The Cost of Capital: Cost of Retained Earnings

The cost of common equity is based on the rate of return that investors require on the company's common stock. New common equity is raised in two ways: (1) by retaining some of the current year's earnings and (2) by issuing new common stock. Equity raised by issuing stock has a(n)

cost, r_e, than equity raised from retained earnings, r_s, due to flotation costs required to sell new common stock. Some argue that retained earnings should be "free" because they represent money that is left over after dividends are paid. While it is true that no direct costs are associated with retained earnings, this capital still has a cost, a(n)

cost. The firm's after-tax earnings belong to its stockholders, and these earnings serve to compensate them for the use of their capital. The earnings can either be paid out in the form of dividends to stockholders who could have invested this money in alternative investments or retained for reinvestment in the firm. Therefore, the firm needs to earn at least as much on any earnings retained as the stockholders could earn on alternative investments of comparable risk. If the firm cannot invest retained earnings to earn at least r_s, it should pay those funds to its stockholders and let them invest directly in stocks or other assets that will provide that return. There are three procedures that can be used to estimate the cost of retained earnings: the Capital Asset Pricing Model (CAPM), the Bond-Yield-Plus-Risk-Premium approach, and the Discounted Cash Flow (DCF) approach.

CAPM

The firm's cost of retained earnings can be estimated using the CAPM equation as follows:

r_s = r_RF + (RP_M)b_i = r_RF + (r_M - r_RF)b_i

The CAPM estimate of r_s is equal to the risk-free rate, r_RF, plus a risk premium that is equal to the risk premium on an average stock, (r_M - r_RF), scaled up or down to reflect the particular stock's risk as measured by its beta coefficient, b_i. This model assumes that a firm's stockholders are

diversified, but if they are diversified, then the firm's true investment risk would not be measured by and the CAPM estimate would

the correct value of r_s.

Bond Yield Plus Risk Premium

If reliable inputs for the CAPM are not available as would be true for a closely held company, analysts often use a subjective procedure to estimate the cost of equity. Empirical studies suggest that the risk premium on a firm's stock over its own bonds generally ranges from 3 to 5 percentage points. The equation is shown as: r_s = Bond yield + Risk premium. Note that this risk premium is

the risk premium given in the CAPM. This method doesn't produce a precise cost of equity, but does provide a ballpark estimate.

DCF

The DCF approach for estimated the cost of retained earnings, r_s, is given as follows:

Investors expect to receive a dividend yield, , plus a capital gain, g, for a total expected return. In

, this expected return is also equal to the required return. It's easy to calculate the dividend yield; but because stock prices fluctuate, the yield varies from day to day, which leads to fluctuations in the DCF cost of equity. Also, it is difficult to determine the proper growth especially if past growth rates are not expected to continue in the future. However, we can use growth rates as projected by security analysts, who regularly forecast growth rates of earnings and dividends.

Which method should be used to estimate r_s? If management has confidence in one method, it would probably use that method's estimate. Otherwise, it might use some weighted average of the three methods. Judgment is important and comes into play here, as is true for most decisions in finance.

Quantitative Problem: Barton Industries estimates its cost of common equity by using three approaches: the CAPM, the bond-yield-plus-risk-premium approach, and the DCF model. Barton expects next year's annual dividend, D₁, to be $1.50 and it expects dividends to grow at a constant rate g = 3.1%. The firm's current common stock price, P₀, is $28.00. The current risk-free rate, r_RF, = 4%; the market risk premium, RP_M, = 5.3%, and the firm's stock has a current beta, b, = 1.2. Assume that the firm's cost of debt, r_d, is 6.11%. The firm uses a 3.3% risk premium when arriving at a ballpark estimate of its cost of equity using the bond-yield-plus-risk-premium approach. What is the firm's cost of equity using each of these three approaches? Round your answers to 2 decimal places.

What is your best estimate of the firm's cost of equity?

Suppose that sales for a shirt are 900 units per month. It costs $60 to generate an order. The item to be ordered has a unit cost of $14 and the inventory holding ratio is 8%. Find the answers to the following questions.

1) Calculate the optimal lot size to purchase.

2) How frequently should an order be placed throughout the year?

3) Calculate the annual order cost

4) Calculate the annual carrying cost

5) Find the total cost

Suppose that sales for a shirt are 900 units per month. It costs $60 to generate an order. The item to be ordered has a unit cost of $14 and the inventory holding ratio is 8%. Find the answers to the following questions.

1. Calculate the optimal lot size to purchase

2. How frequently should an order be placed throughout the year?

3. Calculate the annual order cost.

4. Calculate the annual carrying cost

5. Find the total cost.

1. Assume diminishing marginal product, constant returns to scale and perfect competition.
   1. Draw short-run marginal cost, average total cost and average variable cost curves for the firm.
   2. Identify market prices that induce entry, exit and shutdown on this graph.
   3. Draw the short-run supply curve for the market. Describe the relationship between the short-run supply curve for the market and the firm’s cost curves.
   4. Draw the long-run supply curve.

Acme Inc. manufactures widgets. This year was a great year with a increase in both sales and production volume. In addition, the cost per unit dropped significantly from the prior year. These facts (probably) imply that:

25. An important application of regression in manufacturing is the estimation of cost of production. Based on DATA from Ajax Widgets relating cost (Y) to volume (X), what is the cost of producing 600 widgets?

Mora Company has the following production data for March: no beginning work in process, 28,600 units started and completed, and 4,700 units in ending work in process that are 100% complete for materials and 40% complete for conversion costs. Mora uses the FIFO method to calculate equivalent units. Unit materials cost is $6 and unit conversion cost is $12. The total costs to be assigned are $565,560. Prepare the cost section of the production cost report for Mora Company.

Amsterdam Company uses a periodic inventory system. For April, when the company sold 600 units, the following information is available. Units Unit Cost Total Cost April 1 inventory   250 $10 $ 2,500 April 15 purchase   400  12   4,800 April 23 purchase   350  13   4,550 1,000 $11,850 Compute the April 30 inventory and the April cost of goods sold using the average-cost method.

Firms in the market for soccer balls are selling in a purely competitive market. A firm in the soccer ball market has an output of 1,000 balls, which it sells for $9 each. At the output level of 1,000, the average variable cost is $8, the average total cost is $11.00, and the marginal cost is $9.

1. What would you expect the firm to do in the short run? in the long run?