# Profitability Index

November 7, 2019
###### Global Economic Environment
November 7, 2019

Week 3 Assignment
Case UVa Health System: The Long-Term Acute Care Hospital Project

Wk 3 is the first of two consecutive weeks on CAPITAL BUDGETING.

You will learn the three steps in capital budgeting:
1 Identify relevant incremental cash flows
2 Calculate cost of capital (k-wacc) to use as the discount rate
3 Calculate the metrics of capital budgeting: Net Present Value, Profitability Index,
Internal Rate of Return, and Payback Period.
Then, you will apply the metrics and information in the case study to make a recommendation
whether to accept or reject the LTAC project.
The essence of the capital budgeting process is to make sure, BEFORE an investment is made,
that its prospective rate of return is high enough to justify the investment.

Reading Cohen Finance Workbook chapter 4 is a review of Time Value of Money, which you covered in a previous course.
Review it as necessary, but defer the review until you look at the TVM applications in chapter 5 beginning on p 79.
You need to know TVM to understand the capital budgeting metrics of NPV, PI, and IRR. Make sure you
have that context in mind before reviewing the TVM chapter 4 (only if you need to).

Give the Uva Health Care System: The Long-Term Acute Care Hospital Project Case a quick read to understand what is going on – about
calculating k-wacc and the decision metrics for the project, to give it either a green light or a red light.

Wk 3 gives you practice on the basics. You won’t have a full understanding of what the LTAC Project case is about at
the end of Wk3. In Wk4, you will return to the case, analyze the project, and make a recommendation.

Look at the Wk 3 assignment questions in the Q1, Q2, Q3 tabs.

Read Cohen Finance Workbook chapter 5 selectively. Focus on:
See the FLOW DIAGRAM in GREEN depicting the CAPITAL BUDGETING template.
See the IS/BS Model in GREEN depicting the connection between PPE (BS) and operating expense (IS).
Read pps 61-65 as a general introduction to capital budgeting.
Read pps 70-76 on weighted average cost of capital to answer Q1.
Read bottom p 67 to 69 on Net Working Capital to answer Q2.

Questions
See tabs for Q1, Q2, Q3
THESE QUESTIONS MUST BE ANSWERED USING EXCEL.
MAKING CALCULATIONS OUTSIDE THE SPREADSHEET AND ENTERING THE RESULTS IS NOT USING EXCEL.
YOU MUST USE EXCEL FORMULAS FOR MAKING CALCULATIONS!
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Week 4 Assignment
UNIVERSITY OF VIRGINIA MEDICAL CENTER
Long Term Acute Care Hospital Free Cash Flow Projections

Revenue and Cost Assumptions Results-No NWC Recovery Results-NWC Recovery
Number of Beds 50 NPV \$5,687 NPV \$10,425 (000 ommited)
Year 1 Utilization 26% IRR 17.6% IRR 21.2%
Year 2 Utilization 60%
Annual Increase in Utilization 4%
Operating Expense (% of Revenue) 7.0%
K-wacc 10%

Year 1 2 3 4 5 6 7 8 9 10
VOLUME
Patient Day Capacity 18,250 18,250 18,250 18,250 18,250 18,250 18,250 18,250 18,250 18,250
Utilization 26% 60% 62% 65% 67% 70% 73% 76% 79% 82%
Patient Days Used 4,745 10,950 11,388 11,844 12,317 12,810 13,322 13,855 14,409 14,986
Average Patient Census per Day 13 30 31 32 34 35 36 38 39 41
Average Length of Stay 30 27 27 27 27 27 27 27 27 27
Number of Patients per Year 158 406 422 439 456 474 493 513 534 555
Full-Time Employees/Census 4.8 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5
Full-Time Employees 62 105 109 114 118 123 128 133 138 144

INSURANCE PAYER Patient Mix
Medicare 36% 57 146 152 158 164 171 178 185 192 200
Medicaid 29% 46 118 122 127 132 138 143 149 155 161
Commercial Payers 24% 38 97 101 105 109 114 118 123 128 133
Other 9% 14 37 38 39 41 43 44 46 48 50
Indigent 2% 3 8 8 9 9 9 10 10 11 11
158 406 422 439 456 474 493 513 534 555

Billing Annual Incr
Medicare—bill per patient \$27,795 0.0% 1,583 4,058 4,220 4,389 4,565 4,747 4,937 5,135 5,340 5,554
Medicaid—bill per patient \$35,000 1.3% 1,605 4,170 4,337 4,510 4,691 4,878 5,073 5,276 5,487 5,707
Commercial Payers—bill per day \$2,800 5.0% 3,189 7,726 8,035 8,357 8,691 9,039 9,400 9,776 10,167 10,574
Other—bill per patient \$38,500 1.3% 548 1,424 1,480 1,540 1,601 1,665 1,732 1,801 1,873 1,948
Indigent—bill per patient \$35,000 1.3% 111 288 299 311 323 336 350 364 378 394
Total Revenue (000 omitted) 7,035 17,665 18,372 19,107 19,871 20,666 21,493 22,352 23,246 24,176
Less Uncollectable 1% 70 177 184 191 199 207 215 224 232 242
Total Net Revenue (000 omitted) 6,965 17,489 18,188 18,916 19,672 20,459 21,278 22,129 23,014 23,935

