weighted average cost of capital (WACC)

WACC = rb (1Tc)(B/V) + rs(S/V) (eq. 5)

Where:

WACC = weighted average cost of capital

rb = pretax market expected yield to maturity

Tc = corporate tax rate

B = market value of debt

S = market value of equity

Here is something to think about (and discusssee activity 5)

In the example above, assume Plan I and Plan II refer to firms I and II. We saw above the levered

project (now firm) will play less in taxes and the reduction in taxes was calculated using equation 3. This

amount, $312,000, if often called the tax shield from debt similar to a tax shield from depreciation.

Assuming the firm remains in a positive tax bracket and the savings from debt is perpetual the present

value of the tax shield is:

Tc x rb x B / rb = Tc B (eq. 6)

If the firm is unlevered, there would be no tax shield. Firm I represents the unlevered firm and the

Value of the unlevered firm Vu would be equal to the discounted after tax cash flows. Assuming the

cash flows occur perpetually the value of the unlevered firm would be:

Vu = EBIT x (1 Tc)/ ru (eq. 7)

MBAA 518 - Managerial Finance

May 2015 4

Where ru = cost of capital for unlevered firm

Vu = 2,000,000 (1 0.39) / 0.10 = $13,800,000

The value of the levered firm (Firm II) would have to incorporate the present value (PV) of the debt tax

shield (recall comment above about the cost of equity). Combining equations 5 and 6 results in the

value of the levered firm.

Vl = EBIT x (1 Tc)/ ru + Tc x rb x B / rb (eq. 8)

Resulting in:

Vl = 2,000,000 x (1 0.39)/ 0.10 + 0.39 x 8,000,000 = $14,112,000

The value of the levered firm is higher than the unlevered firm due to the savings in taxes.