Question

Describe in detail how to calculate component costs of capital and how to create graphs of the marginal cost of capital (MCC) for each of the methods in the case (DCF, CAPM, and BY+RP). Also explain a situation where there is no retained earnings break point for the CAPM and BY+RP methods?

Answer 1

Component costs of capital

As the majority of businesses run on borrowed funds, the cost of capital becomes an important parameter in assessing a firm’s potential of net profitability. Analysts and investors use weighted average cost of capital (WACC) to assess an investor’s returns on an investment in a company.

Companies often run their business using the capital they raise through various sources. They include raising money through listing their shares on the stock exchange (equity), or by issuing interest-paying bonds or taking commercial loans (debt). All such capital comes at a cost, and the cost associated with each type varies for each source.

WACC is the average after-tax cost of a company’s various capital sources, including common stock, preferred stock, bonds, and any other long-term debt. In other words, WACC is the average rate a company expects to pay to finance its assets.

Since a company’s financing is largely classified into two types – debt and equity – WACC is the average cost of raising that money, which is calculated in proportion to each of the sources.
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WACC=( (E/V) ×Re)+( (D/V) ×Rd×(1−Tc))

where:
E=Market value of the firm’s equity
D=Market value of the firm’s debt
V=E+D
Re=Cost of equity
Rd=Cost of debt
Tc=Corporate tax rate

How to Calculate WACC
WACC is calculated by multiplying the cost of each capital source (debt and equity) by its relevant weight, and then adding the products together to determine the value.

In the above formula, E/V represents the proportion of equity-based financing, while D/V represents the proportion of debt-based financing.

WACC formula is the summation of two terms:

((E/V)×Re)
( (D/V) ×Rd×(1−Tc))

The former represents the weighted value of equity-linked capital, while the latter represents the weighted value of debt-linked capital.

Equity and Debt Components of WACC Formula

It's a common misconception that equity capital has no concrete cost that the company must pay after it has listed its shares on the exchange. In reality, there is a cost of equity.

The shareholders' expected rate of return is considered a cost from the company's perspective. That's because if the company fails to deliver this expected return, shareholders will simply sell off their shares, which will lead to a decrease in share price and the company’s overall valuation. The cost of equity is essentially the amount that a company must spend in order to maintain a share price that will keep its investors satisfied and invested.

One can use the CAPM (capital asset pricing model) to determine the cost of equity. CAPM is a model that established the relationship between the risk and expected return for assets and is widely followed for the pricing of risky securities like equity, generating expected returns for assets given the associated risk and calculating costs of capital.

The debt-linked component in the WACC formula, [(D/V) * Rd * (1-Tc)], represents the cost of capital for company-issued debt. It accounts for interest a company pays on the issued bonds or commercial loans taken from bank.

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Example of How to Use WACC
Let's calculate the WACC for retail giant Walmart Inc. (WMT).

As of October 2018, the risk-free rate, represented by annual return on 20-year treasury bond was 3.3 percent, beta value for Walmart stood at 0.51, while the average market return, represented by average annualized total return for the S&P 500 index over the past 90 years, is 9.8 percent.

From the balance sheet, the total shareholder equity for Walmart for the 2018 fiscal year was $77.87 billion (E), and the long term debt stood at $36.83 billion (D). The total for overall capital for Walmart comes to:
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V=E+D=$114.7 billion

The equity-linked cost of capital for Walmart is:

(E/V)×Re= ( 77.87/114.70) ×6.615%=0.0449
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The debt component is:

(D/V)×Rd×(1−Tc)= (36.83/114.7) ×6.5%×(1−21%)=0.0165
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Using the above two computed figures, WACC for Walmart can be calculated as:

0.0449+0.016=0.0609 or 6.1%
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On average, Walmart is paying around 6.1% per annum as the cost of overall capital raised via a combination of debt and equity.

The above example is a simple illustration to calculate WACC. One may need to compute it in a more elaborate manner if the company is having multiple forms of capital with each having a different cost.

For instance, if the preferred shares are trading at a different price than common shares, if the company issued bonds of varying maturity are offering different returns, or if the company has a (combination of) commercial loan(s) at different interest rate(s), then each such component needs to be accounted for separately and added together in proportion of the capital raised.

Marginal cost of capital

Marginal cost of capital is the weighted average cost of the last dollar of new capital raised by a company. It is the composite rate of return required by shareholders and debt-holders for financing new investments of the company. It is different from the average cost of capital which is based on the cost of equity and debt already issued.

The weighted average cost of capital (WACC), the most common measure of cost of capital used in capital budgeting and business valuation, is the weighted average of the marginal cost of common stock, marginal cost of preferred stock and marginal after-tax cost of debt.

The distinction between average cost of capital and marginal cost of capital is important. The marginal cost of capital rises as the company raises more and more capital. This is because capital is scarce, just like any other factor of production, and must be compensated through a higher required return. The return available on new projects must be compared with the marginal cost of capital and not the average cost of capital and the projects should be accepted only when the expected return is higher than the required return.

Marginal cost of capital increases in steps and not linearly. This is because a company can finance a certain portion of new investments by reinvesting earnings and raising enough debt and/or preferred stock to maintain the target capital structure. The reinvestment of earnings comes without any increase in cost of equity. However, as soon as the expected capital exceeds the combined amount of retained earnings and debt and/or preferred stock raised to maintain the target capital structure, the marginal cost of capital increases.

