Question

A company is analyzing two mutually exclusive projects, S and L, with the following cash flows:

A company is analyzing two mutually exclusive projects, S and L, with the following cash flows: 0 1 2 3 4 Project S -$1,000 $882.50 $250 $15 $5 Project L -$1,000 $5 $260 $420 $769.95 The company's WACC is 9.5%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places.   %

Project S	-$1,000	$882.50	$250	$15	$5
Project L	-$1,000	$5	$260	$420	$769.95

The company's WACC is 9.5%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places.

  %

Answer 1

Let’s compute NPV of both the projects.

NPV = PV of future cash inflow – Initial investment

	Project S	Project L
Year	Computation of PV Factor	PV Factor @ 9.5 % (F)	Cash Flow (CS)	PV (CS x F)	Cash Flow (CL)	PV (CL x F)
0	1/ (1+0.095)0	1	-$1000	-$1,000	-$1,000	-$1,000
1	1/ (1+0.095)1	0.913242009132420	882.5	805.93607	5	4.56621
2	1/ (1+0.095)2	0.834010967244219	250	208.50274	260	216.84285
3	1/ (1+0.095)3	0.761653851364584	15	11.42481	420	319.89462
4	1/ (1+0.095)4	0.695574293483638	5	3.47787	769.95	535.55743
			NPVS	$29.34149	NPVL	$76.86111

NPV of Project S = $ 29.34

NPV of Project L = $ 76.86

Project L seems to be better as it has higher NPV and it adds higher value to the firm.

Computation of IRR of Project L using trial and error method:

Computation of NPV at discount rate of 11 %.

Year	Computation of PV Factor	PV Factor @ 11 % (F)	Cash Flow (CL)	PV (CL x F)
0	1/ (1+0.11)0	1	-$1,000	-$1,000
1	1/ (1+0.11)1	0.900900900900901	5	4.50450
2	1/ (1+0.11)2	0.811622433244055	260	211.02183
3	1/ (1+0.11)3	0.731191381300950	420	307.10038
4	1/ (1+0.11)4	0.658730974145000	769.95	507.18991
			NPV1	$29.81662

As NPV is positive let’s compute NPV at discount rate of 12 %

Year	Computation of PV Factor	PV Factor @ 12 % (F)	Cash Flow (CL)	PV (CL x F)
0	1/ (1+0.12)0	1	-$1,000	-$1,000
1	1/ (1+0.12)1	0.89285714285714	5	4.46429
2	1/ (1+0.12)2	0.79719387755102	260	207.27041
3	1/ (1+0.12)3	0.71178024781341	420	298.94770
4	1/ (1+0.12)4	0.63551807840483	769.95	489.31714
			NPV2	-$0.00046

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

= 11 % + [$ 29.81662 x (12% - 11%)/ ($ 29.81662 – (-$ 0.00046))]

= 11 % + [($ 29.81662 x 1 %)/ ($ 29.81662 + $ 0.00046)]

= 11 % + ($ 0.2981662 / $ 29.81709)

= 11 % + 0.009999846

= 11 % + 0.999984573 % = 12.00 %

IRR of the better project, project L is 12 %