Question

Farrah Corporation is considering two projects (see below). For your analysis, assume these projects are mutually exclusive with a required rate of return of 12%.

Project 1 Initial investment $185,000 Cash inflow Year 1 $230,000 Project 2 Initial investment $1,100,000 Cash inflow Year 1 $1,450,000 Compute the following for each project: • NPV (net present value) • PI (profitability index) • IRR (internal rate of return) Which project should be selected? Why?

Answer 1

	Project 1	Project 2
NPV	$ 20,357.14	$ 184,642.86
PI	1.11	1.17
IRR	24.32%	30.63%

Based on NPV, PI and IRR decision, Project 2 should be selected as it has higher NPV, PI and IRR than Project 1

Explanation:

Computation of NPV:

NPV = PV of future cash flow – Initial investment

			Project 1		Project 2
Year	Computation of PV Factor	PV Factor @ 12 % (F)	Cash Flow (C1)	PV (C1 x F)	Cash Flow (C2)	PV (C2 x F)
0	1/ (1+0.12)0	1	($185,000)	($185,000.00)	($1,110,000)	($1,110,000.00)
1	1/ (1+0.12)1	0.89285714285714	$230,000	$205,357.14	$1,450,000	$1,294,642.86
			NPV1	$20,357.14	NPV2	$184,642.86

Computation of Profitability index:

PI = PV of future cash flows/Initial investment

PI for Project 1 = $205,357.14/$185,000 = 1.110038594595 or 1.11

PI for Project 2 = $1,294,642.86 /$1,110,000 = 1.166344919 or 1.17

Computation of IRR using trial and error method:

IRR for Project 1:

Let’s compute NPV at discount rate of 24 %

Year	Computation of PV Factor	PV Factor @ 24 % (F)	Cash Flow (C)	PV (C x F)
0	1/ (1+0.24)0	1	($185,000)	($185,000.00)
1	1/ (1+0.24)1	0.80645161290323	$230,000	$185,483.87
			NPV1	$483.87

As NPV is positive, let’s compute NPV at discount rate of 25 %

Year	Computation of PV Factor	PV Factor @ 25 % (F)	Cash Flow (C)	PV (C x F)
0	1/ (1+0.25)0	1	($185,000)	($185,000.00)
1	1/ (1+0.25)1	0.8000	$230,000	$184,000.00
			NPV2	($1,000.00)

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

       = 24 % + [$ 483.87 x (25 % - 24 %)/ [$ 483.87 – (-$ 1,000)]

       = 24 % + ($ 483.87 x 0.01)/ ($ 483.87 + $ 1,000)

       = 24 % + ($ 4.8387 / $ 1,483.87)

       = 24 % + 0.003260865

       = 24 % + 0.3260865%

       = 24.32 %

IRR for Project 2:

Let’s compute NPV at discount rate of 30 %

Year	Computation of PV Factor	PV Factor @ 30 % (F)	Cash Flow (C)	PV (C x F)
0	1/ (1+0.30)0	1	($1,110,000)	($1,110,000.00)
1	1/ (1+0.30)1	0.76923076923077	$1,450,000	$1,115,384.62
			NPV1	$5,384.62

As NPV is positive, let’s compute NPV at discount rate of 31 %

Year	Computation of PV Factor	PV Factor @ 31 % (F)	Cash Flow (C)	PV (C x F)
0	1/ (1+0.31)0	1	($1,110,000)	($1,110,000.00)
1	1/ (1+0.31)1	0.763358778625954	$1,450,000	$1,106,870.23
			NPV2	($3,129.77)

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

       = 30 % + [$ 5,384.62 x (31 % - 30 %)/ [$ 5,384.62 – (-$ 3,129.77)]

       = 30 % + ($ 5,384.62 x 0.01)/ ($ 5,384.62 + $ 3,129.77)

       = 30 % + ($ 53.84.62 / $ 8,514.39)

       = 30 % + 0.006324141

       = 30 % + 0.6324141 %

       = 30.63 %