Question

Project cost	$100 000
Estimated life	5 years
Estimated residual value	$20 000
Annual Net Cash flow	$30 000
Required rate of return	10%

Given the data above, calculate the internal rate of return (IRR). (not using excel)

Answer 1

Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 19% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 19%	Present Value of Cash Flow ($)
1	30,000	0.840336	25,210.08
2	30,000	0.706165	21,184.94
3	30,000	0.593416	17,802.47
4	30,000	0.498669	14,960.06
5	50,000 [30,000 + 20,000]	0.419049	20,952.47
TOTAL			100,110.03

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $100,110.03 - $100,000

= $110.03

Step – 2, NPV at 19% is positive, Calculate the NPV again at a higher discount rate, Say 20% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 19%	Present Value of Cash Flow ($)
1	30,000	0.833333	25,000.00
2	30,000	0.694444	20,833.33
3	30,000	0.578704	17,361.11
4	30,000	0.482253	14,467.59
5	50,000 [30,000 + 20,000]	0.401878	20,093.88
TOTAL			97,755.92

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $97,755.92 - $100,000

= -$2,244.08 (Negative NPV)

The calculation of Internal Rate of Return using Interpolation method is as follows

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.19 + [$110.03 x (0.20 – 0.19)]

              $110.03 – (-$2,244.08)

= 0.19 + [$1.10 / $2,354.12]

= 0.19 + 0.0005

= 0.1905 or

= 19.05%

“Hence, the Internal Rate of Return (IRR) for the Project will be 19.05%”

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.