Question

Bruin, Inc., has identified the following two mutually exclusive projects: Year 0 هه Cash Flow (A) -$28,700 14,100 12,000 9,050 4,950 Cash Flow (B) -$28,700 4,150 9,650 14,900 16,500 م ليا 6.66 points ط eBook 8-1 What is the IRR for each of these projects? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places. e.a.. 32.16.) Print References Project A Project B a-2 Using the IRR decision rule, which project should the company accept? Project A Project B

Answer 1

a-1

Computation of IRR using trial and error method:

IRR for Project A:

Let’s compute NPV at discount rate of 17 %

Year	Cash Flow (CA)	PV Factor Computation	PV Factor @ 17 % (F)	PV (CA x F)
0	($28,700)	1/ (1+0.17)0	1	($28,700.00)
1	$14,100	1/ (1+0.17)1	0.8547008547009	$12,051.28
2	$12,000	1/ (1+0.17)2	0.7305135510264	$8,766.16
3	$9,050	1/ (1+0.17)3	0.6243705564328	$5,650.55
4	$4,950	1/ (1+0.17)4	0.5336500482332	$2,641.57
			NPV1	$409.57

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

Year	Cash Flow (CA)	PV Factor Computation	PV Factor @ 18 % (F)	PV (CA x F)
0	($28,700)	1/ (1+0.18)0	1	($28,700.00)
1	$14,100	1/ (1+0.18)1	0.8474576271186	$11,949.15
2	$12,000	1/ (1+0.18)2	0.7181844297616	$8,618.21
3	$9,050	1/ (1+0.18)3	0.6086308726793	$5,508.11
4	$4,950	1/ (1+0.18)4	0.5157888751519	$2,553.15
			NPV2	($71.37)

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

       = 17 % + [$ 409.57 x (18 % - 17 %)/ [$ 409.57 – (-$ 71.37)]

       = 17 % + ($ 409.57 x 0.01)/ ($ 409.57 + $ 71.37)

       = 17 % + ($ 4.0957 / $ 480.94)

       = 17 % + 0.008516103549

       = 17 % + 0.8516103549 %

        = 17.85 %

IRR for Project B:

Let’s compute NPV at discount rate of 17 %

Year	Cash Flow (CB)	PV Factor Computation	PV Factor @ 17 % (F)	PV (CB x F)
0	($28,700)	1/ (1+0.17)0	1	($28,700.00)
1	$4,150	1/ (1+0.17)1	0.8547008547009	$3,547.01
2	$9,650	1/ (1+0.17)2	0.7305135510264	$7,049.46
3	$14,900	1/ (1+0.17)3	0.6243705564328	$9,303.12
4	$16,500	1/ (1+0.17)4	0.5336500482332	$8,805.23
			NPV1	$4.81

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

Year	Cash Flow (CB)	PV Factor Computation	PV Factor @ 18 % (F)	PV (CB x F)
0	($28,700)	1/ (1+0.18)0	1	($28,700.00)
1	$4,150	1/ (1+0.18)1	0.8474576271186	$3,516.95
2	$9,650	1/ (1+0.18)2	0.7181844297616	$6,930.48
3	$14,900	1/ (1+0.18)3	0.6086308726793	$9,068.60
4	$16,500	1/ (1+0.18)4	0.5157888751519	$8,510.52
			NPV2	($673.45)

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

       = 17 % + [$ 4.81 x (18 % - 17 %)/ [$ 4.81 – (-$ 673.45)]

       = 17 % + ($ 4.81 x 0.01)/ ($ 4.81 + $ 673.45)

       = 17 % + ($ 0.0481 / $ 678.26)

       = 17 % + 0.00007091676

       = 17 % + 0.007091676 %

        = 17.01 %

a-2.

Using the IRR decision rule, Project A should be selected.

a-3.

No, the decision is not necessarily correct.

b-1.

NPV = PV of future cash flow – Initial investment

Computation of NPV for Project A:

Year	Cash Flow (CA)	PV Factor Computation	PV Factor @ 12 % (F)	PV (CA x F)
0	($28,700)	1/ (1+0.12)0	1	($28,700.00)
1	$14,100	1/ (1+0.12)1	0.8928571428571	$12,589.29
2	$12,000	1/ (1+0.12)2	0.7971938775510	$9,566.33
3	$9,050	1/ (1+0.12)3	0.7117802478134	$6,441.61
4	$4,950	1/ (1+0.12)4	0.6355180784048	$3,145.81
			NPV	$3,043.04

Computation of NPV for Project B:

Year	Cash Flow (CB)	PV Factor Computation	PV Factor @ 12 % (F)	PV (CBx F)
0	($28,700)	1/ (1+0.12)0	1	($28,700.00)
1	$4,150	1/ (1+0.12)1	0.8928571428571	$3,705.36
2	$9,650	1/ (1+0.12)2	0.7971938775510	$7,692.92
3	$14,900	1/ (1+0.12)3	0.7117802478134	$10,605.53
4	$16,500	1/ (1+0.12)4	0.6355180784048	$10,486.05
			NPV	$3,789.85

b-2.

Project B should be chosen, if applied NPV decision rule.

c.

Computation of incremental Cash Flow:

Year	Cash Flow (CA)	Cash Flow (CB)	Incremental cash Flow (CA – CB)
0	($28,700)	($28,700)	$0
1	$14,100	$4,150	$9,950
2	$12,000	$9,650	$2,350
3	$9,050	$14,900	($5,850)
4	$4,950	$16,500	($11,550)

Computation of incremental IRR:

Let’s compute NPV at discount rate of 15 %

Year	Cash Flow (CA - CB)	PV Factor Computation	PV Factor @ 15 % (F)	PV (CA -CB) x F
0	$0	1/ (1+0.15)0	1	$0.00
1	$9,950	1/ (1+0.15)1	0.869565217391304	$8,652.17
2	$2,350	1/ (1+0.15)2	0.756143667296787	$1,776.94
3	($5,850)	1/ (1+0.15)3	0.657516232431988	($3,846.47)
4	($11,550)	1/ (1+0.15)4	0.571753245593033	($6,603.75)
			NPV1	($21.11)

As NPV is negative, let’s compute NPV at discount rate of 16 %.

Year	Cash Flow (CA - CB)	PV Factor Computation	PV Factor @ 16 % (F)	PV (CA -CB) x F
0	$0	1/ (1+0.16)0	1	$0.00
1	$9,950	1/ (1+0.16)1	0.862068965517241	$8,577.59
2	$2,350	1/ (1+0.16)2	0.743162901307967	$1,746.43
3	($5,850)	1/ (1+0.16)3	0.640657673541351	($3,747.85)
4	($11,550)	1/ (1+0.16)4	0.552291097880475	($6,378.96)
			NPV2	$197.21

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

       = 15 % + [ - $ 21.11 x (16 % - 15 %)/ (- $ 21.11 – $ 197.21)

       = 15 % + (- $ 21.11 x 0.01)/ - $ 218.32

       = 15 % + (- $ 0.2111 / - $ 218.32)

       = 15 % + 0.0009669292781

       = 15 % + 0.09669292781 %

        = 15.09669292781 or 15.10 %

At discount rate of 15.10 %, the company will be indifferent between these projects.