FM09-CH 10....IM PANDEY

Ch. 10: Determining Cash Flows for Investment Analysis

CHAPTER 10 DTERMINING CASH FLOWS FOR INVESTMENT ANALYSIS Problem 1 Assumption: (1) It is assumed that the given annual  cash inflows are after-tax. (2) ARR is calculated as average cash profit divided by original investment. Alternatively, average investment (original investment/2) can be used for calculation.

Required rate

10%

Tax rate

35%

Projects

A

Outlay

B

C

D

E

-500,000

-120,000

-92,000

-5,750

-40,000

125,000

12,000

15,000

2,000

6,000

8

15

20

5

10

5.3349

7.6061

8.5136

3.7908

6.1446

Annual inflows Life PVAF @10% PV of NCF

666,865.8

NPV

166,865.8 -28,727.0

IRR

35,703.5 1,831.6

-3,132.6

18.6%

5.6%

15.4%

21.8%

8.1%

4.00

10.00

6.13

2.88

6.67

25.0%

10.0%

16.3%

34.8%

15.0%

PB (years) ARR

91,273.0 127,703.5 7,581.6 36,867.4

Rank Project

NPV

IRR

PB

ARR

A

1

2

2

2

B

5

5

5

5

C

2

3

3

3

D

3

1

1

1

E

4

4

4

4

Problem 2

Cost of capital

10%

Tax rate

43%

Cost of project X

20,000

Life of project X

5

Straight line depreciation depreciation

4,000

Cost of project Y

15,000

Life of project Y

5

Straight line depreciation depreciation

3,000

PROJECT X Year BT cash flows AT cash flows (T = 35%) Add: DTS (Dep. × T = 4,000 × .35 ) NCF PVF PV (Rs) NPV (Rs) PI

0

1

2

3

4

5

-20,000

4,200

4,800

7,000

8,000

2,000

2,730

3,120

4,550

5,200

1,300

1,400

1,400

1,400

1,400

1,400

-20,000

4,130

4,520

5,950

6,600

2,700

1.000

0.909

0.826

0.751

0.683

0.621

-20,000

3,755

3,736

4,470

4,508

1,676

-1,855 0.91

1

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

IRR Accumulated cash flows Payback (years)

6.29% -20000

-15870

-11350

-5400

1200

3900

4

PROJECT Y Year BT cash flows AT cash flows (T = 35%)

0

1

2

3

4

5

-15,000

4,200

4,500

4,000

5,000

1,000

2,730 1,050

2,925 1,050

2,600 1,050

3,250 1,050

650 1,050

3,780 0.909 3,436

3,975 0.826 3,285

3,650 0.751 2,742

4,300 0.683 2,937

1,700 0.621 1,056

-11220

-7245

-3595

705 4

2405

Add: DTS (Dep. × T = 3,000 × .35 ) NCF PVF PV (Rs) NPV (Rs) PI IRR Cumulative Cumulative cash flows Payback (years)

-15,000 1.000 -15,000 -1,544 0.90 5.59% -15000

Both projects have negative NPV and IRR less than the cost of capital. They should be rejected. Problem 3

Required rate of return (RRR)

10%

Tax rate

35%

Outlay M:

100,000

Life (years) S L depreciation: depreciation: 100,000/5

5 20,000

Salvage value (SV) Outlay N:

0 140,000

Life (years)

5

SV

20,000

S L depreciation: depreciation: 140,000/5

28,000

PROJECT M Year

0

1

2

3

4

5

100,000

80,000

60,000

40,000

20,000

0

SL depreciation

20,000

20,000

20,000

20,000

20,000

Earnings before depreciation & tax

25,000

25,000

25,000

25,000

25,000

Less: dep.

