# Module 5. Investment decision

Lesson 27

IRR METHOD OF CAPITAL BUDGETING

27.1 Internal Rate of Return (IRR)

In the computation of Internal Rate of Return (IRR), the time value of money is accounted. The method of working IRR provides the knowledge of actual rate of return from the different projects. Thus IRR is known as ‘marginal efficiency of capital or yield on the investment’. It is the discount rate at which the present values of the net cash flows are just equal to zero, i.e., NPW = zero. When NPW is set equal to zero, the equation is solved for ‘I’. This is the internal rate of return. The IRR must be found out by trial and error with some approximation.

In the working procedure, an arbitrary discount rate is assumed and its corresponding NPW is arrived at. The positive NPW value of the project indicates that IRR is still higher and the next assumed arbitrary IRR value must be comparatively higher than the initial level. This process is continued until NPW becomes negative. Then by interpolation method the exact IRR is found out using the following formula:

(Internal Rate of Return) = (Lower Discount Rate) + (Differences between the two discount rates) (Present worth of the cash flow at the lower discount rate)/Absolute difference between the present worths of the cash flow at the two discount rates)

......... (Eq.27.1)
Table - 27.1: Estimation of IRR for Dairy farm (Hypothetical)

 Year Costs (in Rs.) Gross income (in Rs.) Net income (in Rs.) Discount factor (40%) Net present worth (in Rs.) Discount factor (43%) Net Present worth (in Rs.) 1 38,900 - -38,900 0.7143 -27,786.27 0.6993 -27,202.77 2 9,239 28,475 19,236 0.5102 9,814.21 0.48902 9,406.4 3 10,573 32,550 21,975 0.3644 8,007.69 0.3419 7,513.25 4 11,952 35,610 23,658 0.2603 6,158.17 0.2391 5.656.62 5 12,858 39,802 26,944 0.1859 5,008.89 0.1672 4,505.04 52,913 1,202.69 -121.46

IRR = 40 + 3 (1202.69 / 1202.69+121.46)

= 40 + 3 (0.9083)

= 40 + 2.7249

= 42.7249

Table 27.2 Estimation of IRR for Dairy farm (Hypothetical)

 Year Costs (in Rs.) Gross income (in Rs.) Net income (in Rs.) Discount factor (40%) Net present worth (in Rs.) Discount factor (30%) Net Present worth (in Rs.) End of 6th year 25,000 - -25,000 0.262 -6550 0.207 -5,175 End of 7th year 4,250 10,260 6,010 0.21 1,262.01 0.159 955.59 End of 8th year 4,792 12,550 7,758 0.168 1,303.30 0.123 954.23 End of 9th year 5,368 14,530 9,162 0.134 1,227.71 0.094 861.23 End of 10th year 5,975 16,275 10,300 0.107 1,102.10 0.073 751.90 End of 11th year 6,456 19,396 12,940 0.086 1,112.84 0.056 724.64 End of 12th year 7,187 21,470 14,283 0.069 985.53 0.043 614.17 35,453 443.49 -313.24

IRR = 25 + 5 (443.49 / 443.49+313.24)

= 25 x 5 (0.586)

= 25 + 2.93

= 27.93