The Cost and Capital and WACC Notes/Explanation describe the process of calculating the Weighted Average Cost of Capital (WACC) and go on to apply the results to valuing a firm both unlevered (no debt) and levered (debt). The levered firm is shown to be more valuable. Two identical firms (see the notes/explanation) and the firm with debt is more highly valued.

• Does this make sense? Why or Why not?
• Why not use 100 percent debt financing if debt increases value?

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[Equation 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, then 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:

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.

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
  • 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.
• Be computed on an after-tax basis
• Use nominal rates of return

Formula for estimating WACC

Recall equation 1 from above:

V = B + S

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

1 = B/V + S/V[Equation 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 less than the stated interest rate.

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.

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 between the two plans 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:

T_c x rb x B[Equation 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 T_c)(r_b)[Equation 4]

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

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 = r_b (1T_c)(B/V) + r_s(S/V)[Equation 5]

Where:

WACC = weighted average cost of capital r_b = pretax market expected yield to maturity T_c = corporate tax rate B = market value of debt S = market value of equity

Here is something to think about and discusssee Activity 6.5.

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:

T_c x r_b x B / r_b = T_c B[Equation 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[Equation 7]

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.

V_l = EBIT x (1 T_c)/ r_u + T^c x r_b x B / r_b[Equation 8]

Resulting in:

V_l = 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.