Why 8.8 Percent and Not 8: Building and Defending a Cost of Capital for a Private Cold Storage Company
Student Name
American College of Education
FIN5003: Financial Decision Making
Module 2 Assignment
Instructor Name
July 10, 2028
Why the Old Rate Needs Replacing
Fenwick Cold Chain, the composite refrigerated warehouse operator in this course, has used 8 percent as its discount rate for every capital decision for at least a decade. No one on the finance team can say how it was set. Since then, interest rates have changed, the company has taken on more debt and it is now considering its largest investment ever, a 40,000-pallet freezer facility. A rate that is too low would make poor investments look attractive; one that is too high would reject good ones. The company is private, so it cannot observe its own stock's behavior, and the rate must be built from comparable companies and market data. A discount rate nobody can explain is not conservative or aggressive; it is simply unexamined.
Cost of Equity From Peers
For the return owners require, this paper relies on the capital asset pricing model, which sets it equal to the risk-free rate plus the company's beta, its sensitivity to market movements, times the market risk premium. In the survey of finance executives by Graham and Harvey (2001), the capital asset pricing model was the most popular way to estimate the cost of equity, which is one reason to use it here: it is the method the company's lenders and any future investors will expect. Because Fenwick has no stock price, its beta is estimated from two publicly traded temperature-controlled logistics companies, composites for this paper, with observed equity betas of 1.05 and 0.95 and debt-to-equity ratios of 0.8 and 0.6.
Those betas include the effect of each peer's debt, which makes equity riskier. Using the approach set out by Hamada (1972), each beta is unlevered to remove that effect, dividing it by one plus the after-tax debt-to-equity ratio, using a 21 percent tax rate. Both peers produce an asset beta of about 0.64. The asset beta is then relevered at Fenwick's target debt-to-equity ratio of 0.5 and its combined tax rate of 25 percent, giving an equity beta of about 0.89. With a risk-free rate of 4.3 percent, the yield on 20-year Treasury bonds in this case, and a market risk premium of 5.5 percent, the base cost of equity is about 9.2 percent.
The Contested Adjustment
The analysis adds a premium of 1.5 percentage points for Fenwick's size and lack of a public market for its shares, bringing the cost of equity to about 10.7 percent. This is the most contestable input, and it needs defending. The case for it is that Fenwick's owners cannot sell their shares easily, the company depends on a handful of large customers and it has less access to capital than its public peers, all risks the peers' betas do not capture. The case against is that evidence for a general small-company premium in stock returns has weakened over time, and an arbitrary premium can be used to reject projects that should be accepted.
The paper keeps the premium but limits its use. It reflects Fenwick's real concentration: its three largest customers provide 58 percent of revenue. Should that concentration fall, or the company gain access to public markets, the premium should be reduced. The finance committee should also see the result without it, a weighted cost of capital of about 7.8 percent, so that any project whose acceptance depends on the premium is identified and discussed rather than decided silently by an assumption.
Cost of Debt and the Weights
Fenwick's bank offers term debt for the freezer project at 6.9 percent, which is also the rate on its existing term loan, so the marginal pretax cost of debt is 6.9 percent. Interest reduces taxable income, so each dollar of it really costs Fenwick only 75 cents at a 25 percent tax rate, which brings the effective cost down to about 5.2 percent. The weights use Fenwick's target capital structure, one-third debt and two-thirds equity, not its current book values, because the rate should reflect how the company intends to finance itself over the life of its investments. The weighted average cost of capital is two-thirds of 10.7 percent plus one-third of 5.2 percent, about 8.8 percent.
The Limits of the Model
The capital asset pricing model is widely used but empirically imperfect. Fama and French (2004), reviewing the evidence, concluded that the model's empirical record is poor enough to invalidate the way it is used in many applications, noting that the relation between beta and average return is flatter than the model predicts. That criticism argues for treating the 8.8 percent figure as an estimate with a range, not a precise hurdle. Reasonable changes in the inputs, a market risk premium of 5 or 6 percent, or a peer beta range from 0.9 to 1.1, would move the rate by about half a percentage point either way. The committee should expect decisions near the margin to be tested at 8.3 and 9.3 percent as well.
Checking the Result Against the Market
A cost of capital built from a model should be compared with evidence from outside the model. Three checks were made. First, the bank's 6.9 percent rate on Fenwick's senior secured debt sets a floor: equity, which is paid only after the bank, must require a higher return than debt, and the 10.7 percent estimate comfortably exceeds it. Second, two recent sales of private refrigerated warehouse businesses in the region, whose terms Fenwick's owners learned of when they were approached as possible buyers, were priced at multiples of operating cash flow that imply investors required returns in the range of 8 to 10 percent on the whole business, consistent with the 8.8 percent estimate. Third, the peers' own disclosed hurdle rates for development projects, where they give them, fall between 8 and 9 percent.
None of these checks is precise, and each has its own biases; acquisition prices, for example, include expected synergies. But together they suggest that 8.8 percent is in the right range and that the old 8 percent, while not wildly wrong, understated the return the company's investors and lenders now require. That matters most for long projects like the freezer facility, where a difference of eight-tenths of a point in the discount rate changes the present value of distant cash flows substantially.
How the Rate Should Be Used
The weighted average cost of capital is the right rate for projects with the same risk as Fenwick's existing business. The freezer facility is close to that: it is backed by a 15-year contract with a large food manufacturer, which lowers its revenue risk, but it concentrates Fenwick's exposure to one customer. The paper recommends using 8.8 percent for the freezer project's net present value analysis in the next module, with 7.8 and 9.3 percent as sensitivity cases. For comparisons of costs alone, such as the refrigeration choice in Module 1, the choice between 8 and 8.8 percent does not change the ranking, because the carbon dioxide system's advantage holds at both rates. The old 8 percent should be retired as a general rate, and the committee should review the new one every year and whenever the company's financing changes materially.
References
Fama, E. F., & French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25-46. https://doi.org/10.1257/0895330042162430
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
Hamada, R. S. (1972). The effect of the firm's capital structure on the systematic risk of common stocks. The Journal of Finance, 27(2), 435-452. https://doi.org/10.1111/j.1540-6261.1972.tb00971.x
How this FIN 5003 Module 2 example is structured
FIN 5003 Module 2 typically builds a cost of capital you then have to defend in prose; your classroom's instructions decide the method and the inputs required. This example builds the rate step by step, but spends as much space on defending each assumption as on calculating it, because the module brief asks for a defense. A section on the limits of the model acknowledges published criticism of the capital asset pricing model, and the conclusion states how the rate should and should not be used.
FIN5003 Module 2 questions, answered
What does FIN5003 Module 2 usually ask for?
FIN5003 Module 2 typically asks students to estimate a company's cost of capital and defend the assumptions behind it. Many sections expect the capital asset pricing model, a cost of debt and a weighted average cost of capital with explained weights. Your classroom's instructions decide the method and inputs.
How do I estimate beta for a private company?
Use comparable public companies. Unlever each peer's equity beta to remove the effect of its debt, average the asset betas and relever the average at the private company's target debt-to-equity ratio and tax rate.
Should I add a size or private company premium?
It is contested. If you add one, explain the specific risks it represents, show the result with and without it and identify any decision that depends on it, so the premium does not decide outcomes silently.
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