EXPENSES Annual Incr
Salary, Wage, Benefits (based on \$ per employee) \$60,250 3% 3,760 6,516 6,980 7,477 8,009 8,580 9,190 9,845 10,546 11,297
Supplies, Drugs, Food (% net revenue) 16.3% 1,135 2,851 2,965 3,083 3,207 3,335 3,468 3,607 3,751 3,901
Management Fees (% net rev) 8% 557 1,399 1,455 1,513 1,574 1,637 1,702 1,770 1,841 1,915

Operating Expenses (fixed + 7 % net rev) \$1,200,000 NA 1,688 2,424 2,473 2,524 2,577 2,632 2,689 2,749 2,811 2,875
Land Lease per year \$200,000 3% 200 206 212 219 225 232 239 246 253 261
Depreciation (straight line 30yrs) \$15,000,000 500 500 500 500 500 500 500 500 500 500
Total Expenses (000 omitted) 7,840 13,896 14,585 15,316 16,092 16,915 17,789 18,717 19,702 20,749

Total Expenses 7,840 13,896 14,585 15,316 16,092 16,915 17,789 18,717 19,702 20,749

Operating Profit (804) 3,769 3,787 3,791 3,779 3,751 3,703 3,635 3,544 3,427
Operating Margin -11.4% 21.3% 20.6% 19.8% 19.0% 18.1% 17.2% 16.3% 15.2% 14.2%

Net Working Capital Notes:
Accounts Receivable 30 days 572 1,437 1,495 1,555 1,617 1,682 1,749 1,819 1,892 1,967
Inventory Supplies, Drugs, Food 60 days 187 469 487 507 527 548 570 593 617 641
Accounts Payable 30 days 93 234 244 253 264 274 285 296 308 321
Net Working Capital 666 1,672 1,739 1,808 1,880 1,956 2,034 2,115 2,200 2,288
Change in NWC 666 1,006 67 70 72 75 78 81 85 88

Free Cash Flows Calculation
Operating Profit (804) 3,769 3,787 3,791 3,779 3,751 3,703 3,635 3,544 3,427
Add Depreciation 500 500 500 500 500 500 500 500 500 500
Less Capital Expenditures (7,500) (7,500) 0 0 0 0 0 0 0 0 0
Less Increase in Net Working Capital (666) (1,006) (67) (70) (72) (75) (78) (81) (85) (88)
Free Cash Flows (000 omitted) (7,500) (8,470) 3,263 4,220 4,221 4,207 4,176 4,125 4,054 3,959 3,839

NPV (no recovery in year 10) \$5,687 (000 ommited)
IRR (no recovery in year 10) 17.6%

Year 1 2 3 4 5 6 7 8 9 10
NWC Recovery 0 0 0 0 0 0 0 0 0 \$2,288
Sale of Facility at Book Value 0 0 0 0 0 0 0 0 0 \$10,000

NPV with Year 10 Recovery \$10,425 (000 ommited) (7,500) (8,470) 3,263 4,220 4,221 4,207 4,176 4,125 4,054 3,959 16,127
IRR with Year 10 Recovery 21.2%

Net Profit (Operating Profit – Interest) (000 ommited) (2,004) 2,569 2,587 2,591 2,579 2,551 2,503 2,435 2,344 2,227
Net Profit/Net Revenue -28.8% 14.7% 14.2% 13.7% 13.1% 12.5% 11.8% 11.0% 10.2% 9.3%

Study the above analysis carefully, examining the inputs, outputs, and formulas used to do the calculations.

Q1a Mulroney did not use working capital cash flows in her original analysis. The analysis above includes incremental investment in working capital. Discuss why she was either correct or incorrect not to include them.
Q1b Compare the decision metrics NPV & IRR for the “no recovery of NWC” and “recovery of NWC” scenarios, stating which scenario best captures reality. Based on your answer, give the project a green or red light.
Q1c Examine the decision metric ‘profit margin’, and explain if it leads to a green or red light for this project. Even though the board of directors uses this metric, it is defective. Explain why. HINT: FCF definition.

Q2a Calculate the K-wacc for HCA using the template above. Enter the data that you have in the case and the table above. If you need additional data, assume it using your good judgment from what you have learned so far in the course. In the answer box, cite your result, compare it to the K-wacc used in the Q1 analysis, and explain how your revised K-wacc would change the Q1 results.

Q2b If LATC was a project in a for-profit hospital like HCA above, would the NPV be higher or lower? Explain ‘analytically’ by examining all relevant inputs to NPV.
Q2c If LATC was a project in a for-profit hospital like HCA above, would the IRR be higher or lower? Explain. HINT: To avoid getting trapped by this question, make sure your answer is’analytical’, i.e., examine all relevant inputs and output.
Q2d Can a non-profit hospital accept projects that a for-profit hospital would reject?

Q3a The analysis above is identical to the one on the Q1 tab. Do a sensitivity analysis by systematically changing certain assumptions in the spreadsheet above: 1 change the K-wacc to 8.3%
2 change year 2 utilization to 45%
3 change commercial payers to 30% of patient mix
Use the answer box to prepare a summary of the original (Q1) results and the revised (Q3) results, i.e., a summary table.

Q3b Revise the decision you made in Q1 based on the above sensitivity analysis, comparing Mulroney’s assumptions and the sensitivity analysis assumptions to expectations stated in the case. Be sure to consider both ‘hard quantitative data” from decision metrics and ‘soft qualitative information’ from the case.