We began the course by looking at the types of funding that corporations decide upon for their company. We then examined the reasons why firms chose their own particular capital structure and dividend policy. Now we focus on the effect of these policy decisions on the evaluation of real investments.

The outline of the lecture is:

1. Capital Budgeting Techniques: The After-Tax Weighted-Average Cost of Capital (WACC)
2. Capital Budgeting Techniques: Adjusted Present Value (APV)
3. Capital Budgeting Techniques: Flow-to-Equity Approach (FTE)
4. A Comparison of the APV, FTE and WACC Approaches

The reading for this lecture is:

Myers, S., Finance Theory and Financial Strategy, p.119-127.

This paper looks at the practical problems that arise when firms use capital budgeting techniques as part of their financial strategy.

When carrying out a capital budgeting analysis in the past you have probably viewed the potential investment as a mini firm. This means that you estimated the cash flows arising from the project and discounted those cash flows at the opportunity cost of capital for projects of that type. However, this is the incorrect approach for most companies.

In practical situations, you need to incorporate the effect of financing decisions into the analysis. There are three techniques in doing this: After-tax weighted-average cost of capital, adjusted present value and flow to equity approach.

You may recall from Finance III that in perfect markets, Modigliani and Miller (MM) showed that the opportunity cost of capital for a firm is just a weighted average of the expected returns on debt and equity regardless of the amount of debt the firm has.

The relevant formula is:

Unfortunately, things are rarely ever this easy. A major omission of MM is the effect of taxes on the weighted average cost of capital.

Taxes provide a discount on the use of debt in the form of a tax-shield on the interest payments charged to service the debt.

We will now derive a new formula to express the after-tax weighted average cost of capital of a new project.

Three major assumptions are required:

1. The new project is assumed to produce the same cash flow into perpetuity.
2. The firm will maintain its debt ratio. Remember that the debt and equity values are market values and not book values.
3. The project is of the same risk as the firm’s average projects.

Consider a firm that wishes to invest a sum, I, in a new project. The firm has a debt to market value ratio of D/V. The return on its debt is r_D, the return on its equity is r_E and the tax rate is T_c.

If the firm maintains its debt ratio with the new project, it will need to issue I*(D/V) of debt. In addition, it will also need to issue I*(E/V) of new equity.

If the project is worthwhile, the cash flow from the project must cover the after-tax interest charges on the debt as well as provide an acceptable return to equityholders.

The after tax interest costs on the additional debt is:

The minimum acceptable income to equity holders is

Therefore for a project to be acceptable, the after tax cash flow, C, from the project must exceed

With a perpetuity, the return on an investment is C/I. If we divide both sides of the above equation by the investment value, I, we find a project’s minimum acceptable rate of return on the investment.

This is called the after-tax weighted average cost of capital. The return on a project must exceed this value.

Example. Consider a firm, ABC Ltd, that has decided to build a new flood prevention mechanism that will reduce the risk of flooding in the west of Scotland. The market value of the firm is currently £12million. The company has £3million of debt outstanding, yielding 10%. The firm’s shares offer an expected rate of return of 22.2% in the next year. The marginal corporate tax rate is 34%.

The cost of the new project which is similar in type to the company’s other activities is £475,000. Cash flows arising from the project will be £140,000 per year in perpetuity. Should ABC undertake the project?

The market value of the firm is £12million and the market value of the debt is £3million. This means that the market value of equity is (12-3) = £9 million.

We need to estimate the after tax cash flows to the project

The WACC is

We now use NPV analysis with the WACC as the appropriate discount rate:

NPV=-£475,000+£92,400/0.183=-£475,000+£504,918 = £29,918

Therefore the company should undertake the project.

When a firm’s capital structure is composed of more than debt or equity, the WACC formula becomes:

where the sum of the market values of all sources of funding is equal to the market value of the company.

Example. Consider a company with five sources of financing: straight debt, D, ordinary equity, E, preferred stock, P, convertible bonds, C, and subordinated debt (junk bonds), J. The WACC for this company would be:

Each debt instrument has an associated tax-shield and D+E+P+C+J=V.

The inclusion of short-term debt in a company’s WACC is dependent on the use of that debt. If the debt is used to finance short term working capital and is only temporary or incidental, it should not be included. However, if it is part of a financing strategy and is continually maintained it should then be included.

The return on each financing element can usually be calculated from stock market data. CAPM or some variant may be used to estimate the return on equity and the return on debt can be directly observed. However, for debt securities with a high risk of default such as junk bonds the return is difficult to estimate.

Adjusted present value approaches the evaluation of investments from a different perspective. Instead of adjusting the discount rate, it adjusts each cash flow to incorporate the effects of financing decisions.

The adjusted present value approach (APV) can be described by the formula:

APV = NPVE + NPVF

That is, the adjusted present value of a project in a levered firm is equal to the net present value of the project in an all equity firm plus the net present value of financing.

