HCS/385 Week 2: Problem-Solving Analysis Report, sample paper

Problem-Solving Analysis Report: Paying Cash Now or Installments Over Five Years for a Clinic's Digital X-Ray System

[Student Name]

University of Phoenix

HCS/385: Health Care Finance

Week 2 Summative Assessment

[Instructor Name]

[Date]

The clinic, vendor terms and figures are a composite written for a model report.

Problem Statement

A composite orthopedic clinic owned by a regional health system must replace its digital radiography system, which is nine years old and failing. The clinic performs about 11,000 x-ray studies a year, and downtime has caused rescheduled visits and patient complaints. The vendor offers two payment options for the same system, installation and warranty: pay $420,000 at installation, or pay $95,000 at the end of each year for five years. The clinic manager must recommend one option to the system's finance committee. The installment plan costs $55,000 more in total dollars, yet that is the wrong comparison, because the dollars are paid at different times.

Options

Option A: pay $420,000 now from the clinic's capital allocation.

Option B: pay five annual installments of $95,000, for a nominal total of $475,000, with the first payment one year after installation.

A third possibility, leasing the equipment from a separate leasing company, was considered, but the lease quote included a higher total cost and a purchase option at the end, and the finance office asked that the report focus on the vendor's two options.

Analysis: Present Value

The time value of money holds that a dollar received today is worth more than a dollar received in the future, because money in hand can be invested or used to avoid borrowing (Pink & Song, 2020). To compare options with different timing, each stream of payments is converted to its present value using a discount rate that reflects the organization's opportunity cost of money.

The health system's finance office uses a 6% cost of capital for equipment decisions. Option A's present value is simply $420,000, since it is paid today.

Option B is an ordinary annuity: equal payments at the end of each period. Its present value equals the payment multiplied by the present value annuity factor, which is one minus 1.06 raised to the negative fifth power, divided by 0.06 (Brigham & Houston, 2022). At 6% for five years, the factor is 4.2124. The present value of Option B is therefore $95,000 multiplied by 4.2124, or about $400,175.

In present value terms, Option B costs about $19,825 less than Option A, even though its nominal total is $55,000 higher. The installments are cheaper because the clinic keeps $420,000 today and pays for the equipment gradually with money that, in the meantime, retains value for the system at 6%.

Sensitivity Analysis

The recommendation depends on the discount rate, so the analysis tested alternatives. At 4%, the annuity factor is 4.4518, and the present value of Option B rises to about $422,923, slightly more than paying cash. The break-even rate, at which the two options have equal present value, is about 4.25%. Above that rate, installments are cheaper; below it, paying cash is cheaper.

The system's cost of capital of 6% is comfortably above the break-even rate, so the recommendation is robust to modest changes. If the system's cost of capital fell below about 4.25%, for example because it could borrow very cheaply or had idle cash earning little, the decision would reverse. Cleverley and Cleverley (2018) note that health care organizations often underestimate the value of their cash because unrestricted reserves support credit ratings and borrowing costs, which is another reason to preserve cash when the price of doing so is low.

Non-Financial Factors

Several non-financial factors support the installment option. Preserving $420,000 in cash keeps the clinic's capital allocation available for a second project, the replacement of a failing ultrasound unit, which the clinic had deferred. The installment contract includes the same five-year warranty, so there is no difference in service. The vendor confirmed that no interest or penalty applies to the installments and that the contract can be paid off early without penalty if the system's cash position changes.

One consideration favors paying cash: installments create a fixed obligation for five years, which reduces flexibility if the clinic's volume falls. Given stable orthopedic volume over the past four years and a growing local population, this risk appears modest.

Budget and Accounting Treatment

The choice also affects how the purchase appears in the clinic's budgets. Under either option, the x-ray system is a capital asset recorded on the balance sheet and depreciated over its useful life, so depreciation expense in the operating budget is the same. What differs is cash flow and, under the installment plan, a liability. With Option A, the clinic's capital budget absorbs $420,000 this year. With Option B, the system records the equipment and a corresponding obligation to the vendor, and the clinic's cash budget shows $95,000 a year for five years. The finance office confirmed that the vendor contract carries no stated interest, so the difference between the $475,000 in payments and the equipment's value is treated as an implicit financing cost under the system's accounting policies. Department managers should understand these effects because they determine how the purchase shows up in the monthly reports they are held accountable for.

Implementation

If the committee approves Option B, the clinic manager will coordinate the contract with the system's purchasing department, schedule installation over a weekend to avoid rescheduling patients and ask the finance office to set up the five annual payments with reminders so none is missed.

Recommendation

The clinic should choose Option B, five annual installments of $95,000. At the system's 6% cost of capital, the installments have a present value of about $400,175, roughly $19,825 less than paying $420,000 up front. The recommendation holds for any discount rate above about 4.25%, preserves cash for the deferred ultrasound replacement and carries no penalty for early payoff. The finance committee should revisit the decision only if the system's cost of capital falls below the break-even rate before the contract is signed.

Conclusion

Comparing payment options in nominal dollars would have favored paying cash, since the installments total $55,000 more. Comparing them in present value, the correct basis for decisions involving money over time, shows the installment plan is less expensive at the system's cost of capital and remains so across a reasonable range of rates. Time value of money analysis turned an apparent extra cost into a saving and gave the clinic a clear, defensible recommendation.

References

Brigham, E. F., & Houston, J. F. (2022). Fundamentals of financial management (16th ed.). Cengage Learning.

Cleverley, W. O., & Cleverley, J. O. (2018). Essentials of health care finance (8th ed.). Jones & Bartlett Learning.

Pink, G. H., & Song, P. H. (2020). Gapenski's healthcare finance: An introduction to accounting and financial management (7th ed.). Health Administration Press.