Question

Profitability index =	NPV
	Investment cost

To illustrate the use of this measure, let us assume that Midwest Region Hospital is considering an investment in linen service shared with hospitals in the region.

The initial investment cost is $150,000 for the purchase of new equipment and light delivery trucks.

Savings in operating costs are estimated to be $50,000 per year for the entire 5-year life of the project.

If the discount rate is assumed to be 10%, the following calculations could be made, ignoring the effect of cost reimbursement and using the discount factors of Table 18-4.

The previous calculations give no consideration to the effects of cost reimbursement.

If we assume that 60% of the facility’s capital expenses are reimbursed and 40% of its operating expenses are reimbursed, then the following additional calculations must be made:

Arwin: Problems on to solve the problem is as follows: The calculation 14% represent the periodic deposits that are consta each period. It should be einpbasized that the ch are made at the end of each period. Such a sys deposits is often described is an ordinary a The values presented in Tables 18-3 and 18-4 un ordinary annaty situation in which depos ceipts occur at the end of the period p= fx plin) or - $100.000 p(12%, 2) or p - $100.000 x 0.7972 or p $79.720 0.8772 0.9091 0.8264 0.7695 0.6750 0.5921 STS 0.7513 le that the values of Tablc 18-1 7598 LEARNING OBJECTIVE 4 0.6890 0.6209 0.5645 6906 important to note that the values 18-1 are reciprocals of each other. That is (in) = 1/pin) 0.5192 Calculate the future value of an amoun and Table 18-2 annuity. 895 dos 0.4065 0.4241 bude nieans that only one on the two tables is solve either a present-value or future 002 12% 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0,4039 0.3606 0.3220 0.2875 0.2567 0.2292 0.2046 0.1827 0.1631 0.1456 0.1300 0.1161 0.1037 0.0334 0.0107 0.3855 0.3505 $32 In attor, thuis nie Sy in solve moblenu in ulving a single sum the problen in olving 071 0.5194 0.4556 0.3996 0.3506 0.3075 0.2697 0.2366 0.2076 0.1821 0.1597 0.1401 0.1229 0.1078 0.0946 0.0829 0.0728 0.0196 0.9186 0.2897 02633 0.2394 105 ANYUTY PROBLEMS 152 0.2176 919 0.1978 Future Value 0.1799 02 0.1635 0.1486 0.0573_- 0.0221--- payment or receipt receipts, when each y business situations there is more than one of receipt. In the case of multiple payments or shen each payment or receipt is constant per riod, we have an annuity situation Figure 16-4 depicts a time uraph for an annuity, 0.0053 The hasic equation for a future value F=RX FU,n) The factor F,n) represents the future invested each period for a periods at i ra Values for Fin) can be found in Table L three of the four variables (FR1, and Ous equation are known, the equation c determine the fourth. Thus, if we know cun solve for R. Assume that a hospital wants to value of $50,000 worth of annual de fund for professional malpractice ins 3 years if the fund earns 8c per yea for this problem is depicted in Figur The calculation to solve the pro follows: F=Rx Fino F = $50,000 x F(8% F = $50,000 x 3.24 F = $162,320 LEARNING OBJECTIVE: 3 Explain the difference between an ordinary annuity and an annuity due. The generale a l equation used to solve present-value ele-sum problems is the following: p=fx plin) The factor in represents the present value of $1 Svedig periods at an interest rate of i. Values to ) can be found in Table 18-2. sume that your health maintenance organization $100.000 debt service obligation due in 2 vears are interested in learning how much money must et aside today to meet the obligation iſ the ex d weld on the investment is 12%. The relevant graph is depicted in Figure 18-3. To figure 18-4, F represents the future value of the invested annuity deposits al the end of period 1. (Note at Fis used to denote future value for annuities, hereas / is used for single sums.) The values for R F = Future value ain R -- Periodic payment - 12% f $100.000 50K -- 5 - L--+- - -- n-1 N Figure 18-5 Determining the n = 2 Figure 18-4 Future Value of an Annuity 18-3 Present Value of a Future Sum

Answer 1

The Present value of Cashflows = 50000/1.1 + 50000/1.1^2+...+50000/1.1^5

From the table

= 50000*( 0.9091+ 0.8264+0.7513+0.6830+0.6209)

= $ 189,535

So, Profitability Index = 189535/150000 = 1.263567

If 60% Capital Expenditure is reimbursed , Capital expenditure = 40% of $150000 = $60000

40% of operating expenditure are reimbursed, so annual savings = 60% of $50000 = $30000

The Present value of Cashflows = 50000/1.1 + 50000/1.1^2+...+50000/1.1^5

From the table

= 30000*( 0.9091+ 0.8264+0.7513+0.6830+0.6209)

= $ 113,721

So, Profitability Index = 113721/60000 = 1.89535