The Marginal Cost of Capital Schedule As you raise more and more money, the cost of each additional dollar of

The Marginal Cost of Capital Schedule As you raise more and more money, the cost of each additional dollar of

new capital may increase. The reasons are the flotation costs and the demand for the security representing the capital to be raised.

For example, the cost of internal funds from retained earnings will differ from the cost of funds from issuing common stock due to flotation costs. If a firm expects to generate $1,000,000 entirely from what’s available in internal funds—retained earnings—there are no flotation costs. But if the firm needs $1,000,001, that $1 above $1,000,000 will have to be raised externally, requiring flotation costs.

Let’s consider a simple example using the dividend valuation method for the cost of common stock. Suppose a firm pays a dividend of $5 per share this year and dividends are expected to grow at a rate of 5% per year, forever. The current price of the stock is $50. The cost of this internal source of funds is:

$5 1 + 0.05 r e = --------------------------------- ( ) + 0.05

$50 = 0.1550 or 15.5% per year

If the firm is expected to generate $2,000,000 in retained earnings in the next period, it will cost 15.5% per year to use this amount as capital.

If the firm needs more than $2,000,000, each additional dollar of equity capital will cost more than 15.5% because it will be raised from the other two sources and both have flotation costs.

EXHIBIT 11.3 Costs of Capital

Source Weight Cost of Capital

Debt 40%

r = 6%

Preferred stock 10%

r p = 12%

Common stock 50%

r e = 14%

THE FUNDAMENTALS OF VALUATION

Suppose in addition to the retained earnings the firm expects to be able to issue new shares at $50 per share, but receives only $48 per share—the investment bankers get the $2 difference. The cost of this external equity is:

$5 1 ( + 0.05 ) r e = --------------------------------- + 0.05

$48 = 0.1594 or 15.94% per year

The first $2,000,000 costs 15.5% per year and anything over that costs 15.94% per year. So, the marginal cost of common stock capital is 15.5% per year to raise from $1 to $2,000,000 from equity, and is 15.94% per year to raise each dollar above $2,000,000 from common stock.

Flotation costs also play a role in creating layers of cost for debt. For example, a firm may expect to be able to privately place a debt issue of $1,000,000 with an insurance company. If more than $1,000,000 of new debt capital is needed, the firm would have to sell another debt issue publicly, incurring higher issuance costs. The first $1,000,000 of debt capital would be at one cost, and any additional debt capital is at a higher cost.

Additional capital may be more costly since the firm must offer higher yields to entice investors to purchase ever larger issues of securities. Considering the effects of flotation costs and the additional yield necessary to entice investors, we most likely face a schedule of marginal costs of debt capital and a schedule of marginal costs of equity capital. Hence, we need to determine at what level of raising funds the marginal cost of capital for the firm changes.

Capital structure is the mix of long-term sources of funds. Suppose

a firm has a target capital structure of 40% debt and 60% common stock and will raise new funds in these proportions. In consultation with its investment bankers, the firm has determined the cost of raising new capital from debt and equity, for different levels of financing. These costs are shown in Exhibit 11.4. For example, if the firm issues $1,500,000 of new debt, the first $1,000,000 costs 5% per year and the next $500,000 costs 6% per year.

Suppose the firm raises capital in the proportions of 40% debt and 60% equity and raises $2,000,000 of new capital comprising $800,000 debt and $1,200,000 common stock. Looking at the schedules, we see the cost of debt is 5% up to the first $1,000,000 of debt. However, the cost of equity changes once we have raised $1,000,000: The first $1,000,000 of equity costs 9% and the additional $200,000 costs 10%. The cost of capital of the first $2,000,000 of new capital is:

The Cost of Capital

Equity at 10% =

Equity at 9%

0.010 = 0.075 or 7.5% per year

The average cost of raising a dollar of capital for the first $2,000,000 of capital is 7.5%. The marginal cost of capital for the first $1,800,000 is

Marginal cost of capital for first $1,800,000

$1,080,000 = ------------------------------ 0.05 + ------------------------------ 0.09

= 7.4% per year

EXHIBIT 11.4 Marginal Costs of Debt and Common Stock

Debt Amount of New Debt

Marginal Cost of Debt per Year

Up to $1,000,000

Equity Amount of New Equity

Marginal Cost of Common Stock per Year

Up to $1,000,000

$1,000,001 to $3,000,000

$3,000,001 to $5,000,000

$5,000,001 to $8,000,000

THE FUNDAMENTALS OF VALUATION

and the marginal cost of capital for the next $200,000 is:

$120,000 = ------------------------- 0.05 + ------------------------- 0.10

= 8% per year If we raise one more dollar of capital beyond the $2,000,000, but

not more than $1,000,000 in total debt nor more than $3,000,000 in total equity, then it costs 5% for the additional debt and 10% for the additional equity:

Weighted average cost of capital beyond = ( 0.40 0.05 ) 0.60 0.10 + ( ) $2,000,000 but less than $4,000,000

0.08 or 8% per year The marginal cost of capital is 8% at $2,000,001 of new capital.

