The Marginal Cost of Capital (MCC)
Topic 6. The Cost of Capital
A firm’s capital is supplied by its creditors and owners. Firms raise capital by borrowing it (using bonds to investors or promissory notes to banks), or by issuing preferred or common stock. The overall cost of a firm’s capital depends on the return demanded by each of these suppliers of capital.
To determine a firm’s overall cost of capital, the first step is to determine the cost of capital from each supplier. The cost of capital from a particular source, such as bondholders or common stockholders, is known as the component cost of capital.
Sources of Capital
The firm’s cost of debt when it borrows money by using bonds is the interest rate demanded by the bond investors. When borrowing money from an individual or financial institution, the interest rate of the loan is the firm’s cost of debt.
The after-tax cost of debt, AT rd, is the cost to the company of obtaining debt funds. Because the interest paid on bonds or banks loans is a tax-deductible expense for a business, a firm’s AT rd is less than the required rate of return of the suppliers of debt capital. For example, suppose Ellis Industries borrowed $100 000 for one year at 10% interest compounded annually. The interest rate on the loan is 10 %, so Ellis must pay the lender $10 000 in interest each year the loan is outstanding (10% of $100 000). However, look at what happens when Ellis takes its taxes for the year into account:
| Before making loan | After making loan | |
| EBIT | 50 000 | 50 000 |
| Interest Expense | 0 | 10 000 |
| EBT | 50 000 | 40 000 |
| Income Tax (40%) | 20 000 | 16 000 |
| Net Income | 30 000 | 24 000 |
The $10 000 interest charge caused a $6 000 decrease in Ellis’s net income ($30000 - $24 000 = $6 000). Assuming a tax rate of 40%, we see that the true cost of the loan is only $6 000 (6 %), not $10 000 (10 %).
The following formula converts rd into AT rd:
AT rd = rd (1 – T)
where rd– the before-tax cost of debt
T – the firm’s marginal tax rate
AT rd= 0.1 (1 – 0.4) = 0.06
The Cost of Preferred and Common Stock Funds
The cost of preferred stock:
rp = Dp/ PV
гдеDp– the amount of the expected preferred stock dividend
PV – the current price of the preferred stock
Example, Ellis Industries issued preferred stock that has been paying annual dividends of $2.50 and is expected to continue to do so indefinitely. The current price of Ellis’s preferred stock is $20 a share.
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rp = 2.5/20 = 0.125 = 12.5%
The cost of common stock:
rs = D1/PV + g
where:
D1 – the dollar amount of the common stock dividend expected one period from now
PV – the current price of the common stock
g – expected constant growth rate per period of the company’s common stock dividends
Example:
Ellis Industries’ common stock is selling for $40 a share. Next year’s common stock dividend is expected to be $4.20, and the dividend is expected to grow at a rate of 5% per year indefinitely.
rs = 4.2/40 + 0.05 = 0.155 = 15.5%
The cost of common stock might be calculated using the CAPM model:
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The cost of new common stock:
rsn = D1/(PV – F) + g
where:
D1 – the dollar amount of the common stock dividend expected to be paid in one year
PV – the price of one share of the common stock
g – expected constant growth rate per period of the company’s common stock dividends
F – the flotation cost per share
Example:
Suppose, again that Ellis Industries’ anticipated dividend next year is $4.20 a share, its growth rate is 5% a year, and its existing common stock is selling for $40 a share. New shares of stock can be sold to the public for the same price. But to do so Ellis must pay its investment bankers 5% of the stock’s selling price, or $2 per share.
rsn = 4.2/(40 – 2) + 0.05 = 0.1605 = 16.05%
The Weighted Average Cost of Capital (WACC)
WACC = (Wd* AT rd) + (Wp* rp) + (Ws* rs)
where WdWpWs– the weight, or proportion of the sources of capital
Example: from our previous calculations, we know the following costs of capital:
AT rd = 6%
rp = 12.5%
rs = 15.5%
Capital Ctructure: (from balance sheet)
| in dollars | in % | |
| Long-& Short-Term Debt | 400 000 | 40% |
| Preferred Stock | 100 000 | 10% |
| Common Stock | 500 000 | 50% |
| Total Liabilities & Equity | 1 000 000 | 100% |
WACC = (0.4 * 0.06) + (0.1 * 0.125) + (0.5 * 0.155) = 11.4%
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Thus, a firm must earn a return equal to the weighted average cost of capital (WACC) to pay suppliers of capital the return they expect. In the case of Ellis Industries, for instance, its average risk capital budgeting project must earn a return of 11.4% to pay its capital suppliers the return they expect.
To illustrate how earning the WACC ensures that all capital suppliers will be paid their required cost of capital, let’s return to our example. Suppose Ellis Industries undertakes a plant expansion program that costs $1 million and earns an annual return of 11.4 %, equal to Ellis’s WACC. Capital for the project is supplied as follows:
· 40 % оf the $1 mln. ($400 000) is supplied by lenders expecting a return equal to before-tax rd, 10%.
· 10 % оf the $1 mln.($100 000) – is supplied by prferred investors expecting a return equal 12.5%
· 50 % оf the $1 mln. ($500 000) – is supplied by common stockholders expecting a return equal 15.5%
If the project does in fact produse the expected 11.4 % return, will all these suppliers of capital receive the return they expect?
| First-year return from the project | |
| Net interest cost to the firm | |
| Preferred dividend paid to preferred stockholders | |
| Dividends paid to common stockholders |
The Marginal Cost of Capital (MCC)
A firm’s WACC will change if one component cost of capital changes.
The weighted average cost of the next dollar of capital to be raised is the marginal cost of capital (MCC).
To find the MCC, financial managers must:
1. assess at what point a firm’s cost of debt or equity will change the firm’s WACC;
2. estimate how much the change will be;
3. calculate the cost of capital up to and after the points of change.
The Firm’s MCC Schedule
The breakpoint in the firm’s MCC schedule is the point where one of the component sources of capital changes.
Finding the breakpoints in the MCC schedule.
To find breakpoints in the MCC schedule, financial managers determine what limits, if any, there are on the firm’s ability to raise funds from a given source at a given cost. Suppose that Ellis Industries’ financial managers, after consulting with bankers, determined that the firm can borrow up to $300 000 at an interest rate of 10%, but any money borrowed above that amount will cost 12%.
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AT rd (up to $300 000) = 6%
AT rd (over $300 000) = 0.12 * (1- 0.4) = 7.2%
To find a firm’s marginal cost of capital breakpoint, we use the formula:
ВР = limit/proportion of total
BPd= 300 000/0.4 = 750 000
The Equity Breakpointis the point at which the marginal cost of capital changes because the cost of equity changes.
We will assume that Ellis Industries expects to realize $600 000 in income this year after it pays preferred stockholders their dividends. The $600 000 in earnings belong to the common stockholders. The firm may either pay dividends, or retain the earnings. Let’s assume Ellis retains the $600 000. The finite supply of capital from the existing common stockholders is the $600 000 addition to retained earnings. To find the equity breakpoint, then, Ellis’s managers must know at what point the firm will exhaust the common equity capital of $600 000, assuming existing common stock equity is 50 % of the firm’s capital budget.
BPs =600 000/0.5 = 1 200 000
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