The Optimal Capital Budget

Chapter 3. The Optimal Capital Budget

Up this point, we have discussed some of the issues regarding a firm's cost of capital and capital budgeting decisions. In the process, we have looked at some of the techniques a financial manager can use in identifying the cost of various forms of capital and choosing projects that are "profitable" to the firm. Based on our earlier discussions, we know there is a significant relationship between a firm's cost of capital and capital budgeting decisions. In order to decide whether a project is desirable, a financial manager uses the cost of capital the firm faces to determine the project's net present value; or compare the project's IRR with the cost of capital. In addition, we also know that the cost of capital a firm faces might not be constant (i.e. the firm's MCC schedule might experience several break points). In that case, how does a firm decide what is the appropriate cost of capital? And how does it decide the optimal budget it needs for project investments? In order to answer those questions, we need to first look at a firm's investment opportunity schedule (IOS).

The Investment Opportunity Schedule (IOS)

The concept behind the IOS is very similar to that of the MCC schedule. The MCC schedule represents the cost of capital faced by the firm (ranking from the cheapest to the most expensive) while the IOS represents the projects that are available to the firm (ranking from the most desirable to the least desirable).

In order to construct the IOS, the firm needs to first estimate the IRR of each of the project it is considering. Once that is accomplished, the financial manager can plot the IOS, which is a chart of the IRRs of the firm's projects arranged from the highest IRR to the lowest IRR.

Example: Microsoft is interested in five independent projects, and the financial information regarding those projects is presented in the following table.

Year Project 1 Project 2 Project 3 Project 4 Project 5

Initial Cost $250,000 $100,000 $100,000 $120,000 $200,000

IRR 34.54% 39.03% 33.87% 14.28% 16.41%

Payback 2.21 1.50 1.83 3.50 4.33

Using the IRR information above, we can arrange the projects from the highest IRR to the lowest IRR as follows: Projects 2, 1, 3, 5 and 4. This information is used to plot the Microsoft's IOS and it is depicted below.

From the IOS above, we know that if Microsoft decides to undertake all five projects, it will need an investment budget of $770,000. However, Microsoft does not know if this is advisable because it does not know if all the projects will be able to generate a high enough return (i.e. IRR) to cover the cost of raising the new capital. In order to make the correct decisions, Microsoft needs to combine its IOS with its MCC schedule to determine which project it should undertake and which project it should reject.

Combining the MCC and IOS Schedules

A financial manager will continue to accept project as long as the marginal return generated by the project is higher than the marginal cost the firm needs to pay to finance it. The financial manager will stop accepting projects once the marginal return generated by the project is exactly offset by the marginal cost faced by the firm. This is the point where the IOS and MCC schedule of the firm intersects.

The intersection point indicates the marginal cost of capital faced by the firm. In other words, the cost the firm will have to pay if it decides to raise one additional dollar. This is usually the rate the firm uses to evaluate its average risk projects (i.e. finding the NPVs).

The marginal cost of capital a firm faced depends on the availability of projects. If the firm has fewer available projects, the IOS will shift to the left and the firm will face a lower marginal cost. Whereas an increase in available projects will shift the IOS to the right, and this will raise the marginal cost.

The following graph shows the MCC schedule and IOS of a particular firm. The IOS indicates that the firm faces five potential projects, and its MCC schedule indicates the firm will experience a break point (most probably when it exhausts its retained earnings). From the graph below, we know from the intersection of the firm's IOS and MCC schedule that the marginal cost of capital for the firm is 15.5%. The firm will use this marginal cost of capital to pick its projects. From our earlier discussion, we know a firm will pick a project only if its IRR is greater than its cost of capital. In this particular case, the firm will pick projects A, B and C (and rejects projects D and E). In addition, we know the optimal capital budget for the firm is $150 million.

Example: The financial manager of Surf the Net, Inc. (STN) is planning next year's capital budget. STN expects its net income to be $2,700,000 next year, and its payout ratio is 30%. The company's earnings and dividends are growing at a constant rate of 8%; the last dividend, , was $1.00; and the current equilibrium stock price is $16. STN can raise up to $1,800,000 of debt at 11% before-tax cost, the next $1,800,000 will cost 12%, and all debt after $3,600,000 will cost 13%. If STN issues new common stock, a 12% underwriting cost will be incurred. STN can sell the first $200,000 of new common stock at the current market price, but to sell any additional new stock, STN must lower the price to $14. STN is at its optimal capital structure, which is 60% debt and 40% equity, and the firm's marginal federal-plus-state tax rate is 40%. STN has the following independent, indivisible, and equally risky investment opportunities:

Project Cost IRR (%)

A $3,200,000 13.0

B 1,300,000 10.7

C 1,750,000 12.0

D 450,000 11.2

What is STN's optimal capital budget?

The first thing we need to determine is STN's MCC schedule. In order to do that, we will follow the 3-step procedure. First, we will identify the different break points in the MCC schedule. In this scenario, there will be 4 break points in the MCC schedule.

Break Point 1: When the firm exhausts its retained earnings and issues new common stocks.

We will let represents the