Chapter 5 Income Approach: Estimating the Cost of Capital
| Jurisdiction | United States |
Chapter 5: Income Approach: Estimating the Cost of Capital
A. Fundamentals of the Cost of Capital13
The cost of capital is one of the most important concepts used in business and security valuation. In both the transactional and litigation areas, it is an important factor in performing valuations for solvency purposes, in calculating economic damages, in M&A and LBO analyses, and in other applications. To company executives, it is the "hurdle rate" that any new investment in acquisitions, equipment or projects should exceed to be worth doing. In the simplest terms, if a company's cost of capital is 15%, then any of its new business investments should have at least a 15% rate of return to be considered for funding.
As stated above, there are numerous applications for the cost of capital within a bankruptcy or other litigation environment, which include:
• solvency analysis related to preference payments and fraudulent conveyances;
• lost profits and other economic damages calculations;
• confirmation of the plan of reorganization;
• purchase or sale price of a business;
• merger or buyout analyses;
• divestiture or acquisition price of a division or other business unit;
• warrant or option valuations; and
• breach of contract and related economic damages analyses.
In each of these situations, the analyst may assess value, whether it is for a company, a division or subsidiary, or an investment stream of cash flow. We've already seen how the discounting of future cash flow to present value is a powerful tool in estimating the value of a business. As part of the valuation process, the analyst may ask: what is the appropriate discount rate? The typical answer: the company's cost of capital.
This cost of capital analysis has powerful uses in each of the situations listed above. In bankruptcy cases, for example, creditors will often assess whether a debtor company is of greater value as an ongoing-concern business enterprise or as a set of saleable assets. As a result, an important input into the decision process is the cost of capital.
In cases involving damages from a tort or a breach of contract, lost future sales result in the loss of future cash flow. Analysts often express that future lost income (however measured) as a present value. Again, an appropriate discount rate is part of the solution. The appropriate discount rate is typically the company's cost of capital. Similarly, when damages are estimated by the decrease in the subject company value (e.g., deepening insolvency), the two value indications often depend on the choice of the cost of capital.
Cost of Capital for a Business
The cost of capital for a debtor company is based on the return (expressed as a percentage) that its creditors and its shareholders expect to receive. Some analysts mistakenly think that cost of capital is simply the company's cost of borrowing money. As we'll soon see, the cost of borrowing is relevant only for loans to the company and for other IOUs, such as bonds. But shareholders also have expectations for returns, and the cost of meeting those expectations is a component of the company's overall cost of capital.
As a prelude to any discussion of cost of capital, we need to consider the debtor company's sources of capital — i.e., how the debtor company is financed. Let's consider the hypothetical example of SkyWarrior Software, a developer of computer games. Its simplified balance sheet, presented in Exhibit 5-1, indicates two sources of capital: debentures (unsecured bonds) and stockholders' equity. The debentures in this case are bonds that mature in 10 years. These bonds pay their holders' interest at a rate of 14%.
We can see from this balance sheet that the total long-term capital employed in the company (the debentures plus the stockholders' equity) is $250 million. Obviously, some funds are also being provided through current liabilities. In all likelihood, these would include accounts payable, accrued income taxes, accrued wages, and perhaps a bank loan of less than one year. In the world of finance, "current" sources of funds — those due in less than one year — are usually not thought of as part of the company's permanent capital. Capital is typically a more permanent source of funding.
However, for purposes of determining debt for calculating the cost of capital, the current portion of the long-term debt (i.e., the debt that has to be repaid within 12 months) is also considered in the cost of debt analysis — because it is an interest-bearing debt.
Exhibit 5-1: SkyWarrior Software, Inc. Illustrative Balance Sheet ($ Millions)
| ASSETS | LIABILITIES |
| Current assets | $330 Current liabilities $150 |
| Net plant & equipment | 70 Debentures 150 |
| Stockholders' equity 100 | |
| Total assets | $400 Total liabilities and $400 equity |
The purpose of ascertaining the SkyWarrior capital structure is to understand what proportion is represented by long-term, interest-bearing debt and what proportion is represented by stockholders' equity. Here, debt and equity are 60% and 40%, respectively. Understanding this, we can begin to calculate the company's cost of capital, which is the "weighted average" of the cost of debt capital and the cost of equity capital, or the WACC. The chart below, Determination of Weighted Average Cost of Capital, illustrates the "big picture" of the concept:
For SkyWarrior Software, the weighted average cost of capital is represented by the following equation:
Cost of Debt
Measuring the cost of debt is usually more straightforward than measuring the cost of equity. The cost of debt is the interest rate (or yield) that the company must promise to creditors to induce them to provide long-term funds. In the case of SkyWarrior Software, which has a single source of debt, determining the cost of debt would appear to be simple. But most companies, especially larger ones, have many sources of debt with complex sets of features, issued at different interest rates. This complicates the of calculating the cost of debt.
