For this module week's discussion, respond to the following:

Thesupplemental materialsdescribe the process of calculating 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. These are two identical firms (see the supplemental materials), yet the firm with the debt is more highly valued. Does this make sense? Why or why not? Why not use 100% debt financing if debt increases value?

See Below for Supplemental Materials

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 bonds...hence 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.

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, you 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 from 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 firm's 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 (T_c) 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 (r_b). 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 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_cx r_bx 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) =

(800,000-312,000)/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)..............................................................................(eq.4)

(1-0.39)(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 cast of capital. Numbers that are required are the risk free rate, market risk premium, and beta. The details for estimating the market opportunity cost of capital is beyond the scope of this course. The cost of equity should be the market cost of equity for a similar project or firm. For the analysis in this course we will use a cost of equity equal to the long term average return to US equities which is approximately 10 percent unless otherwise stated.

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

WACC = r_b(1-T_c)(B/V) + r_s(S/V).............................................(eq.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 discuss...see this week's discussion).

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, is often called the tax shield from debt (recall the 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_cx r_bx B / r_b= T_cB..............................................................(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 V_uwould be equal to the discounted after tax cash flows. Assuming the cash flows occur perpetually the value of the unlevered firm would be:

V_u= EBIT x (1 - T_c)/ r_{u..........................................................................................}(eq.7)

Where r_u= cost of capital for unlevered firm

V_u= 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_cx r_bx B / r_{b..........................................................}(eq.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.