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Cost of Common Equity

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Why are several formulas often used to estimate the cost of common equity instead of the "right" formula?

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Please see response below, some of which is also attached. I hope this helps and take care.
RESPONSE:

1. Why are several formulas often used to estimate the cost of common equity instead of the "right" formula?

The annual rate of return that an investor expects to earn when investing in shares of a company is known as the cost of common equity. That return is composed of the dividends paid on the shares and any increase (or decrease) in the market value of the shares. For example, if an investor expects a 10% return from McDonald's stock and she buys a share at $67.25, her expectation is to receive $6.72 during the year through a combination of dividends (currently $.34 per share during 1998) and the appreciation of the stock price (presumed to be $6.38 to give her the 10% expected return totaling $6.72) during the year (http://www.valuepro.net/approach/equity/equity.shtml).

There are three formulas to calculate the cost of common equity:

1. Use CAPM (uses beta)
2. (GORDON MODEL) The constant dividend growth model - same as DCF method
3. Bond yield - plus - risk premium (http://www.exinfm.com/training/cost_of_capital.doc).

More than one formula is used to address the different return components, mainly because the estimator of some measures will give a biased result depending on the what component you are interested in measuring. Thus, using different models increases the likelihood the estimate of the cost of equity is a reasonable one.

So, let's take a look at what rate of return, in general, an investor should expect from a stock.

For example, the return expected of any risky common stock should be composed of at least three different return components: (1) a return commensurate with a risk-free security (Rf); (2) a return that incorporates the market risk associated with common stocks as a whole (Rm); and (3) a return that incorporates the business and financial risks specific to the stock of the company itself, known as the company's beta.

1) The first measure of return (Rf) relates to what market ...

Solution Summary

The solution defines the cost of common equity. It then identifies and explains why several formulas are often used to estimate the cost of common equity instead of the "right" formula. Illustrative examples are also provided.

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Berkshire Instruments: Cost of Capital

To be honest, I don't even know where to start with this problem and would appreciate any help that you feel is allowed. At least something that could get me started and allow me to check my work when finish. Thank you for your help.

Please see attachment for the entire problem I need help with...

Berkshire Instruments
Cost of Capital

A1 Hansen, the newly appointed vice president of finance of Berkshire Instruments, was eager to talk to his investment banker about future financing for the firm. One of Al's first assignments was to determine the firm's cost of capital. In assessing the weights to use in computing the cost of capital, he examined the current balance sheet, presented in Figure 1.

In their discussion, Al and his investment banker determined that the current mix in the capital. structure was very close to optimal and that Berkshire Instruments should continue with it in the future. Of some concern was the appropriate cost to assign to each of the elements in the capital structure. Al Hansen. requested that his administrative assistant provide data on what the cost to issue debt and preferred stock had been in the past. .The information is provided in Figure 2.

When Al got the data, he felt he was making real progress toward determining the cost of capital for the firm. However, his investment banker indicated that he was going about the process in an incorrect manner. The important issue is the current cost of the funds, not the historical cost. The banker suggested that a comparable firm in the industry, in terms of size and bond rating (Baa), Rollins Instruments, had issued bonds a year and a half ago for 9.3 percent interest at a $1,000 par value, and the bonds were currently selling for $890. The bonds had 20 years remaining to maturity. The banker also observed that Rollins Instruments had just issued preferred stock at $60 per share, and the preferred stock paid an annual dividend of $4.80.

In terms of cost of common equity, the banker suggested that A1 Hansen use the dividend valuation model as a first approach to determining cost of equity. Based on that approach, Al observed that earnings were $3 a share and that 40 percent would be paid out in dividends (D1). The current stock price was $25. Dividends in the last four years had grown from 82 cents to the current value.

The banker indicated that the underwriting cost (flotation cost) on a preferred stock issue would be $2.60 per share and $2.00 per share on common stock. Al Hansen further observed that his firm was in a 35 percent marginal tax bracket.

With all this information in hand, A1 Hansen sat down to determine his firm's cost of capital. He was a little confused about computing the firm's cost of common equity. He knew there were two different formulas: one for the cost of retained earnings and one for the cost of new common stock. His investment banker suggested that he follow the normally accepted approach used in determining the marginal cost of capital. First, determine the cost of capital for as large a capital structure as current retained earnings will support; then, determine the cost of capital based on exclusively using new common stock.

Figure 1

BERKSHIRE INSTRUMENTS
Statement of Financial Position
December 31, 2003

Assets

Current assets:
Cash $ 400,000
Marketable securities 200,000
Accounts receivable $2,600,000
Less: Allowance for bad debts 300,000 2,300,000
Inventory 5,500,000
Total current assets $ 8,400,000
Fixed assets:
Plant and equipment, original cost 30,700,000
Less: Accumulated depreciation 13,200,000
Net plant and equipment 17,500,000
Total assets $ 25,900,000
Liabilities and Stockholders' Equity
Current liabilities:
Accounts payable $ 6,200,000
Accrued expense 1,700,000
Total current liabilities 7,900,000
Long-term financing:
Bonds payable 6,120,000
Preferred stock 1,080,000
Common stock } Common Equity 6,300,000
Retained earnings 4,500,000
Total common equity 10,800,000
Total long-term financing 18,000,000
Total liabilities and stockholders' equity $ 25,900,000

Figure 2

Security Year of Issue Amount Yield

Bond 1988 $ 1,120,000 6.1%
Bond 1992 3,000,000 13.8%
Bond 1998 2,000,000 8.3%
Preferred stock 1993 600,000 12.0%
Preferred stock 1996 480 7.9%
Cost of prior Issues
of debt and preferred
stock

Berkshire Instruments

Required 1. Determine the weighed average cost of capital based on using retained earnings
in the capital structure. The percentage composition in the capital structure for
bonds, preferred stock, and common equity should be based on the current capital
structure of long term financing as shown in Figure 1 (it adds up to $18 million).
Common equity will represent 60 percent of financing throughout this case.
2. Re-compute the weighed average cost of capital based on using new common stock
in the capital structure. The weights remain the same, only common equity is now
supplied by new common stock, rather than by retained earnings. After how much
new financing will this increase in the cost of capital take place? Determine this
by dividing retained earnings by the percent of common equity in the capital
structure.
3. Assume the investment banker also wishes to use the capital asset pricing model,
to compute the cost (required return) on common stock. Assume Krf = 6 percent, β is 1.25, and Km is 13 percent. What is the value of Ks? How does this compare to the value of Ks computed in question 1?

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