Consider the case of Macy's Department Stores, which, after its leveraged buyout, had the following debt on its balance sheet (Exhibit 5-2):
Exhibit 5-2: Macy's Cost of Debt
| Type of Debt | Interest Rate (%) | Amount (millions) | Portion of Total Debt |
| Existing (pre-LBO) long-term debt | 8.0 | $120 | 0.04 |
| Real estate mortgage | 11.0 | 800 | 0.27 |
| Bank loan | 12.0 | 795 | 0.26 |
| Senior notes | 13.5 | 200 | 0.07 |
| Senior subordinated debentures | 14.5 | 400 | 0.13 |
| Subordinated debentures | 15.5 | 450 | 0.15 |
| Subordinated discount debentures | 17.0 | 250 | 0.08 |
| Total | $3,015 | 1.00 |
As illustrated in Exhibit 5-2, the largest debt component is an $800 million real estate mortgage, and the smallest is $120 million in existing (pre-LBO) long-term debt. The exhibit provides the interest rate charged on each of these debt instruments and the respective weights of each debt component as a percentage of Macy's total debt. To measure the cost of debt in this case, we multiply the interest rate by the weight of this type of debt as a percentage of total debt, then sum it up, as shown below:
Macy's cost of debt = (.04 x 8.0) + (.27 x 11.0) + (.26 x 12.0) + (.07 x 13.5) + (.13 x 14.5) + (.15 x 15.5) + (.08 x 17.0) = 12.93%
We use the example of post-LBO Macy's here for a particular reason: With the exception of the $120 million in existing (pre-LBO) debt, the debt on its balance sheet was assumed as part of the leveraged buyout. In contrast, the debt of the typical large company is acquired over some period of time. For example, on the balance sheet of a typical company, we may find one set of debentures issued 20 years ago at 6% and another set of debentures issued last week at 12%. Obviously, the cost of debt for this company today is very far from 6% — and it is today's cost of debt that matters. Analysts call this the "marginal cost of debt" — i.e., the cost of acquiring the next block of debt capital.
Since debt recorded on the balance sheet of a company is historical, and the cost of that debt is rarely a true indicator of the current cost of debt, what practical procedure can we use to determine what a company's cost of debt is today? For companies with publicly traded debt securities, the yield-to-maturity of their debt securities is a good rule of thumb. Yield-to-maturity indicates what rate of interest is needed to induce an investor to buy or hold a company's debt. A debt security's yield-to-maturity (YTM) is the rate of return that an investor will receive from a bond given its purchase price, stated interest rate (coupon rate), its value at maturity, and the time remaining to maturity.
If a bond is purchased at its face value, the YTM is the same as the stated coupon rate. But bonds trading in the public bond market are rarely traded at face value; they are either bought at a discount to the face value or at a premium to the face value. For example, in an environment of lower interest rates, consider a bond that was issued at face value when interest rates were higher, say 8%, and is now trading at $1,041. It will continue paying its stated interest payments of $80 (8% x $1,000) and upon maturity will be redeemed at $1,000. The YTM is the result of a time-value calculation that recognizes these cash flows. For a five-year bond with an 8% coupon assumed to be paid annually, and purchased at $1,041, we would have the following cash flow:
| Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| ($1,041) | $80 | $80 | $80 | $80 | $80 |
| $1,000 | |||||
| $1,080 |
The yield to maturity is the discount rate that will equate the present value of the expected cash flow to the purchase price of $1,041. Financial calculators make this calculation easy. We can simply follow these steps:
PV = -1041, PMT = 80, n = 5, FV = 1000
Depending on...
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