Break point is the total amount of new investments that can be financed and the new capital that can be raised before a jump in marginal cost of capital is expected. It is the point at which the marginal cost of capital curve breaks out from its flat trend.

The break point can be worked out by dividing the retained earnings for the period by the weight of the retained earnings in the target capital structure. The retained earnings in a period equals the product of net income for the period and the retention rate (also called plow-back rate), which equals 1 minus the dividend payout ratio.

The following equation can be used to calculate the break point:

Break Point =   NI × (1 - DPR)

We

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Where NI is the net income for the period, DPR is the dividend payout ratio, i.e. the dividends declared dividend by net income and We is the weight of retained earnings in the target capital structure.

The break points are helpful in creating the marginal cost of capital curve, a graph that plots capital raised on the X-axis and marginal weighted average cost of capital on the Y-axis.

Your company's marginal cost of capital was 10% at the start of 2017. Its net income for the year was $30 million, 30% of which was paid out in dividends. Retained earnings form 45% of the target capital structure of the company.

The company's break point equals retained earnings for the period divided by proportion of retained earnings in target capital structure.

Retained earnings for the period equals $21,000,000 (i.e. $30,000,000 × (1 – 30%)).

Break Point =   $21,000,000   = $46.67 million
0.45
The new marginal cost of capital once $46.67 million of capital is raised is 12%.

Using the above data, the marginal cost of capital curve can be graphed as follows:

Investment Opportunity Schedule
Investment opportunity schedule is the table/graph of cumulative investment opportunities and their expected return. It plots the expected return on the Y-axis and the initial investment required on the X-axis. The investment opportunity schedule is a down-ward sloping curve because investment opportunities are rare and each new opportunity is expected to generate a diminishing return.

Let's say the following is a list of potential investment opportunities available to your company and their expected return:

Project Initial Investment Expected Return
  A $25,000,000 25%
B $40,000,000 18%
C $25,000,000 12%
D $15,000,000 8%

The investment opportunity schedule can be plotted as follows:

Optimal Capital Budget
A company's optimal capital budget is the point at which its marginal cost of capital equals the incremental expected return. A company should raise new capital as long as the marginal cost of capital is lower than or equal to the available return.

The following chart plots the marginal cost of capital and investment opportunity schedule. The point of intersection of the marginal cost of capital curve and investment opportunity schedule is the optimal capital budget.

Why is there a cost for retained earnings?

Earnings can be reinvested or paid out as dividends.
Investors could buy other securities, and therefore earn a return.
Thus, there is an opportunity cost if earnings are retained instead of being paid out

Opportunity cost in this sense refers to the return that stockholders could earn on alternative investments of equal risk. Stockholders could buy similar stocks and earn a particular rate kic , therefore this rate, kic is the cost of retained earnings.

There are three ways to determine this cost of internal common equity, kic:

1. Capital Asset Pricing Model (CAPM) approach.

2. Own-Bond-Yield-Plus-Risk Premium approach

3. Discounted Cash Flow (DCF) approach.

1. Capital Asset Pricing Model (CAPM) approach.

We may recall that theCapital Asset Pricing Model (CAPM) approach utilises the Security Market Line Equation to the determine the required rate of return for a stock given its beta.

There a few limitations of this approach. If a company's stock holders are well diversified, they may be concerned with stand-alone risk rather than just market risk. In that case, the company's true investment risk would not measured by its beta, and the CAPM procedure would understate the correct value of kic. Further, even if the CAPM is valid, it is hard to obtain correct estimates of the inputs required to make it operational because (1) there is controversy about whether to use short term or long term Treasury yields for krf , (2) it is hard to estimate the beta that investors expect the company to have in the future, and (3) it is difficult to estimate the market risk premium.

2. The own-bond-yield-plus-risk-premium approach

This approach stems from the theory that it is logical to think that companies with risky low-rated, and consequently high-interest-rate debt will also have risky, high-cost equity. This logic is utilised to estimate the cost of equity by adding a judgmental risk premium (of say 3 to 5 percentage points) to the interest rate on the company's own long-term debt. This subjective and adhoc approach is often times used by analysts who have little confidence in the CAPM approach.

3. Discounted Cash Flow (DCF) approach.(also known as the 'Dividend-Yield-Plus-Growth-Rate' approach)

The is the same approach we had used to compute the rate of return on a common stock

Cost of common equity - New common stock - kec

When a company issues new common stock they have to pay floatation costs to the underwriter. Floatation costs basically refer to all those administrative and processing costs that are incurred when issuing new securities.

Two approaches that can be used to account for floatation costs:

Include the flotation costs as part of the project’s up-front cost. This reduces the project’s estimated return.

Adjust the cost of capital to include flotation costs. This is most commonly done by reducing the sale proceeds by the flotation costs to arrive at a net selling price

Why is the cost of retained earnings cheaper than the cost of issuing new common stock?

1. When a company issues new common stock they have to pay flotation costs to the underwriter

2. Issuing new common stock may send a negative signal to the capital markets, which may depress stock price.