The marginal cost of capital at $4,000,000 of capital ($1,600,000 debt and $2,400,000 equity) is 8.4%. The cost of debt is 6% and the cost of equity is 10%:

Weighted average cost of capital = ( 0.40 0.06 ) 0.60 0.10 + ( ) = 0.084 or 8.4% per year

Each time the marginal cost of either the equity or the debt changes, the marginal cost of capital changes. These changes are referred to as break-points. We can see break-points in Exhibit 11.5, which represents graphically how the marginal cost of capital ratchets upward as the total dollars raised increases. The set of marginal costs of capital for different levels of capital raised makes up the marginal cost of capital schedule.

We can figure out where these break-points occur by looking at: ■ The marginal cost of debt schedule.

■ The marginal cost of stock schedule. ■ The capital structure proportions.

Let’s first look at the marginal cost of debt schedule. The marginal cost of capital breaks when the marginal cost of debt changes from 5% to 6%—once we have used up the first $1,000,000 of debt capital. Because our total capital structure consists of 40% debt:

0.40(Total capital raised) = $1,000,000

The Cost of Capital

EXHIBIT 11.5 Marginal Costs of Capital for Different Levels of Capital

Using a bit of algebra,

Total capital raised = $2,500,000

= ------------------------------

Once we have raised $2,500,000 of capital, we have hit the $1,000,000 break in the marginal cost of debt capital schedule.

We can repeat this for each break in the marginal cost of debt sched- ule and each break in the marginal cost of equity capital schedule. The results of computing the breaks in the marginal cost of capital schedule are shown in Exhibit 11.6. By comparing the breaks in this table with the graph in Exhibit 11.5, you see a correspondence between these break-points in the graph and the shifts in the marginal cost of capital schedule. For example, if $5 million new capital is raised, the marginal cost of debt is 7% and the marginal cost of equity is 10%, resulting in a marginal cost of capital of 8.4%. If one more dollar of capital is raised (that is, $5,000,001 in total) the marginal cost of debt remains at 7%, the marginal cost of equity jumps from 10% to 11%, and the marginal cost of capital becomes 9.4%. The $5 million represents a break-point because the marginal cost of capital changes after that amount of new capital is raised.

EXHIBIT 11.6 Marginal Cost of Capital Schedule

Marginal Marginal Amount of

Amount

Amount of

Marginal

Cost of Cost of Capital Raised

of Debt

Common

Cost of

Raised

Stock Raised

Debt

Common Stock Capital

4,000,001 to 5,000,000

7 10 8.4 5,000,001 to 6,000,000

7 11 9.4 6,000,001 to 7,000,000

7 11 9.4 7,000,001 to 8,000,000

8 11 9.8 8,000,001 to 9,000,000

8 12 10.4 9,00,000 to 10,000,000

8 12 10.4 10,000,001 to 11,000,000

9 12 10.8 11,000,001 to 12,000,000

The Cost of Capital

We an generalize the calculation of the break-point in the marginal cost of capital schedule as:

Break-point in marginal cost of capital Break-point in marginal

cost of capital from source (11-8) = ---------------------------------------------------------------------------------------

Proportion of capital from source In general, as the marginal cost of any component of capital changes, so

does the marginal cost of capital. Marginal Cost of Capital and Shareholder Wealth Maximization

Let’s see what maximizing shareholder wealth means in terms of making investment and financing decisions.

To maximize shareholder wealth we must invest in a project until the marginal cost of capital is equal to its marginal benefit. What is the benefit from an investment? It is the internal rate of return—also known as the marginal efficiency of capital. If we begin by investing in the best projects (those with highest returns), and then proceed by investing in the next best projects, and so on, the marginal benefit from investing in more and more projects declines.

Also, as we keep on raising funds and investing them, the marginal cost of funds increases. To maximize shareholders’ wealth, we should invest in projects to the point where the increasing marginal cost of funds is equal to the marginal benefit from our investment.

We can see this concept illustrated in Exhibit 11.7. Here we plot the marginal cost of capital and marginal efficiency of investment against the capital expenditure. The optimal capital budget is the capital expen- diture where the marginal cost of capital intersects the marginal effi- ciency of capital. In this graph, the optimal capital budget is $2,750,000. This is the amount of capital investment where the mar- ginal cost equals the marginal benefit which equals 8.85%. This means that the firm should take on an investment as long as its return exceeds or is equal to the marginal cost of capital to make the investment.