Project Appraisal Methods
Various Projects that the organization is considering are appraised using the following methods:
Project Evaluation Methods
Payback Period Present Value ARR
NPV IRR PI Discounted Payback
I. Payback period method:
This method is simple to understand and apply. In this method, the period, during which the Cash inflows of a project repay its cost, is calculated. Whichever project repays the project cost earlier is considered as better.
Illustration 1:
If the initial outlay of a ProjectA is Rs.100000 and the Cash inflows are estimated @ Rs.20000 p.a., the Payback period is 5 years (i.e., 100000/20000).
The projected inflows may not be equal always. If the inflows are not equal, we have to calculate the cumulative inflows and interpolate and find out the exact “Payback period”. Now, consider the following illustration:
Illustration 2:
Initial outlay Rs.100000/ The inflows during the first four years are estimated at Rs.25000/, Rs.70000/, Rs.20000/ and Rs.50000/. The cumulative cash inflows are calculated as follows:
Year Cash inflows Cumulative inflows
I 25000 25000
II 70000 95000
III 20000 115000
IV 50000 165000
It is apparent that the project cost of Rs.100000 is recovered during the third year. Assuming that the rate of earning during the third year is uniform through out the year, we can say that the Payback period is 2 1/4 years (i.e., 2 years and 5000/20000 wherein 5000=100000(Project cost)Less: Cumulative cash inflows up to the 2^{nd} year i.e., Rs.95000).
Though this method is a simple method to operate, it is a layman’s method and it has no scientific background, especially it does not take into account the most important interest factor which may have major impact on the real and effective value of the inflows. For overcoming this major adverse feature of this method, the concept of “Time value of money”, should be understood. The said concept is used in the Methods using the Present value wherein inflows are considered after adjusting the effects of Cost of Capital (by using the present value factors).
II. Present Value of Cash Inflows:
Rs.10000/ that one holds today will not be equal to Rs.10000/ that is estimated to flow in at the end of one year due to the presence of the interest factor. If one invests Rs.10000 now @ 10% p.a., the investment will grow up to Rs.11000/ at the end of the first year along with interest of Rs.1000 ( Rs.10000 x 10%). In other words, the present value of Rs.11000 that one is going to get after one year at a cost of capital of 10% is Rs.10000. This is used to create the present value factor of 0.909 (i.e., 10000/11000). Using the said factor the present value of the inflow at the end of the first year is calculated. Similarly, the inflows at the end of the second year, third year etc., are discounted and the total Present value is arrived at, the present value factors for the 2^{nd}, 3^{rd} and subsequent years being (10000/11000)^2, (10000/11000)^3 , and so on.
Cost of Capital:
In short, it is the rate at which the Capital is obtained by the person who has started the project. For example, for a person who has borrowed the capital from a Bank, the rate of interest charged by the Bank is the cost of capital. For a person who has invested his own money, it is the opportunity cost of Capital. For a person who has got both types of capital, it is the weighted average of both the rates.
II (1) Discounted Payback Period Method:
In this method, features of the above two concepts are combined and used. First the Cash flows are discounted at the cost of capital rate and then after finding the cumulative discounted cash flows (as explained in Illustration 2) the Pay back period is arrived at which is much more reliable than the Payback period method explained earlier.
II (2) NPV:
In this method the Present value of all the inflows and outflows are found out and totaled to arrive at what is known as “Net present value”. A project which gives a positive NPV is accepted and the one which gives a negative NPV is rejected. When two projects are compared, the one which gives more NPV has to be accepted.
II (3) Profitability Index (PI) (Also known as Benefit cost ratio):
PI= Present value of Inflows x 100 / Present Value of outflows
If the NPV is Zero, PI will be equal to 1.
Alternatively, some authors use a formula wherein the NPV is taken in the numerator instead of the Present value of Inflows.
The students can use any one of the above formulae consistently, especially when two projects are being compared.
II (4) Internal Rate of Return: (IRR)
It is the rate at which the project is generating the inflows. In this method, the cost of capital will not be given. We have to find out the rate at which the project generates the funds. It is the rate at which the “Discounted Cash inflows = Discounted Cash outflows”, i.e., the NPV=0. When a project is being evaluated, it has to be accepted if the IRR is greater than the cost of capital or the “expectancy rate”. When two projects are compared, the one with higher IRR should be accepted. In this connection, the students’ attention is invited to the following paragraph:
IRR vs NPV:
Where IRR and NPV of two projects are furnished both may give a different conclusion. This is so especially in cases where the cost of capital is different in both the projects.
Now, consider the following illustration:
PS Dutta Ltd., is considering two mutually exclusive projects X and Y, the details of
which are as follows:
Project X Project Y
Investment 0^{th} year Rs. 100000 150000
Cash inflows Year ended 1 42000 55000
2 42000 60000
3 42000 65000
The Present value factors are furnished hereunder using which you are required to
compute the IRR for the above projects.
8% 9% 10% 11% 12% 13%
0.926 0.917 0.909 0.901 0.893 0.885
0.857 0.842 0.826 0.812 0.797 0.783
0.794 0.772 0.751 0.731 0.712 0.693
Project X Project Y Discounting factors
X Y
100000 150000 12 13 9 10
42000 55000 0.893 0.885 0.917 0.909
42000 60000 0.797 0.783 0.842 0.826
42000 65000 0.712 0.693 0.772 0.751
Discounted Inflows 100884 99162 151135 148370
Proj X IRR= 12+(884/(884+838))=12.51
Proj Y IRR= 9+(1135/(1135+1630))=9.41
On seeing the above calculations it may seem that Proj X is acceptable.
If we consider 13% and 8% as the cost of capital for the projects respectively, the NPV works out to Rs.()832 and Rs. (+)3965 (see calculations below), indicating that the Proj Y is better.
X

Y

100000

13

100000

150000

8

150000

42000

0.885

37168

55000

0.926

50926

42000

0.783

32892

60000

0.857

51440

42000

0.693

29108

65000

0.794

51599

NPV


832



3965

In such cases, NPV is a better guide and the students should rely on the NPV method rather than the IRR method. When evaluating the mutually exclusive projects, the one with a higher IRR may not be the one with the best NPV. This is due to the following:
 The IRR assumes that the cash flows are reinvested at the rate of IRR.
 The NPV assumes that the cash flows are reinvested at the rate of Cost of Capital.
This is especially so when the cost of capital and the life of the projects are not similar or wide variations are there.
Tutorial Note:
The students should know that wherever we talked about Cash flows, we really meant cash inflow and outflow only. Such cash inflows are calculated as follows:
Cash inflow=Net profit after DepreciationTax thereon + Depreciation
The Depreciation is added back simply because, there is no cash outflow when it is written off, though it is deductible for calculating the tax on income which has to be actually paid out.
III. ARR: (Accounting Rate of return or Average Rate of return)
It is known as the Accounting Rate of return as it considers only the accountant’s profit i.e., Profit after depreciation and tax. It is called Average rate of return as it considers the average Profit after depreciation and tax during the life time of the Project.
ARR= Average Return / Net Investment