1) Suppose that two projects each cost $12,000. The first project returns $4,000

Question

1) Suppose that two projects each cost $12,000. The first project returns $4,000 per year for 6 years. The second project returns $6,000 per year for 2 years. Which has the better payback period? Are there any issues with this method of analysis?

2)  The Ward County Hospital Center (WCHC) wants to buy a new mobile primary care van to use in screening residents in an underserved local neighborhood. The van will last 5 years and costs $68,000. WCHC will pay for the acquisition and maintenance of the van partially from foundation grants and partially from receipts from the county health department. The county has agreed to reimburse WCHC $15 for each patient it screens using the new van. They expect to have 800 patients per year with the van. It will cost $3,000 per year to maintain the vehicle, which includes all relevant costs. WCHC uses a discount rate of 5%. How much will WCHC need in foundation grants this year to make the purchase break-even financially? (Hint: What is the net present value of the costs of buying and operating the van over its lifetime, less the payments that will be received from the county? Are the payments from the county sufficient? If not, how much must be raised in grants before the van is purchased?)

3) Community Health Center (CHC) is considering spending $50,000 on a blood analyzer. The annual cash profits from the machine will be $7,000 for each of the 7 years of its useful life. The board of directors wants to pursue this investment, because they think the $49,000 CHC will receive is close to the $50,000 cost. What is wrong with the board’s logic? What is the IRR on the investment?

Explanation / Answer

1 Project 1 Project 2 Initial Investment 12000 12000 Cash flows/yr. 4000 6000 Payback period=Initial Investment/ Net Annual cash in-flows 12000/4000= 12000/6000= 3 2 Ranking according to pay-back period 2 1 Project 2 has a shorter& hence better pay-back period,ie. The initial investment can be recouped/recovered in a lesser no.of years in the case of Project 2 ,when compared to Project 1 Cash flows have not been given time value of money 2 NPV of buying & operating the van=-68000-(3000*4.32948)+(800*15*4.32948)= -29034.68 PV of costs : PV Cost of the van 68000 PV of maintenance costs 3000*4.32948 12988 (PVOA F 5%,5 Yrs.) PV of Total costs 80988 So, to break-even , the PV of grants should be   $ 80988 At present, the county payments will not be sufficient. There will be a short-fall of   29035 (Negative NPV) So, $ 29035 must be raised in grants before the van is purchased 3. The board's logic is incorrect ,as it does not take into account the time value of money. PV of $ 7000 received at successive years will not be the same. Hence,it cannot be 7000*7=49000 ,but something less, depending on the discount rate applied. Year 0 -50000 1 7000 2 7000 3 7000 4 7000 5 7000 6 7000 7 7000 IRR as per Excel -0.50% Or as per the equation assuming r for IRR where NPV of cash flows is 0 -50000+7000*(1-(1+r)^-7)/r=0 solving for r, in an online equation solver,we get, r= -0.0050 -0.50% IRR= -0.50%

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