20,000

20,000

20,000

20,000

20,000

Earnings before tax

5,000

5,000

5,000

5,000

5,000

Tax at 35%

1750

1750

1750

1750

1750

Earnings after tax (EAT)

3,250

3,250

3,250

3,250

3,250

20,000

20,000

20,000

20,000

20,000

Book value (BV)

Plus: dep. Plus: SV

0

NCF

-100,000

23,250

23,250

23,250

23,250

23,250

PVF

1.000

0.909

0.826

0.751

0.683

0.621

-100,000

21,136

19,215

17,468

15,880

14,436

PV (Rs) NPV (Rs) IRR

-11,864 5.24%

2

Ch. 10: Determining Cash Flows for Investment Analysis

Cumulative Cumulative NCF

-100,000

Payback (years)

-76,750

-53,500

-30,250

-7,000

16,250

4 1/2

Project N Year Book value S L depreciation depreciation Earnings before depreciation & taxes Less: dep. Earnings before taxes Tax Earnings after tax Plus: dep. After-tax salvage NCF PVF PV (Rs) NPV (Rs) IRR Cum. NCF Payback

0

1

2

3

4

5

140,000

112,000 28,000 40,000

84,000 28,000 40,000

56,000 28,000 40,000

28,000 28,000 40,000

0 28,000 40,000

28,000 12,000 4,200 7,800 28,000

28,000 12,000 4,200 7,800 28,000

28,000 12,000 4,200 7,800 28,000

28,000 12,000 4,200 7,800 28,000

35,800 0.909 32,545

35,800 0.826 29,587

35,800 0.751 26,897

35,800 0.683 24,452

28,000 12,000 4,200 7,800 28,000 13,000 48,800 0.621 30,301

-104,200

-68,400

-32,600

3,200

52,000

-140,000 1.000 -140,000 3,782 11.0% -140,000 4

* After-tax salvage: 20,000 - .35(20,000 – 0) = Rs 13,000. Problem 4

Year

0

1

2

3

IRR NPV, 12%

O

-50,000 25,270 25,270 25,270 0.24

P

-25,000

5,000 25,570 0.15

1,650.5

Q

-28,000 12,670 12,670 12,670 0.17

2,431.2

(P - Q)

3,000

5,000 -7,670

10,694.3

-7,670 12,900

(780.7)

Project O has the highest NPV; hence it should be preferred over other projects. Between Between projects P and Q, Q is better with higher NPV. The incremental cash flow analysis also shows that P losses NPV when compared with Q. Problem 5

Year A

0

1

-6,000

B (A - B)

2

3

NPV, 10%

IRR

8,000

2,000 2,000

2,000

4,428.2 65.6%

-8,000

12,000

4,000

5,649.9 78.1%

-6,000 16,000 -10,000 -2,000

(1,221.6)

Both absolute and incremental analyses reveal that B is a better project than A. Problem 6 Year

Cash flow

0

1

2

3

7,000 7,000 7,000 7,000 -25,000

Problem 7 RRR

10%

Tax rate

40%

Purchase price Installation Total cost

4

NPV, 10% 7,332.6

40,000 8,000 48,000

3

IRR -4.5%

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

Plus: WC

10,000

Less: SV, old

20,000 no tax assumed

Initial outlay

38,000

SV, new (4 yrs)

14,000

SV, old (4 yrs)

4,000

Differential SV after 4 years

10,000 no tax assumed

BV, old

16,000

Life (years), new

4

Life (years), old

4

SL dep., new

12,000

SL dep., old

4,000

Differential Differential dep.

8,000

Diff. DTS (depreciation (depreciation tax shield): 8,000 × 0.40

3,200

Year Initial outlay

0

1

2

3

4

-38,000

BT cash flows

16,000 16,000 16,000 16,000

AT cash flows: 16,000 × (1-.4)

9,600

9,600

9,600

9,600

DTS

3,200

3,200

3,200

3,200

Differential Differential SV

10,000

NCF

-38,000 12,800 12,800 12,800 22,800

NPV

9,404.4

IRR

20%

Problem 8

Investment Required rate Tax rate Investment period Building Merchandise Working capital Total investment

300,000 15% 30% 13 140,000 100,000 60,000 300,000

Annual receipts Less: Costs Less: SL dep. on build. (140,000/13)

