HCA 125 Module 5 assignment: capital budgeting analysis: NPV, IRR and payback for equipment, a full sample

Is the Second MRI Worth $2.5 Million? Net Present Value, Internal Rate of Return, and the Assumptions That Decide It

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Health Care Administration Program, Aspen University

HCA 125: Healthcare Finance

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Month Day, Year

Is the Second MRI Worth $2.5 Million? Net Present Value, Internal Rate of Return, and the Assumptions That Decide It

Buying major equipment commits an organization's money for years, so the decision should rest on the cash the equipment will produce over its life, valued in today's dollars. This paper evaluates whether Lakeview Regional Hospital, a composite not-for-profit hospital, should buy a second MRI scanner for its outpatient imaging center, where the existing scanner is booked three weeks out. It lays out the investment's cash flows, calculates net present value, internal rate of return, and payback, and tests how the answer changes when key assumptions move.

Why Discounted Cash Flow

A dollar received in year five is worth less than a dollar today, because today's dollar could be invested or used to pay down debt in the meantime. Net present value discounts each future cash flow at the organization's cost of capital and subtracts the initial investment; a positive value means the project earns more than the cost of the money it uses (Reiter & Song, 2021). The internal rate of return is the project's own yield, the rate that would make the discounted inflows exactly repay the investment, and payback is the number of years needed to recover the investment. Net present value is the primary decision rule because it measures value directly, while payback ignores cash flows after the payback point and ignores the time value of money (Brealey et al., 2020).

Assumptions

The scanner and site preparation cost $2.5 million, paid now. The useful life is seven years, with a salvage value of $150,000. Volume starts at 3,000 scans in year one, about 10 a day over 300 operating days, based on the current waiting list and referral counts, and grows 2 percent a year. That growth rate is deliberately modest: in a study of seven U.S. health systems, annual growth in MRI use slowed to 1.3 percent among adults from 2007 to 2016 after rising more than 11 percent a year in the early 2000s (Smith-Bindman et al., 2019). Net revenue averages $420 per scan across the center's payer mix, and variable costs, including contrast, supplies, and billing, are $85 per scan. Fixed costs are $210,000 for two technologists including benefits, $60,000 for space and utilities, and a $140,000 service contract beginning in year two after the warranty ends. The hospital's cost of capital is 8 percent. As a not-for-profit hospital, Lakeview pays no income tax, so no tax effects are included.

Cash Flows

Table 1 shows the annual cash flows.

Choosing the Discount Rate

The 8 percent discount rate is the hospital's cost of capital, the blended return it must earn to satisfy the lenders who hold its bonds and to preserve the equity it has built from past surpluses. A not-for-profit hospital has no shareholders, but its equity still has a cost: money spent on a scanner cannot be used for another project or held as reserves. Using the cost of capital as the discount rate means that a positive net present value shows the project earns more than those alternatives. Because the rate itself is an estimate, the analysis also reports the result at 10 percent, a rate that would apply if the hospital's borrowing costs rose or if management judged outpatient imaging riskier than its average project.

Results

Discounted at 8 percent, the cash flows produce a net present value of about $1,105,700. The internal rate of return is about 19.6 percent, well above the 8 percent cost of capital, and payback occurs at about 3.8 years. At a 10 percent discount rate, the net present value is still about $865,500. On these assumptions the scanner is a sound investment. Depreciation does not appear in the cash flows because it is not a cash expense; the cost of the scanner is captured once, as the year-zero outflow.

Sensitivity Analysis

The result depends on assumptions that could prove wrong, so each key assumption was varied. If volume starts 15 percent lower, at 2,550 scans, the net present value falls to about $277,300 and the internal rate of return to 11.1 percent. If net revenue per scan is 10 percent lower, at $378, perhaps because a large payer cuts imaging rates, the net present value falls to about $413,300. If both happen together, the project destroys value: net present value falls to about negative $311,300 and the internal rate of return to 4.4 percent. The break-even starting volume, holding other assumptions constant, is about 2,400 scans a year, or 8 a day. The scanner is a good investment unless volume and price fall together, and the hospital's current waiting list is the best evidence that volume will not.

Factors the Numbers Do Not Capture

Some considerations fall outside the model. A three-week wait for MRI delays diagnosis and may send patients and referring physicians to competitors, so the second scanner may also protect volume in other services, such as orthopedic surgery, that depend on imaging. On the other side, a second scanner creates capacity that must be filled, and there is a risk of encouraging imaging that adds cost without benefit. The center should monitor the appropriateness of orders using national criteria, which protects both patients and the hospital's reputation with payers.

Recommendation

Lakeview should buy the second MRI. The investment has a positive net present value of about $1.1 million at the hospital's cost of capital and remains positive under a 15 percent volume shortfall or a 10 percent price cut alone. Before committing, management should confirm the referral estimates behind the 3,000-scan starting volume and negotiate the service contract price, since those assumptions most affect the result. After purchase, volume should be tracked monthly against the model's 2,400-scan break-even.

Conclusion

Discounted cash flow analysis shows that a second MRI at Lakeview would create value on reasonable assumptions, with a 19.6 percent internal rate of return and payback in under four years. The decision is robust to a single adverse change but not to a simultaneous drop in volume and price, which defines the risk management must watch.

References

Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of corporate finance (13th ed.). McGraw-Hill Education.

Reiter, K. L., & Song, P. H. (2021). Gapenski's healthcare finance: An introduction to accounting and financial management (7th ed.). Health Administration Press.

Smith-Bindman, R., Kwan, M. L., Marlow, E. C., Theis, M. K., Bolch, W., Cheng, S. Y., Bowles, E. J. A., Duncan, J. R., Greenlee, R. T., Kushi, L. H., Pole, J. D., Rahm, A. K., Stout, N. K., Weinmann, S., & Miglioretti, D. L. (2019). Trends in use of medical imaging in US health care systems and in Ontario, Canada, 2000-2016. JAMA, 322(9), 843-856. https://doi.org/10.1001/jama.2019.11456