Question

Project K costs $57,758.92, its expected cash inflows are $13,000 per year for 9 years, and its WACC is 9%. What is the project's IRR? Round your answer to two decimal places.

Answer 1

Let’s use trial and error method to compute IRR.

Let’s compute NPV at discount rate of 17 %

Year	Cash Flow (C)	Calculation of PV Factor	PV Factor @ 17 % (F)	PV(= F x C)
0	($57,758.92)	1/(1+17%)^0	1	($57,758.92)
1	$13,000	1/(1+17%)^1	0.854700855	$11,111.11
2	$13,000	1/(1+17%)^2	0.730513551	$9,496.68
3	$13,000	1/(1+17%)^3	0.624370556	$8,116.82
4	$13,000	1/(1+17%)^4	0.533650048	$6,937.45
5	$13,000	1/(1+17%)^5	0.456111152	$5,929.44
6	$13,000	1/(1+17%)^6	0.389838592	$5,067.90
7	$13,000	1/(1+17%)^7	0.333195378	$4,331.54
8	$13,000	1/(1+17%)^8	0.284782374	$3,702.17
9	$13,000	1/(1+17%)^9	0.243403738	$3,164.25
			NPV1	$98.441178

As NPV is positive let’s compute NPV at discount rate of 18 %.

Year	Cash Flow (C)	Calculation of PV Factor	PV Factor @ 18 % (F)	PV(= F x C)
0	($57,758.92)	1/(1+18%)^0	1	($57,758.92)
1	$13,000	1/(1+18%)^1	0.847457627	$11,016.95
2	$13,000	1/(1+18%)^2	0.71818443	$9,336.40
3	$13,000	1/(1+18%)^3	0.608630873	$7,912.20
4	$13,000	1/(1+18%)^4	0.515788875	$6,705.26
5	$13,000	1/(1+18%)^5	0.437109216	$5,682.42
6	$13,000	1/(1+18%)^6	0.370431539	$4,815.61
7	$13,000	1/(1+18%)^7	0.313925033	$4,081.03
8	$13,000	1/(1+18%)^8	0.266038164	$3,458.50
9	$13,000	1/(1+18%)^9	0.225456071	$2,930.93
			NPV2	($1,819.636236)

IRR= R1+ [NPV1 x (R2-R1) %/( NPV1-NPV2)]

       = 17 % + $ 98.44 x (18 % - 17 %)/ ($ 98.441178 - (-$ 1,819.636236)

      = 17 % + $ 98.44 x (18 % - 17 %)/ ($ 98.441178 + $ 1,819.636236)

       = 17 % + $ 98.441178 x 0.01/ $ 1,918.07741369

       = 17 % + $ 0.98441178/$ 1,918.07741369

       = 17 % + 0.00051323

       = 17 % + 0.051323 %

       = 17.05 %

IRR of the project is 17.05 %