390,000 300,000 10,769

Pre-tax savings Tax @ 30%

79,231 23,769

Post-tax savings Add: Dep. Less: Loss of salary (no tax on salary assumed) NCF (annuity)

55,462 10,769 36,000

Post-tax SV: 50,000 × (1 – 0.3)

35,000

Release of WC and merchandise

30,231

160,000

4

Ch. 10: Determining Cash Flows for Investment Analysis

Year-end CF

195,000

PVAF, 15%, 13 PVF, 15%, 13 PV of annuity PV of year-end CF NPV

5.5831 0.1625 168,781 31,688 -99,531

Problem 9

BV, old Life, old (years) Cost, new Life, new (years) SV, new Savings, new WDV dep. rate Tax rate Required rate

64,000 6 80,000 6 0 16,000 25% 35% 10%

Situation I SV, old (now) SV, (after 6 years) BV, old Dep. base, new Diff. dep. base (80,000-64,000)

0 0 64,000 80,000 16,000

Year Depreciated value WDV dep. Investment Savings Less: depreciation* depreciatio n* Taxable savings Less: Tax @ 35% Post-tax savings Add: depreciation* depreciation * After-tax SV (old) lost NCF PVF PV NPV

0

1

2

3

4

5

6

16,000

12,000

9,000

6,750

5,063

3,797

2,848

4,000

3,000

2,250

1,688

1,266

949

16,000 4,000 12,000 4,200 7,800 4,000

16,000 3,000 13,000 4,550 8,450 3,000

16,000 2,250 13,750 4,813 8,938 2,250

16,000 1,688 14,313 5,009 9,303 1,688

16,000 1,266 14,734 5,157 9,577 1,266

11,800 0.909 10,727

11,450 0.826 9,463

11,188 0.751 8,405

10,991 0.683 7,507

10,843 0.621 6,733

16,000 3,797 12,203 4,271 7,932 3,797 0 11,729 0.564 6,621

-80,000

-80,000 1.000 -80,000 -30,545

* New machine has zero salvage value. Its book value of Rs 2,848 at the end of 6th year will be treated as loss and will save taxes. This amount has been added to the sixth year's depreciation. Situation II SV, old (now) BV, old After-tax SV, old: 16,000 - .35(16,000-64,000) SV, old (after 6 years) Cost of new Less: After-tax SV, old Net cost of new Diff. dep. Base (80,000-64,000)

16000 64,000 32,800 0 80,000 32,800 47,200 16,000

5

Assumption Assumption given in the problem

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

Year Depreciated value WDV depreciation depreciation Investment Savings Less: depreciation* depreciatio n* Taxable savings Less: Tax Post-tax savings Add: depreciation* depreciation * After-tax SV (old) lost NCF PVF PV NPV

0

1

2

3

4

5

6

16,000

12,000

9,000

6,750

5,063

3,797

2,848

4,000

3,000

2,250

1,688

1,266

949

16,000 4,000 12,000 4,200 7,800 4,000

16,000 3,000 13,000 4,550 8,450 3,000

16,000 2,250 13,750 4,813 8,938 2,250

16,000 1,688 14,313 5,009 9,303 1,688

16,000 1,266 14,734 5,157 9,577 1,266

11,800 0.909 10,727

11,450 0.826 9,463

11,188 0.751 8,405

10,991 0.683 7,507

10,843 0.621 6,733

16,000 3,797 12,203 4,271 7,932 3,797 0 11,729 0.564 6,621

-47,200

-47,200 1.000 -47,200 2,255

* New machine has zero salvage value. Its book value of Rs 2,848 at the end of 6 th year will be treated as loss and will save taxes. This amount has been added to the sixth year’s depreciation. Situation III SV, old (now) BV, old After-tax SV, old: 16,000 - .35(16,000-64,000) SV, (after 6 years) BV, old (after six years): 64,000 × (1-0.25)6 

16000 64,000 32,800 2,000 11391

After-tax SV, old: 2,000 - .35(2,000-11,391) Cost of new Less: After-tax SV, old Net cost of new Diff. dep. base (80,000-64,000)

