Financial Management & Cost Accounting

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