Question

The Department of Chemistry at the University conducts chemical analysis of water, soil and industrial wastes as mandated by the Environmental Protection Agency (EPA). The department customers include local government bodies, who are responsible for insuring that local water supplies are safe for drinking and manufacturing companies, who must verify that the wastes that they release into water or landfills comply with strict regulatory standards. The Chemistry department does not have the technology to run the necessary test, so it will have to buy several machines called gas chromatographs. Two different types of gas chromatographs are available, both of which have a useful operating life of about six years. One type, Type A, is less expensive than the other, and is cheaper to operate. The other type, Type B, costs a great deal more, but in principle it can be used to perform many additional kinds of chemical tests. The HOD of the department believes that over time he could find new customers who would pay for the additional types of tests that the Type B chromatographs can perform. At the end of its life , the Type B machine must be removed from department facility at great cost, a coast large enough that in the final year of operating the Type B machines, the net cash flow is negative. The estimated cash flows associated with each type of machine appear below:

Year	Type A Chromatographs	Type B Chromatographs
0	-$1000 000	-$3200 000
1	450 000	500 000
2	350 000	550 000
3	250 000	1000 000
4	200 000	1500 000
5	150 000	2000 000
6	125 000	-600 000

The HOD has requested you to provide analysis to help him determine which chromatograph to purchase. He is particularly interested in knowing how quickly each machine will pay back its initial cost and the rate of return that each machine offers. He tells you that if he does not spend money on new gas chromatographs, he will probably replace some existing equipment in the lab, and he would expect to earn a return of about 10% on that type of investment. As you sit down to begin your analysis, a number of questions come to mind.

1. What is the payback period of each machine?                                                
2. What are the pros and cons focusing on payback as a decision criterion in this particular case?

                                                                                                                       

3. What is the internal rate of return provided by each machine?                                   
4. What problems could arise if the HOD chooses the machine with the highest internal rate of return?

Answer 1

Payback period of each machine

The period from now to the moment when your investment will be recovered is called the payback period.Discounted payback is a useful way to work out how long it takes to get your capital back from the cash flows. It shows the number of years you will need to get that money back based on present returns. Each present value cash flow is calculated and then added together. The result is the discounted payback period or DPP

Given Discount rate = 10%

Discounted Payback period of Machine A = 3 + (113824.19*/136602.69)
= 3.833 Years

* Unrecovered investment at start of 4th year:
= Initial cost – Cumulative cash inflow at the end of 3rd year
= $1000000 – $ 886175.81
= $113824.19

Discounted Payback period of Machine B = 4 + (515074.12*/1241842.65)
= 4.415 Years

* Unrecovered investment at start of 5th year:
= Initial cost – Cumulative cash inflow at the end of 3rd year
= $ 3200000 – $ 2684925.88

= $ 515074.12

Pros and cons focusing on payback as a decision criterion in this particular case

Advantages of the Payback Method

The most significant advantage of the payback method is its simplicity. It's an easy way to compare several projects and then to take the project that has the shortest payback time

Ignores a project's profitability: Just because a project has a short payback period does not mean that it is profitable. If the cash flows end at the payback period or are drastically reduced, a project might never return a profit and therefore, it would be an unwise investment.

in the given case even though Machine A has shorter payback period, Machine B gives us more Profit. This can be explained :

Particulars	Machine A	Machine B
Investment	1000000	3200000
Total Present value of Cash Inflow	1186475.94	3588084.17
Profit	186475.94	388084.17

Internal rate of return provided by each machine

Internal Rate of Return is the interest rate that makes the Net Present Value zero. here IRR is obtained using Trial and error Method

IRR of Machine A = 18 %

IRR of Machine B = 14 %

Problems that could arise if the HOD chooses the machine with the highest internal rate of return

The disadvantage of the internal rate of return is that the method does not consider important factors like project duration, future costs, or the size of a project. The IRR simply compares the project's cash flow to the project's existing costs, excluding these factors.