5,287 80,000 32,800 47,200 16,000

Year Depreciated value WDV depreciation depreciation Investment Savings Less: depreciation* depreciatio n* Taxable savings Less: Tax Post-tax savings Add: depreciation* depreciation * After-tax SV (old) lost NCF PVF PV NPV

Assumption Assumption given in the problem

0

1

2

3

4

5

6

16,000

12,000

9,000

6,750

5,063

3,797

2,848

4,000

3,000

2,250

1,688

1,266

949

16,000 4,000 12,000 4,200 7,800 4,000

16,000 3,000 13,000 4,550 8,450 3,000

16,000 2,250 13,750 4,813 8,938 2,250

16,000 1,688 14,313 5,009 9,303 1,688

16,000 1,266 14,734 5,157 9,577 1,266

11,800 0.909 10,727

11,450 0.826 9,463

11,188 0.751 8,405

10,991 0.683 7,507

10,843 0.621 6,733

16,000 3,797 12,203 4,271 7,932 3,797 -5,287 6,442 0.564 3,636

-47,200

-47,200 1.000 -47,200 -729

* New machine has zero salvage value. Its book value of Rs 2,848 at the end of 6th year will be treated as loss and will save taxes. This amount has been added to the sixth year's depreciation.

6

Ch. 10: Determining Cash Flows for Investment Analysis

Problem 10 Old Machine:

BV

0

Current MV

20,000

After-tax SV: 20,000-.35(20,000-0)

13,000

SV after 8 years

0

Remaining life (years)

8

New Machines (Vs Old): I 102,500

II 175,000

SV after 8 years

12,500

25,000

BV after 8 years

10,262

17,520

After-tax SV: SV-.35(SV-BV)

11,717

22,382

8

8

Dep. rate (WDV)

0.25

0.25

Tax rate

0.35

0.35

Cost of capital

0.11

0.11

Increase in sales

12,500

12,500

Cost

Life (years)

Cost savings

12,500

30,000

Gross savings

25,000

42,500

After-tax savings (T = 35%)

16,250

27,625

102,500

175,000

89,500

162,000

Diff. dep. base: Cost, new – BV, old New investment: cost – After-tax SV, old (Rs 13,000) New machine I (Vs Old):

Years Diff. dep. Base

0

1

102,500

76,875

57,656 43,242 32,432 24,324 18,243 13,682 10,262

25,625

19,219 14,414 10,811

Depreciation Depreciation Dep. Tax shield

8,969

After-tax savings

16,250

2

6,727

3

5,045

4

3,784

5

6

7

8,108

6,081

4,561

3,421

2,838

2,128

1,596

1,197

16,250 16,250 16,250 16,250 16,250 16,250 16,250

SV

11,717

NCF

-89,500

25,219

PVF

1.000

0.901

-89,500

22,720

PV (Rs)

8

NPV (Rs)

23,040

IRR

18.1%

22,977 21,295 20,034 19,088 18,378 17,846 29,164 0.812

0.731

0.659

0.593

0.535

0.482

0.434

18,648 15,571 13,197 11,328

9,826

8,596 12,655

New machine II (Vs Old) :

Years Diff. dep. Base

0

1

2

3

4

5

6

7

8

175,000

131,25 0 43,750

98,438

73,828

55,371

41,528

31,146

23,360

17,520

32,813

24,609

18,457

13,843

10,382

7,787

5,840

15,313 27,625

11,484 27,625

8,613 27,625

6,460 27,625

4,845 27,625

3,634 27,625

2,725 27,625

2,044 27,625 22,382

42,938 0.901 38,682

39,109 0.812 31,742

36,238 0.731 26,497

34,085 0.659 22,453

32,470 0.593 19,269

31,259 0.535 16,712

30,350 0.482 14,618

52,051 0.434 22,586

Depreciation Depreciation Dep. Tax shield After-tax savings SV NCF PVF PV (Rs)

