Question

In: Finance

- Langton Inc. is considering Projects S and L, whose cash flows are shown below. These...

- Langton Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much, if any, value will be forgone? In other words, what's the NPV of the chosen project versus the maximum possible NPV? You must show each project's IRR as well as its NPV. The firm's cost of capital is 7%.

Year CF from S CF from L
0 -1200 -2650
1 550 725
2 700 750
3 200 800
4 300 1400

What is the crossover point for the two projects? What is the significance of this?

Solutions

Expert Solution

Computation of NPV:

NPV = PV of future cash flows – Initial investment

Year

Cash Flow (CS)

Computation of PV Factor

PV Factor @ 7 % (F)

PV (CS x F)

0

-$ 1,200

1/ (1+0.07)0

1

-$ 1,200.00

1

$ 550

1/ (1+0.07)1

0.934579439252336

$ 514.01869

2

$ 700

1/ (1+0.07)2

0.873438728273212

$ 611.40711

3

$ 200

1/ (1+0.07)3

0.816297876890852

$ 163.25958

4

$ 300

1/ (1+0.07)4

0.762895212047525

$ 228.86856

NPV

$ 317.55394

NPV of Project L is $ 317.55

Year

Cash Flow (CL)

Computation of PV Factor

PV Factor @ 7 % (F)

PV (CL x F)

0

-$ 2,650

1/ (1+0.07)0

1

-$ 2,650.00

1

$ 725

1/ (1+0.07)1

0.934579439252336

$ 677.57009

2

$ 750

1/ (1+0.07)2

0.873438728273212

$ 655.07905

3

$ 800

1/ (1+0.07)3

0.816297876890852

$ 653.03830

4

$ 1,400

1/ (1+0.07)4

0.762895212047525

$ 1,068.05330

NPV

$ 403.74074

NPV of Project L is $ 403.74

Computation of IRR:

Project S:

Computation of NPV of Project S at discount rate of 20 %.

Year

Cash Flow (CS)

Computation of PV Factor

PV Factor @ 20 % (F)

PV (CS x F)

0

-$ 1,200

1/ (1+0.2)0

1

-$ 1,200.00

1

$ 550

1/ (1+0.2)1

0.833333333333333

$ 458.33333

2

$ 700

1/ (1+0.2)2

0.694444444444445

$ 486.11111

3

$ 200

1/ (1+0.2)3

0.578703703703704

$ 115.74074

4

$ 300

1/ (1+0.2)4

0.482253086419753

$ 144.67593

NPVS1

$ 4.86111

As NPV is positive let’s compute NPV at discount rate of 21 %.

Year

Cash Flow (CS)

Computation of PV Factor

PV Factor @ 21 % (F)

PV (CS x F)

0

-$ 1,200

1/ (1+0.21)0

1

-$ 1,200.00

1

$ 550

1/ (1+0.21)1

0.826446280991736

$ 454.54545

2

$ 700

1/ (1+0.21)2

0.683013455365071

$ 478.10942

3

$ 200

1/ (1+0.21)3

0.564473930053777

$ 112.89479

4

$ 300

1/ (1+0.21)4

0.466507380209733

$ 139.95221

NPV S2

-$ 14.49813

IRR S = R1 + [NPVS1 x (R2 – R1)/ (NPVS1 – NPVS2)]

    = 20 % + [$ 4.86111 x (22 % – 21 %)/ ($ 4.86111 – (- $ 14.49813)]

    = 20 % + [$ 4.86111 x 1 %/ ($ 4.86111 + $ 14.49813)]

    = 20 % + ($ 0.0486111/ $ 19.35924)

    = 20 % + 0.002511

    = 20 % + 0.2511 % = 20.25 %

IRR of Project S is 20.25 %

Project L:

Computation of NPV of Project L at discount rate of 12 %.

Year

Cash Flow (CL)

Computation of PV Factor

PV Factor @ 12 % (F)

PV (CL x F)

0

-$ 2,650

1/ (1+0.12)0

1

-$ 2,650.00

1

$ 725

1/ (1+0.12)1

0.892857142857143

$ 647.32143

2

$ 750

1/ (1+0.12)2

0.797193877551020

$ 597.89541

3

$ 800

1/ (1+0.12)3

0.711780247813411

$ 569.42420

4

$ 1,400

1/ (1+0.12)4

0.635518078404831

$ 889.72531

NPVL1

$ 54.36634

As NPV is positive let’s compute NPV at discount rate of 13 %.

Year

Cash Flow (CL)

Computation of PV Factor

PV Factor @ 13 % (F)

PV (CL x F)

0

-$ 2,650

1/ (1+0.13)0

1

-$ 2,650.00

1

$ 725

1/ (1+0.13)1

0.884955752212389

$ 641.59292

2

$ 750

1/ (1+0.13)2

0.783146683373796

$ 587.36001

3

$ 800

1/ (1+0.13)3

0.693050162277696

$ 554.44013

4

$ 1,400

1/ (1+0.13)4

0.613318727679377

$ 858.64622

NPVL2

-$ 7.96072

IRR L = R1 + [NPVL1 x (R2 – R1)/ (NPVL1 – NPVL2)]

    = 12 % + [$ 54.36634 x (13 % – 12 %)/ ($ 54.36634 – (- $ 7.96072)]

    = 12 % + [$ 54.36634 x 1 %/ ($ 54.36634 + $ 7.96072)]

    = 12 % + ($ 0.5436634 / $ 62.32706)

    = 12 % + 0.008722751

    = 12 % + 0.8722751 % = 12.87 %

IRR of Project L is 12.87 %

Project L should be accepted based on NPV decision.

Project S should be accepted based on IRR decision.

Forgone value if we choose Project S based on IRR rule = $ 403.74 - $ 317.55 = $ 86.19

Computation of Crossover rate:

Year

Cash Flow (CL)

Cash Flow (CS)

Cash Flow CL - CS

0

-$ 2,650

-$ 1,200

-$ 1,450

1

$ 725

$ 550

$ 175

2

$ 750

$ 700

$ 50

3

$ 800

$ 200

$ 600

4

$ 1,400

$ 300

$ 1,100

Computation of NPV at discount rate of 8 %

Year

Cash Flow

CL - CS

Computation of PV Factor

PV Factor @ 8 % (F)

PV (CL - CS x F)

0

-$ 1,450

1/ (1+0.08)0

1

-$ 1,450.00

1

$ 175

1/ (1+0.08)1

0.925925925925926

$ 162.03704

2

$ 50

1/ (1+0.08)2

0.857338820301783

$ 42.86694

3

$ 600

1/ (1+0.08)3

jeff jeffy answered 2 years ago
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