ACC 345 Module 6 Cost of Capital Assignment Example

Building a Discount Rate Without a Stock Price: Cost of Capital for a Composite Fire Sprinkler Contractor

[Student Name]

Southern New Hampshire University

ACC 345: Financial Statement Analysis and Business Valuation

Module Six Assignment

[Instructor Name]

[Date]

The organization, setting and figures below are a composite written as a model document. No real employer, client, colleague or patient is described.

Building a Discount Rate Without a Stock Price: Cost of Capital for a Composite Fire Sprinkler Contractor

Introduction

A discounted cash flow valuation is only as good as its discount rate, and for a private company there is no stock price from which to infer one. The Atlanta sprinkler contractor's shares have never traded, so its cost of equity must be estimated from market data for other companies and adjusted for the differences. This assignment builds the cost of equity using the build-up method, estimates the after-tax cost of debt, chooses capital weights consistent with the buyer's plans and calculates the weighted average cost of capital that Project Two will use (Koller et al., 2020). The valuation date is the end of the latest fiscal year.

Cost of Equity: The Build-Up

Table 1. Build-Up Cost of Equity

The first two components describe the return investors demand from a broad portfolio of large companies. The size premium reflects the long-documented tendency of small companies to earn higher average returns than large ones, first identified by Banz (1981), which valuation practice treats as compensation for added risk. The company-specific premium is the most judgmental input. Three facts support it: two customers account for a large share of receivables, the owner holds most key relationships with general contractors and the statements are reviewed rather than audited. A buyer who addressed those risks, for example by signing the owner to a transition agreement, might reasonably reduce it, as the section below explains.

Cost of Debt

The buyer's lender has quoted 7.5 percent on acquisition debt for a company of this size and risk, a floating rate tied to a market benchmark plus a fixed spread. Because interest is deductible, the after-tax cost is 7.5 percent times one minus the 25 percent tax rate, or 5.6 percent.

Capital Weights

The company's book balance sheet shows debt of $4.8 million against book equity of $5.4 million, but book equity is not a meaningful measure of what the business is worth, and the buyer will refinance at closing. The buyer's plan, typical of its platform acquisitions, is to fund the purchase with about 25 percent debt and 75 percent equity measured at value. Using the target structure keeps the rate consistent with the capital that will actually finance the forecast cash flows.

Weighted Average Cost of Capital

Table 2. Weighted Average Cost of Capital

Comparison With CAPM

As a cross-check, the capital asset pricing model uses a beta from comparable public companies. The two publicly traded fire protection and building services companies the advisor considered have an average unlevered beta of about 0.95; relevered at the target structure, the beta is about 1.13, giving a cost of equity of 4.6 percent plus 1.13 times 5.5 percent, or 10.8 percent before any size or company adjustment. The gap between 10.8 and 17.3 percent is exactly the size and company-specific premiums, which is the main judgment in valuing a small private firm. Graham and Harvey (2001) found that CAPM is the method most chief financial officers use, but that practitioners routinely add adjustments for risks the model does not capture, which is what the build-up method makes explicit.

Sensitivity

Table 3. Effect of the Discount Rate on Enterprise Value

A one-point change in the rate moves enterprise value by roughly $1.6 to $2.0 million, close to a tenth of the total, mostly through the terminal value. That sensitivity is why every component in Table 1 needs a stated basis, and why the rate should be revisited whenever the buyer's financing plan changes.

Judgment in the Company-Specific Premium

Of the four components, three come from published market data and one from judgment, and that one deserves scrutiny because it moves value most per point of change. The 3.0 percent premium is not a figure read from a table; it reflects specific risks an investor in this company bears and an investor in a diversified portfolio of small public companies does not. Two of those risks can be reduced after a sale. A transition and noncompete agreement with the owner would reduce key-person risk, and an audit would reduce information risk. Customer concentration would remain. If the first two were addressed, a premium nearer 1.5 to 2.0 percent could be defended, lowering the weighted average cost of capital by roughly one point and raising value by close to $2 million. That is a negotiating point the seller's advisor would raise, and the buyer should be ready to answer it.

Consistency With the Cash Flows

The 14.4 percent rate is a weighted average cost of capital, so it must be applied to cash flows available to all capital providers, before interest payments and debt repayment, which is how Project Two defines free cash flow. Applying it to cash flow after interest would double count the cost of debt, and applying the 17.3 percent equity rate to cash flow before interest would understate value. The rate is also nominal, so the forecast cash flows must include expected inflation in prices and wages, as the 8 percent revenue growth assumption does.

Conclusion

The contractor's cost of equity is estimated at 17.3 percent by the build-up method, its after-tax cost of debt at 5.6 percent and its weighted average cost of capital at 14.4 percent using the buyer's target structure. The size and company-specific premiums account for most of the difference from a public company rate and deserve the most scrutiny, since a one-point change in the rate moves value by close to a tenth.

References

Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9(1), 3-18. https://doi.org/10.1016/0304-405X(81)90018-0

Graham, J. R., & Harvey, C. R. (2001). The theory and practice of corporate finance: Evidence from the field. Journal of Financial Economics, 60(2-3), 187-243. https://doi.org/10.1016/S0304-405X(01)00044-7

Koller, T., Goedhart, M., & Wessels, D. (2020). Valuation: Measuring and managing the value of companies (7th ed.). Wiley.