-162,000 1.000 -162,000

7

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

NPV (Rs) IRR

30,561 16.20%

The company should should go for the new machine costing Rs 175,000 since it has higher NPV. NPV is consistent with shareholder wealth maximisation. Problem 11

The block of assets method of depreciation in India requires adjustment of salvage value in the depreciable base. Thus, if an asset has no salvage value, it can be depreciated for ever (infinity) if the firm keeps the positive balance in the block of assets. If it has a salvage value, the balance of the block will be reduced for the amount of salvage value less depreciation tax shield lost on this amount. Old Machine: Depreciated Depreciated BV

0

Exchange value

40,000

Current MV

30,000

SV after 10 years

6,000

Remaining life (years)

10

New Machine:

Cost

360,000

SV after 10 years.

40,000

Life (years)

10

WDV dep. rate

25%

Required rate

12%

Tax rate

50% Old

Differenc e Profit before tax 373,000 449,000 76,000 Add: dep.

New

2,000 36,000

34,000

Add: allocated overhead PBDT

120,000 130,000 495,000 615,000

10,000 120,000

Tax @ 50%

247,500 307,500

60,000

PBDAT

247,500 307,500

60,000

Years New block

0

1

2

3

4

5

6

7

8

9

10

320,000

240,000

180,000

135,000

101,250

75,938

56,953

42,715

32,036

24,027

18,020

Dep.

80,000

60,000

45,000

33,750

25,313

18,984

14,238

10,679

8,009

6,007

DTS

40,000

30,000

22,500

16,875

12,656

9,492

7,119

5,339

4,005

9,091

PBDAT

60,000

60,000

60,000

60,000

60,000

60,000

60,000

60,000

60,000

60,000

100,000

90,000

82,500

76,875

72,656

69,492

67,119

65,339

64,005

69,091

CFO Investment

-320,000

SV

40,000

Lost DTS on SV

13,514 95,578

NCF PVF PV (Rs)

-320,000

100,000

90,000

82,500

76,875

72,656

69,492

67,119

65,339

64,005

1.000

0.893

0.797

0.712

0.636

0.567

0.507

0.452

0.404

0.361

0.322

-320,000

89,286

71,747

58,722

48,855

41,227

35,207

30,361

26,389

23,081

30,774

NPV (Rs)

135,649

IRR

22.45%

Last year DTS includes depreciation depreciation on the remaining book value: BV × (d × T)/(k + d) = 18.020 × (0.25 × 0.50)/(0.12 + 0.25) = Rs .6,088.

8

Ch. 10: Determining Cash Flows for Investment Analysis

Note: Exchange value is higher than the current market value. Hence, the relevant salvage value of the old machine is Rs 40,000. Problem 12 Old Machine: Original cost (Rs) Original life (yrs) Remaining life (yrs) Depreciation rate BV after 5 years BV after 12 years Current MV New Machine: Cost Installation

175,000 25,000

Total cost Working capital

200,000 25,000

Gross outlay Life (years) Depreciation Depreciation rate SV (Rs) BV after 7 years

225,000 7 0.25 18,000 23,360

129,000 12 7 25% 30,612 4,086 40,000

Cost of capital Tax rate

(1-0.25)^7*175,000

12% 35%

Increase in sales After-tax revenue: 70,000 ×(1.35) Gross outlay Less: SV, old

70,000 45,500 225,000 40,000

Net outlay Diff. Dep. Base: 200,000 40,000 Year

(1-0.25)^5*129,000 (1-0.25)^12*129,000

185,000 160,000

0

1

2

3

4

5

6

7

160,000

120,000 40,000

90,000 30,000

67,500 22,500

50,625 16,875

37,969 12,656

28,477 9,492

21,357 7,119

DTS*

14,000

10,500

7,875

5,906

4,430

3,322

7,542

After-tax revenue SV DTS lost on SV **

45,500

45,500

45,500

45,500

45,500

45,500

45,500 18,000

Diff. dep. base Differential Differential dep.