There are four side effects to financing:

1. Tax shield from new debt
2. The costs of issuing new securities
3. The costs of financial distress
4. Project specific subsidies.

Example. Consider again the case of ABC Ltd. I will reprint the original example below:

"Consider a firm, ABC Ltd, that has decided to build a new flood prevention mechanism that will reduce the risk of flooding in the west of Scotland. The market value of the firm is currently £12million. The company has £3million of debt outstanding, yielding 10%. The firm’s shares offer an expected rate of return of 22.2% in the next year. The marginal corporate tax rate is 34%.

The cost of the new project which is similar in type to the company’s other activities is £475,000. Cash flows arising from the project will be £140,000 per year in perpetuity. Should ABC undertake the project?"

Costs of financial distress are not likely to increase because the target debt ratio is the same after the project has started. The opportunity cost of capital for a project of this type is 20%. The firm will issue £126,229.50 in debt to finance the project (this number is set so that the D/V ratio remains at 0.25 after the project has been accepted).

Recall the equation derived by MM,

We can apply this equation to projects to determine the level of debt to be issued. If a firm’s target debt/value ratio is l . The value of a levered firm is equal to:

When investing in a new project, V_u is the value of the project in an all equity firm. See step 1 below. In this example, V_U = £462,000 and l =0.25. Therefore:

For a firm to maintain its target debt ratio, it would have to issue debt worth:

Step 1. Find the net present value of the project in an all equity firm.

Therefore, we would reject the project if the firm were financed solely by equity

Step 2. Calculate the present value of the financing.

The increase in debt as a result of the new project is £126,229.50.

The present value of the tax-shield is T_cD = 0.34(£126,229.50) = £42,918

Step 3. Calculate the adjusted present value

APV = NPV + NPVF = -£13,000 + £42,918 = £29,918

According to APV the company should take the project. Note that this is the same figure as that arrived at by using WACC.

With the flow to equity approach (FTE), the cash flows from the project are discounted at the cost of levered equity.

There are three steps in the flow-to-equity approach.

Step 1. Calculate the cash flow to equity holders of the levered firm. This entails the incorporation of interest payments and taxes in the final cash flow estimate.

Step 2. Calculate the return on the levered equity

Step 3. Determine the present value of the levered cash flows at the discount rate calculated in step 2. The initial investment is the value of new equity issued.

Example. We will again use the previous example.

Step 1. Calculate the levered cash flow:

Step 2. Calculate the return on levered equity, r_E.

We have already been told the return on the levered equity is 22.2%.

However, if we didn’t know it we could have calculated the figure in the following way.

r_A = 0.20 which is the return on the unlevered firm, r_D = 0.10 which is the return on the debt, D/E = 1/3 and T_c = 0.34.

Step 3. Calculate the NPV of the project

The value of new equity issued is £475,000 - £126,229.50 = £348,770.50

The levered cash flows are £84,069 per annum and the return on levered equity is 22.2%

Thus

The choice of method to use basically depends on the amount of knowledge one has of the firm’s capital structure in the future.

• The APV and FTW requires knowledge of the level of debt in the firm over the life of the project. This is in contrast to WACC (and FTE) where the ratio of debt to value needs to be known. When the level of debt in the future is known, APV should be used. However, it is normally not known and when this is the case, WACC should be used.
• APV has the advantage of calculating separately the value created by the project and the value created by financing. It is more flexible in that it can be used when debt levels or tax rates change over time.
• It should be noted that by far the most popular method of analysis undertaken by corporate management is the WACC approach. This is because firms usually have target debt/equity ratios that do not change from year to year. This makes the WACC method the easiest to apply and can be compared across common use firms. However, WACC cannot be adapted to evaluate investments with strategic options.

1. A firm is considering an investment project that costs £15m, and is expected to generate pre-tax cash flows of £3.52m pa (assume this to be a perpetuity). The required return on the project is 16% (opportunity cost of capital).

1. Calculate the project's NPV
2. Calculate the project's APV assuming 25% of the project's cost is financed by new debt. The interest rate is 10% (assume the debt is permanent). The firm's marginal tax rate is 33 %.
3. Evaluate the project using the after-tax weighted average cost of capital approach.
4. Evaluate the project using the flow to equity approach.
5. Redo the analysis in points i – iv. This time assume that the firm issues £4.019million in debt. All other variables are the same. Compare your answers with your earlier results. Why do you think the three evaluation methods agree more closely when the debt level is set at £4.019million?
6. Assume the issue costs of debt = 2% of the proceeds of the issue. The remainder of the project is financed by equity. It is raised externally and the issue costs are likely to be around 3.25%, including underwriting. What is the new APV.? Assume that the debt issue is £4.019million.

2. Describe the problems that may arise when capital budgeting analysis is used in practice. (Read the Myers paper).