FIN 419 Week 4 Capital Structure and Cost of Capital Example

Borrow, Sell a Stake or Use Its Own Cash? Estimating Bluewater Linen's Cost of Capital and Choosing a Debt Level That Survives a Lost Customer

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University of Phoenix

FIN/419: Finance for Decision Making

Week 4 Assignment

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[Date]

Bluewater Linen Services and all figures are composites written for a model paper; the theories, formulas and research findings come from the sources listed.

The composite laundry from earlier weeks has decided to accept the hospital contract if the termination clause from Week 2 is agreed. It now needs $5.8 million for the tunnel washer line and delivery trucks. Its bank offered a seven-year term loan at 7.5 percent. A customer who sold a business offered to buy a 20 percent stake. The working capital plan from Week 3 will free about $1.6 million over the first year. The owners asked what the money costs and how much debt is safe. The cost of capital is not a number on a loan quote; it is the return every investor in the company, lender and owner alike, expects for the risk they carry. This paper estimates it and chooses a structure.

The Cost of Debt

The bank's 7.5 percent rate is the pretax cost of debt. Because interest is deductible, at a 25 percent combined tax rate the after-tax cost is 7.5 times 0.75, or about 5.6 percent. Bluewater's existing $1.5 million equipment loan carries 7 percent, close enough that the analysis uses the new rate as the marginal cost.

The Cost of Equity Without a Stock Price

Bluewater has no traded shares, so its beta cannot be measured directly. The finance manager used publicly traded uniform and linen services companies as comparables, which the manager estimated have an average asset beta, the beta with the effect of debt removed, of about 0.9. To reflect Bluewater's own target mix of 25 percent debt and 75 percent equity, a debt-to-equity ratio of one third, the beta is relevered: 0.9 times one plus 0.75 times one third, or about 1.13. Taking 4.3 percent from the ten-year Treasury and 5.5 points as the market premium, the capital asset pricing model gives a cost of equity of 4.3 plus 1.13 times 5.5, or about 10.5 percent (Brigham & Ehrhardt, 2022). Some analysts add a premium for small private firms; the manager did not, noting that the evidence for a size premium has weakened, but the owners should expect to demand at least this much.

The Weighted Average

At target weights, 0.75 times 10.5 plus 0.25 times 5.6 puts Bluewater's blended cost near 9.3 percent. That is the rate used for projects of average risk, and the basis for the 11 percent risk-adjusted rate applied to the hospital contract in Week 2.

How the Average Changes With Debt

The table below shows the estimate at four debt levels, holding the asset beta at 0.9 and raising the interest rate as lenders see more risk.

Debt to equity of zero: beta 0.90, cost of equity 9.3 percent, weighted average 9.3 percent.

Debt to equity of one third: beta 1.13, cost of equity 10.5 percent, weighted average 9.3 percent.

Debt to equity of one, with a 9.5 percent loan rate: beta 1.58, cost of equity 13.0 percent, weighted average 10.0 percent.

Debt to equity of two, with a 12 percent loan rate: beta 2.25, cost of equity 16.7 percent, weighted average 11.6 percent.

Moderate debt leaves the cost of capital roughly unchanged, because the cheaper after-tax debt is offset by the higher return owners demand. Heavy debt raises it, as lenders charge more and owners bear far more risk.

What Theory Says

Modigliani and Miller (1958) argued that if there were no taxes, no costs of financial distress and no gaps in what insiders and investors know, the split between debt and equity would leave total value unchanged, because owners would demand more as borrowing rose. Adding taxes gives debt an advantage, since interest shields income from tax. The tradeoff view balances that tax shield against the costs of financial distress, such as lost customers, supplier caution and legal costs, which rise with debt. Myers (1984) offered a different account, a pecking order in which retained cash is tapped before borrowing and new shares come last, partly because outside investors may suspect that owners sell shares when they believe them overvalued.

What Practitioners Weigh

Graham and Harvey (2001) found that the chief financial officers they surveyed cared most about financial flexibility and credit ratings when choosing debt, and that many followed a target debt ratio loosely. For a private company like Bluewater, flexibility means keeping room to borrow when an opportunity or problem arises.

The Stress Test

With the contract, earnings before interest, taxes, depreciation and amortization should reach about $4.73 million. Borrowing $4.5 million on the seven-year term loan adds annual payments of about $850,000, which with the existing loan brings total debt service to about $1.15 million. Coverage of debt service is about 4.1 times in the base case. In the weak case, where the hospital's volume falls 40 percent, earnings drop by about $1.08 million and coverage falls to about 3.2 times, still well above the 1.25 times the bank requires. Interest coverage in the first year is about six times.

Comparing the Three Choices

Borrowing all $5.8 million would raise debt service to about $1.4 million and leave less room in a bad year. Selling a 20 percent stake would cost the owners a fifth of all future profits and a voice in decisions, an expensive source given an equity cost above 10 percent and a business they hope to pass on. Using internal cash first is cheapest and fits the pecking order, but using all of it would leave no cushion.

Recommendation

Bluewater should borrow $4.5 million on the term loan, fund the remaining $1.3 million from cash freed by the working capital plan and keep its line of credit for seasonal needs. That keeps debt near the 25 percent target, preserves full ownership, passes the weak-case stress test with room to spare and leaves capacity to borrow later.

Conclusion

At about 9.3 percent, Bluewater's blended cost of capital changes little at moderate debt levels before rising as debt becomes heavy, as the tradeoff view predicts. A term loan for most of the equipment, internal cash for the rest and no outside equity give the owners low cost, full control and coverage that survives the loss of much of the hospital's volume.

References

Brigham, E. F., & Ehrhardt, M. C. (2022). Financial management: Theory and practice (17th ed.). Cengage.

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

Modigliani, F., & Miller, M. H. (1958). The cost of capital, corporation finance and the theory of investment. The American Economic Review, 48(3), 261-297.

Myers, S. C. (1984). The capital structure puzzle. The Journal of Finance, 39(3), 575-592. https://doi.org/10.1111/j.1540-6261.1984.tb03646.x