GB550 Unit 7 Capital Budgeting Analysis Example

Rebuild Sixty Hoppers or Replace Them With Forty-Five: A Unit 7 Capital Budgeting Analysis

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Purdue University Global

GB550: Financial Management

Unit 7 Capital Budgeting Analysis

[Instructor Name]

[Date]

The barge operator, its fleet and every cost and cash flow are composite and illustrative; the methods and sources cited are real.

Recommendation

Replace the 60 covered hoppers with 45 jumbo hoppers at a cost of $39.6 million. At the company's 8.27 percent cost of capital, replacement adds about $0.520 million of value a year against $0.285 million for rebuilding, and it remains the better choice across the full range of cost of capital estimates from Unit 6.

The Decision

Sixty covered hoppers, the barges that carry grain and other dry cargo, are near the end of their working lives. The company can rebuild them, replacing worn plating and hatch covers to add ten years of life, or replace them with 45 larger jumbo hoppers that carry the same total cargo, since each jumbo holds about a third more than a standard hopper. The two options are mutually exclusive: the company needs the capacity once, not twice.

Assumptions

Rebuild. Cost $310,000 per barge, $18.6 million in all. Adds ten years of service. After-tax cash flow of $3.05 million a year from cargo revenue less operating costs, taxes and the depreciation shield. Scrap value of $0.6 million at the end of year ten.

Replace. Cost $880,000 per jumbo barge, $39.6 million in all. Twenty years of service. After-tax cash flow of $4.55 million a year, higher because jumbo barges need fewer tows and less maintenance per ton carried. Salvage value of $4.0 million at the end of year twenty.

Discount rate. 8.27 percent, the Unit 6 weighted average cost of capital, appropriate because both options carry the company's ordinary cargo risk.

Results

Rebuild. Net present value $1.89 million; internal rate of return 10.46 percent; payback 6.10 years; modified internal rate of return 9.32 percent.

Replace. Net present value $5.01 million; internal rate of return 9.90 percent; payback 8.70 years; modified internal rate of return 8.92 percent.

The measures disagree. Rebuilding has the higher internal return, the higher modified return and the faster payback. Replacing has the higher net present value.

The rebuild earns a higher percentage on a smaller, shorter investment, while the replacement creates more value each year the company owns it.

Why the Higher Internal Return Loses

Internal rate of return measures the percentage earned, not the amount of value created. It says nothing about scale or duration. The rebuild earns 10.46 percent on $18.6 million for ten years; the replacement earns 9.90 percent on $39.6 million for twenty. At an 8.27 percent cost of capital, both earn more than the company's investors require, but the larger and longer investment produces more value above that requirement. Brealey et al. (2023) stress that when projects are mutually exclusive, the one with the higher net present value should be chosen even if its internal return is lower, because the goal is to maximize value, not percentage return.

The modified internal rate of return treats interim cash as earning the 8.27 percent cost of capital instead of each project's own rate. On that basis the gap narrows, 9.32 against 8.92 percent, but still favors rebuilding. It corrects the reinvestment assumption but not the difference in scale and life, so it does not settle the conflict by itself.

Settling the Conflict: Unequal Lives

A raw comparison of net present values is also not quite fair, because the rebuild lasts ten years and the replacement twenty. If the company rebuilt now, it would need to replace or rebuild again in ten years. Two methods correct for this.

Equivalent annual value. Dividing each net present value by the annuity factor for its life converts it into a level annual amount. The rebuild's $1.89 million over ten years equals $0.285 million a year; the replacement's $5.01 million over twenty years equals $0.520 million a year. Replacement wins.

Replacement chain. Assuming the rebuild is repeated at year ten on the same terms, the twenty-year chain has a net present value of $2.74 million, still well below the replacement's $5.01 million. Replacement wins again.

Brigham and Ehrhardt (2020) describe both methods as appropriate when mutually exclusive projects have unequal lives and would be repeated, and the agreement of the two gives the recommendation a firm basis.

Testing the Rate

Unit 6 placed the honest range for the cost of capital between about 8.1 and 9.0 percent.

At 8.08 percent: equivalent annual values of $0.309 million for rebuilding and $0.579 million for replacing.

At 8.99 percent: $0.193 million and $0.293 million.

Replacement wins throughout. The two options' equivalent annual values become equal only near a 9.5 percent cost of capital, well above the top of the range.

Factors Outside the Cash Flows

The cash flow estimates omit three considerations. First, jumbo hoppers need fewer towboat trips to carry the same cargo, which frees towboat capacity the company could use elsewhere; the analysis counts the fuel and crew saving but not any new revenue from that freed capacity, so it understates replacement's value. Second, some locks on smaller tributaries cannot take jumbo barges, which limits where the new fleet can operate; the company's current routes do not use those locks, but a shift in customers could. Third, rebuilt barges would retain older hull designs that may face stricter environmental or safety rules within their ten-year life, a risk the replacement avoids. On balance these factors favor replacement further, but they are noted because a board member may raise any of them.

Payback and Risk

The rebuild's faster payback, 6.10 years against 8.70, is its strongest argument. It returns the company's cash sooner, which matters if the company expects to need cash for other projects. But payback disregards both discounting and any cash arriving after the break-even year, and the replacement's longer life is exactly what it leaves out. The replacement does carry more risk in one respect: it commits $39.6 million rather than $18.6 million, and a prolonged fall in grain exports would leave more capital tied up in barges. Unit 9 examines how to finance it without straining the company's covenant.

Conclusion

Replace the hoppers. The replacement creates more value per year on every measure that accounts for scale and life, and the result holds across the range of plausible costs of capital. Koller et al. (2020) note that capital decisions should be judged by the value they add over their full life, and on that test the jumbo hoppers are the better use of the company's money.

References

Brealey, R. A., Myers, S. C., & Allen, F. (2023). Principles of corporate finance (14th ed.). McGraw Hill.

Brigham, E. F., & Ehrhardt, M. C. (2020). Financial management: Theory and practice (16th ed.). Cengage.

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