In what sense is the cost of capital an opportunity cost? An opportunity cost to whom? And, Is it possible that there could be sources of financing that have a zero cost?

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?

Use the following data on median values of single detached houses of Canadian residents in 20 census metropolitan areas in British Columbia and Ontario in 2017 (source: Statistics Canada) to prepare a statistical report. The data are reported in units of a hundred thousand dollars rounded to the nearest ten thousand dollars (so, for example, 5.7 represents $570,000).

Data: 5.7, 5.2, 12.6, 6.4, 3.7, 2.1, 2.9, 2.4, 4.2, 4.3, 2.9, 3.6, 2.6, 4.2, 4.2, 2.7, 2.5, 2.2, 7.2, 1.9. ):

1. A dotplot or a histogram of the data. Note that you’ll have to group the data into suitable, equal-sized intervals before drawing your graph.

2. A pie graph of the data showing the percentages of the sample in the following categories: 1-3, 3-5, 5-7, 7-10, and 10 or higher.

3. The mean and the median, together with a brief discussion of which of these is the more appropriate measure of what is typical or representative for this dataset.

4. The 5-number summary of the data (i.e., the minimum, lower quartile, median, upper quartile, and maximum

5. The range of the data and the inter-quartile range of the data, together with a brief discussion of exactly what the inter-quartile range represents for this dataset.

6. The following probability calculations, including reasoning. Suppose we select one census metropolitan area at random from the sample of 20. What is the probability that it has a single detached house median value greater than $500k?

7. Suppose we select one census metropolitan area at random from the sample of 20. What is the probability that it has a single detached house median value greater than $500k or less than $200k? (2) Suppose we select two census metropolitan areas at random from the sample of 20. What is the probability that both have a single detached house median value greater than $500k?

A conducting ball is neutralized and then electrically isolated.  A + 3.0 μ C charge is then placed near the conducting ball without touching it.

After the charge is brought in, the net charge on the conducting ball will be                            [ Select ]                       ["zero", "positive", "negative"]         .  The surface charge density will be                            [ Select ]                       ["zero", "positive", "negative"]         at points on the conducting ball nearest to the + 3.0 μ C charge, and will be                            [ Select ]                       ["zero", "positive", "negative"]         at points on the conducting ball farthest from the + 3.0 μ C charge.  The net electrical force acting on the + 3.0 μ C charge will be                            [ Select ]                       ["zero", "directed towards the ball", "directed away from the ball"]         .

                           [ Select ]                       ["None", "One", "Two", "Three", "All four"]         of the correct answers above will remain true if the conducting ball were replaced by a non-conducting ball of the same radius and distance to the + 3.0 μ C charge.  The surface charge density of the non-conducting ball will be
Choose one:                            [ Select ]                       ["(A)", "(B)", "(C)", "(D)"]      

Expand Your Critical Thinking 24-02 a-d Ana Carillo and Associates is a medium-sized company located near a large metropolitan area in the Midwest. The company manufactures cabinets of mahogany, oak, and other fine woods for use in expensive homes, restaurants, and hotels. Although some of the work is custom, many of the cabinets are a standard size. One such non-custom model is called Luxury Base Frame. Normal production is 1,000 units. Each unit has a direct labor hour standard of 5 hours. Overhead is applied to production based on standard direct labor hours. During the most recent month, only 1,060 units were produced; 4,500 direct labor hours were allowed for standard production, but only 4,000 hours were used. Standard and actual overhead costs were as follows. Standard (1,000 units) Actual (1,060 units) Indirect materials $ 14,600 $ 15,000 Indirect labor 52,400 62,200 (Fixed) Manufacturing supervisors salaries 27,400 26,800 (Fixed) Manufacturing office employees salaries 15,800 15,200 (Fixed) Engineering costs 32,900 30,500 Computer costs 12,200 12,200 Electricity 3,000 3,000 (Fixed) Manufacturing building depreciation 9,700 9,700 (Fixed) Machinery depreciation 3,600 3,600 (Fixed) Trucks and forklift depreciation 1,800 1,800 Small tools 900 1,700 (Fixed) Insurance 600 600 (Fixed) Property taxes 400 400 Total $175,300 $182,700

Calculate the 1) total overhead variance, 2) controllable variance, and 3) volume variance. (Round variable overhead to 2 decimal places and final answers to 0 decimal places, e.g. 1,575.)

Sixteen-year-old Michelle Portman was out driving at night near Sandusky, Ohio with her friend Katie Webster in the front passenger seat. They came to a railroad crossing with multiple tracks, where the mechanical arm had descended and warning bells were sounding. A Conrail train had suffered mechanical problems and was stopped 200 hundred feet from the crossing, where it had been stalled for close to an hour. Michelle and Katie saw several cars ahead of them go around the barrier and cross the tracks, despite the fact that Ohio’s vehicle and traffic laws prohibited this practice. Michelle had to decide whether she would do the same.
Long before Michelle made her decision, the train’s engineer (a Conrail employee) had seen the heavy Saturday night traffic crossing the tracks and realized the danger. The conductor and brakeman also understood the peril, but rather than posting a flagman who could have stopped traffic when a train approached, they walked to the far end of their train to repair the mechanical problem. A police officer had come upon the scene, told his dispatcher to notify the train’s parent company Conrail of the situation, and left.
Michelle made the decision to cross the tracks. She slowly followed the cars ahead of her. Seconds later, both girls were dead. A freight train traveling 60 miles per hour struck the vehicle broadside, killing Michelle and Katie instantly.
Michelle’s mother sued Conrail for negligence. The company argued that it was Michelle’s decision, one that violated Ohio traffic laws, which led to her death. Ohio is a comparative negligence state. Discuss both the plaintiff’s claim and Conrail’s defense. What verdict will result?

Please answer in the IRAC format.

Issue

Rule

Analysis

Conclusion