-4,257 25,000

WC released Net outlay

-185,000

NCF PVF PV (Rs) NPV IRR

-185,000 1.000 -185,000 78,014 24.0%

59,500 0.893 53,125

56,000 0.797 44,643

53,375 0.712 37,991

51,406 0.636 32,670

49,930 0.567 28,331

48,822 0.507 24,735

* Last year DTS includes DTS on remaining book value: 21,357 × (.25× .35)/(.12 + .25) = Rs 5,051. ** DTS lost on SV: 18,000 × (.25 × .35)/(.25 + .12) = -4,257.

9

91,786 0.452 41,519

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

Problem 13

Purchase price

175,000

Life (years) SV (Rs)

5 21,000

Maintenance cost

3,500

SL dep.

35,000

Tax rate

0.50

Cost of capital

0.10 0

Outlay

1

2

3

4

5

-175,000

Tax saved on depreciation

17,500 17,500 17,500 17,500 17,500

After-tax SV

10,500 10,500

NCF

-175,000 17,500 17,500 17,500 28,000 27,500

PVF

1.0000 0.9091 0.8264 0.7513 0.6209 0.6209

PV (Rs)

-175,000 15,909 14,463 13,148 17,386 23,905

NPV (Rs)

-102,142

* Tax payable on book profit. After-tax SV = 21,000 – 0.50(21,000 – 0) Hiring option:

0

Hire charges (Rs)

0 -42,000 -42,000 -42,000 -42,000 -42,000

After-tax hire charges (Rs)

0 -21,000 -21,000 -21,000 -21,000 -21,000

PVF

1.0000

PV (Rs)

1

0.9091

2

0.8264

3

0.7513

4

0.6209

5

0.6209

0 -19,091 -17,355 -15,778 -14,343 -13,039

NPV (Rs)

-79,607

Maintenance cost being common in both options is ignored in calculating cash flows. Hiring option is cheaper. Problem 14

Cost of capital

0.18

Tax rate

0.50

Dep. Rate

0.25

Project P

Investment Investment

0

1

2

3

4

5

6

7

8

9

10

250,000

187,500

140,625

105,469

79,102

59,326

44,495

33,371

25,028

18,771

14,078

62,500

46,875

35,156

26,367

19,775

14,832

11,124

8,343

6,257

4,693

Depreciation Additional investment investment

45,000

33,750

25,313

18,984

14,238

10,679

11,250

8,438

6,328

4,746

3,560

19,775

26,082

19,561

14,671

11,003

8,252

Depreciation Total depreciation

62,500

46,875

35,156

26,367

Before-tax cash flows

90,000

90,000

90,000

90,000

90,000

90,000

90,000

90,000

90,000

90,000

After-tax cash flows

45,000

45,000

45,000

45,000

45,000

45,000

45,000

45,000

45,000

45,000

DTS

31,250

23,438

17,578

13,184

9,888

13,041

9,781

7,335

5,502

11,323*

Investment Investment Working capital

-250,000

-45,000

-50,000

Salvage value

30,000

Lost DTS on SV

-8,721#

WC released NCF

50,000 -300,000

76,250

68,438

62,578

58,184

10

9,888

58,041

54,781

52,335

50,502

127,602

Ch. 10: Determining Cash Flows for Investment Analysis

PVF PV

1.000

0.847

0.718

0.609

0.516

0.437

0.370

0.314

0.266

0.225

0.191

-300,000

64,619

49,151

38,087

30,010

4,322 4,322

21,500

17,197

13,923

11,386

24,380

NPV

-25,425

IRR

15.5%

* Includes DTS on the remaining book value: Rs (14,078 + 10,679) × (.25 × .50)/(.25 + .18) = Rs 7,197. # Lost DTS on VS: Rs 30,000 × ( .25 × .50)/(.25 + .18) = Rs 8,721.

11

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

Problem 15

Cost

100,000

Life (years)

5

Straight line dep. (Rs)

20,000

Savage value

0

Savings

40,000

Tax rate

0.50

Cost of capital

0.18

Year

1

2

3

4

5

After-tax savings

20,000

20,000

20,000

20,000

20,000

Tax saved on dep.

