A $54.7 Million System That Costs Less Than a $34.6 Million One? Dating the Cash Flows of Two Refrigeration Systems and Comparing Them Fairly
Student Name
American College of Education
FIN5003: Financial Decision Making
Module 1 Assignment
Instructor Name
July 3, 2028
The Decision
Fenwick Cold Chain, a composite regional operator of refrigerated warehouses invented for this course, is building a 40,000-pallet freezer facility to serve a frozen food manufacturer under a long-term contract. The building's refrigeration system must be chosen before the design is finished. Option A is an ammonia system, the long-standing standard for large freezers, costing $6.8 million installed with an expected life of 25 years. Option B is a transcritical carbon dioxide system, costing $8.1 million installed with an expected life of 20 years, but using less energy in Fenwick's cool northern climate and qualifying for a utility efficiency rebate.
The engineering team has summed each system's lifetime costs: about $54.7 million for ammonia and $34.6 million for carbon dioxide. Those totals are meaningless for a decision, because they add dollars paid today to dollars paid 25 years from now and compare a 25-year system with a 20-year one. A dollar has a date, and two dollars with different dates are not the same amount of money.
The Cash Flows and Their Dates
Each option's cash flows were listed with the date on which they occur. Ammonia: $6.8 million at installation, year 0; energy of about $1.10 million in the first year of operation, rising 3 percent a year with expected electricity prices; maintenance of $180,000 in the first year, also rising 3 percent; and a compressor overhaul of $1.2 million in year 12. Carbon dioxide: $8.1 million at installation; energy of about $0.86 million in the first year, rising 3 percent; maintenance of $150,000, rising 3 percent; and a utility rebate of $600,000, paid at the end of the first year of operation after the savings are verified.
Two conventions matter. First, energy and maintenance are paid monthly, not in a lump at year-end, so each year's costs are dated at the middle of the year, a close approximation to monthly payments. Second, all figures are nominal, including expected price increases, so they are discounted at a nominal rate. Mixing nominal cash flows with a real discount rate, or the reverse, is an easy way to distort any comparison that spans decades; Fisher (1930) set out the relationship between nominal and real interest rates that makes the two approaches consistent when applied correctly.
Discounting to the Present
Fenwick's finance team uses a discount rate of 8 percent for cost comparisons of this kind; the next module examines how that rate should be set. Discounting each cash flow to year 0, the ammonia system's present value of costs is about $25.75 million: $6.80 million of purchase, about $15.87 million of energy, about $2.60 million of maintenance and about $0.48 million for the overhaul. The carbon dioxide system's present value of costs is about $20.40 million: $8.10 million of purchase, about $10.95 million of energy and about $1.91 million of maintenance, less about $0.56 million for the rebate.
Discounting shrinks the comparison dramatically. The undiscounted difference of about $20 million becomes a present value difference of about $5.3 million, because much of the ammonia system's extra energy spending falls in distant years, which count for less today. But the two present values still cannot be compared directly: the ammonia figure covers 25 years of refrigeration and the carbon dioxide figure only 20.
Equal Footing: Equivalent Annual Cost
To compare options with different lives, each present value is converted into an equivalent annual cost, the constant annual payment over the option's life that has the same present value. In practice, the present value is divided by the present value of one dollar a year over the same life at the same rate. At 8 percent, the ammonia system's equivalent annual cost is about $2.41 million over 25 years, and the carbon dioxide system's is about $2.08 million over 20 years. The carbon dioxide system is cheaper by about $334,000 a year in equivalent terms.
The method assumes that each system would be replaced at the end of its life with a similar one, so that the comparison is between two ways of providing refrigeration indefinitely. Fenwick's contract with the frozen food manufacturer runs 15 years with renewal options, and the building is designed for at least 40 years of use, so that assumption is reasonable. Brealey et al. (2023) describe equivalent annual cost as the standard tool for choosing between machines with unequal lives, with the caution that it depends on this replacement assumption.
Does the Timing Convention Matter?
The team tested the mid-year convention against the simpler end-of-year convention. For the ammonia system, treating each year's energy and maintenance as paid at year-end lowers the present value of costs by about $0.7 million, from about $25.75 million to about $25.05 million, because discounting each payment for an extra half year makes it smaller. The same shift applies to the carbon dioxide system in proportion, so the ranking does not change. But the $0.7 million difference is larger than many of the other judgment calls in the analysis, which shows that dating cash flows is not a technicality.
The comparison also passed a survey of practice: Graham and Harvey (2001) found that most chief financial officers they surveyed always or almost always used net present value and internal rate of return in capital budgeting, the methods built on the time value principles applied here.
What the Numbers Do Not Capture
Some differences between the systems are not in the cash flows. Ammonia is toxic, and a freezer system of this size holds far more than the 10,000-pound threshold at which federal process safety management and risk management program rules apply, requiring written hazard analyses, operating procedures, mechanical integrity programs, audits and emergency planning. Fenwick already runs these programs at its existing sites, so the added administrative cost is modest, but a release would put workers and neighbors at risk. Carbon dioxide is not toxic in the same way, though it operates at very high pressures and can displace oxygen in enclosed spaces, which requires its own detection and ventilation. Neither risk is costless, and the safety manager should assign a cost to each program before the final decision.
Two further considerations favor carbon dioxide modestly. Technicians experienced with transcritical systems are fewer than those trained on ammonia, which could raise maintenance costs above the estimate in the early years. But the frozen food customer has asked its warehouse providers to report refrigerant choices as part of its environmental commitments, and a system with a lower safety and environmental profile may help Fenwick retain the contract at renewal. Neither consideration reverses the financial result; both should be noted in the decision record.
Recommendation
On a properly dated and comparable basis, the carbon dioxide system costs about $334,000 a year less than the ammonia system, a present value advantage of more than $3 million over a 25-year horizon when replacement is accounted for. Fenwick should select the carbon dioxide system, subject to two checks the next modules will address: whether 8 percent is the right discount rate for this decision, and how sensitive the result is to electricity prices, which drive most of the difference.
References
Brealey, R. A., Myers, S. C., & Allen, F. (2023). Principles of corporate finance (14th ed.). McGraw Hill.
Fisher, I. (1930). The theory of interest. Macmillan.
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
How this FIN 5003 Module 1 example is structured
FIN 5003 Module 1 often starts with cash flows dated properly and compared on the same footing; your classroom's instructions decide the decision and the discount rate. This example lays out each option's cash flows with their timing, explains the conventions used for timing and inflation, then discounts them. Because the systems last different lengths of time, it converts present values to equivalent annual costs before comparing them, and a final section tests how much the timing conventions matter.
FIN5003 Module 1 questions, answered
What does FIN5003 Module 1 usually ask for?
FIN5003 Module 1 often asks students to compare options whose cash flows occur at different times, using discounting to put them on the same footing. Many sections expect present values, annuities and sometimes equivalent annual cost. Your classroom's instructions decide the decision and the discount rate.
When should I use equivalent annual cost?
Use it when comparing options with different lives that would each be replaced at the end of their life. Convert each option's present value to a constant annual amount over its own life and compare the annual amounts.
Should cash flows be nominal or real?
Either can work, but they must match the discount rate. Nominal cash flows that include inflation are discounted at a nominal rate; real cash flows are discounted at a real rate. Mixing them produces errors.
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