Suppose your firm is considering two mutually exclusive, required projects with

Question

Suppose your firm is considering two mutually exclusive, required projects with the cash flows shown below. The required rate of return on projects of both of their risk class is 10 percent, and that the maximum allowable payback and discounted payback statistic for the projects are 2 and 3 years, respectively.

Time:   0   1   2   3
Project A Cash Flow   -27,000   17,000   37,000   8,000
Project B Cash Flow   -37,000   17,000   27,000   57,000

Use the discounted payback decision rule to evaluate these projects; which one(s) should it be accepted or rejected?
accept both A and B
reject A, accept B
accept neither A nor B
accept A, reject B

Explanation / Answer

It is a capital budgeting problem. Here investment is required in areas which will generate cash flow for more than one year. you have to evaluate them and justify their acceptability. In these projects initially a lump sum money is invested.

Various methods are available for their evaluation. One of them is discounted pay back metod. here pay back is a period which is required to recover initial lump sum amount invested. A project with minimu pay back period is the most preferred one. Objective of this method is how quickly the firm can free his blocked money. It is extremly useful when liquidity or fund crisis is the main area of concern to the firm.

In simple pay back method. you will calculate pay back period from absolute cash inflow figures. But it is not an afficient technique. Since cash flows are available in different years, it is not justified to take same value of cash flows. So you have to consider their time value. It is possible by taking discounted present value figures of those cash flows. For calculating present value use 10% risk clas return as discounting rate. It will ensure that this minimum return is earned from the project.

Steps of calculating discounted present value is shown below:

1. Consider all future cash flows. Here projects will generate cash flows for coming three years. So take all these three figures first.

2. Then use 10% discount rate to estimate their present value.

3. Calculate cumulative cash flows of different time period.

4. Finally compare the cumulative figures and estimate pay back period.

5. Establish a rerquired cut off pay back period. Here it is 3 years.

6. If actual pay back is equal or less than required pay back period then acept it. Other wise reject the project.

On the basis of above steps, discounted pay back has been calculated below:

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Evaluation: Both projects have pay back period less than the minmimum required period of three years. So both are acceptable. However pay back of A is the minimum one. So it is preferred over project B.

Main defect of this method is that it does not consider cash flow figures after pay back. A a result you can reject a project which is the providing you better cash flow. same thing has happened here. If you want to invest in only one project, then you have to go for project a. But cash flow of B is higher than A.

Result: Both A and B are aceptable.

Table showing calculation of discounted pay back period Year Discount Project A Project B factors Cash flow Discounted Cumulative Cash flow Discounted Cumulative cash flows Cash flows cash flows Cash flows 1 0.90909 17,000 15454.55 15454.55 17,000 15454.55 15454.55 2 0.82645 37,000 30578.51 46033.06 27,000 22314.05 37768.60 3 0.75131 8,000 6010.52 52043.58 57,000 42824.94 80593.54 Total 2.48685 62000 52043.58 113531.18 101000.00 80593.54 133816.68 Initial investment 27,000 37,000 Pay back 1+ (27,000-15,454.55)/(30,578.51) 1+(37,000-15,454.55)/37,768.60 =1.378 years =1.570 years

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