IRR

Computing IRR manualy using interpolation methods.
Data
Initial outlay	-10,010
FCF in year 1	1000
FCF in year 2	3000		UNEVEN CASH FLOW
FCF in year 3	6000
FCF in year 4	7000
How to find IRR manualy?
there are 3 steps to find IRR(UNEVEN CASH FLOW)
1 step. You have to find the annuity in FCF
since the FCF is Uneven cash flow, so you have to find the assumed annuity
The assumed annuity as follows
1000		17000
3000		no ofyears
6000
7000		17,000	4250		Assumed annuity
17000		4

2 step. using annuity table to find the range of interpolation
a. Intially outlay devided by assumed annuity
intial outlay = 10,010
assumed annuity = 4250
thus,	10,010	2.36%	using this percent to find the range of interpolation in the annuity table
	4250
b. present value of an annuity table (extracts)
n	16%	17%	18%	19%	20%
1	0.862	0.855	0.847	0.84	0.833
2	1.605	1.585	1.566	1.547	1.528
3	2.246	2.21	2.174	2.14	2.106
4	2.798	2.743	2.69	2.639	2.589		near with 2.36
5	3.274	3.199	3.127	3.058	2.991
6	3.685	3.589	3.498	3.41	3.326
until 50	xxxx	xxxx	xxxx	xxxx	xxxx
now you have to find the value that close with 2.36%
1. take a look at n first, n=4

2. take a look at the percent

3 step. after u've found the range of interpolation, the next step as follows
a. your ranges of interpolation are 19% and 20%
b. the FCF have to dicounted back to the present using present value of interest factor
c. using the present value interest factor to find the Discounted value of FCF (UNVEN CASHFLOW)
n	16%	17%	18%	19%	20%
1	0.862	0.855	0.847	0.84	0.833
2	0.743	0.731	0.718	0.706	0.694
3	0.641	0.624	0.609	0.593	0.579
4	0.552	0.534	0.516	0.499	0.482
5	0.476	0.456	0.437	0.419	0.402
6	0.41	0.39	0.37	0.352	0.335
until 50	xxxx	xxxx	xxxx	xxxx	xxxx
19%				20%
FCF in year 1	1000	0.84	840	FCF in year 1	1000	0.833	833
FCF in year 2	3000	0.706	2118	FCF in year 2	3000	0.694	2082
FCF in year 3	6000	0.593	3558	FCF in year 3	6000	0.579	3474
FCF in year 4	7000	0.499	3493	FCF in year 4	7000	0.482	3374
		Total	10009			Total	9763
d. therefore, 19%= 10,009, 20%=9763
last but not least, using the interpolation formula to find the IRR
numerator=	19%(a)-	Iniatial outlay
Denominator=	19%(a)-	20%(b)
19% = 10,009
20%=9763
Initial outlay = 10,010
Hence,	10,009-	10010=	-1	c
	10009-	9763=	246	d
interpolation formula
aX	c	Xb-a
	d
thus, 19%X	-1	X(20%-19%)
	246
IRR is 19%