10,000

10,000

10,000

10,000

10,000

Investment

0 -100,000

Salvage value

0

NCF

-100,000

30,000

30,000

30,000

30,000

30,000

PVF

1.0000

0.8475

0.7182

0.6086

0.5158

0.4371

-100,000

25,424

21,546

18,259

15,474

13,113

PV (Rs) NPV (Rs)

-6,185

IRR

15.2%

Here we ignore the effect of specific financing. The cost of capital, which assumes a target capital structure, is used as the discount rate. Problem 16

Project cost (Rs)

50,000

Cost savings (Rs)

30,000

Period (years)

5

Tax rate

0.5

Required rate

0.12

Straight line dep. (Rs)

10,000

Salvage value Year Investment Investment (Rs)

0 0

1

2

3

4

5

15,000

15,000

15,000

15,000

15,000

5,000

5,000

5,000

5,000

5,000

-50,000

After-tax cost savings (Rs) Tax saved on dep. (Rs) Salvage value (Rs) NCF (Rs) PVF PV (Rs) NPV (Rs) IRR

0 -50,000

20,000

20,000

20,000

20,000

20,000

1.0000

0.8929

0.7972

0.7118

0.6355

0.5674

-50,000

17,857

15,944

14,236

12,710

11,349

22,096 28.65%

Here we ignore the effect of specific financing. The cost of capital, which assumes a target capital structure, is used as the discount rate. Problem 17

Old

Capacity (units)

New

3

12

4

(Rs 000) New Old 1

Ch. 10: Determining Cash Flows for Investment Analysis

Selling price

200

180

-20

 Revenue

600

720

120

Materials

40

38

2

Labour

60

40

20

Variable overheads

30

15

15

2

-2

130

95

35

Total production cost

390

380

10

Profit

210

340

110

Original cost of machine (Rs)

300

500

Current book value

200

Exchange (salvage) value

100

After-tax salvage value: 100,000-.5(100,000 – 200,000)

150

Cost of production:

Fixed overheads Per unit production cost

Tax saved on book loss

50

Net outlay (Rs): 500,000 - 150,000

350

Salvage value after 10 years

50

After-tax salvage value: 50,000 - .5(50,000 .5(50,00 0 – 0)

25

Remaining life (years)

10

10

Straight line dep.

20

50

Working capital

25

Tax rate

0.5

Required rate of return

30

0.15 (Rs ‘000)

Year

0

1

2

3

4

5

6

7

8

9

10

Cost of machine

-200

-200

Working capital

-25

Tax saved on SV

50 120

120

120

120

120

120

120

120

120

120

10

10

10

10

10

10

10

10

10

10

130

130

130

130

130

130

130

130

130

130

After-tax profits

65

65

65

65

65

65

65

65

65

65

Dep. tax shield

15

15

15

15

15

15

15

15

15

15

Revenue Cost savings Increase in profits

After-tax SV

25

Release of WC

25

NCF

-175

PVF

1.000

PV (Rs)

-175

NPV (Rs)

65.0

IRR

-120

80

80

80

80

80

80

80

80

130

0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247 -104

60

53

46

20.2%

Problem 18

Initial cost (Rs) Life (years)

200,000 5

Cash inflow (Rs)

70,000

Cost of capital (real)

10.0%

Inflation Nominal cost of capital: [(1.10)(1.05) - 1]

5.0% 15.5%

13

40

35

30

26

23

32

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

 Assumptions: (1) It is assumed that both cash flows and the cost of capital are in real terms. (2) Nominal cash flows are calculated as follows: Real cash flows × (1 + inflation rate) n. Year

0

1

2

3

4

5

Dis. rate

NPV

Cash flows (real)

-200,000 70,000 70,000 70,000 70,000 70,000

0.1000 65,355

Nominal cash flows

-200,000 73,500 77,175 81,034 85,085 89,340

0.1550 65,355

It may be noticed that NPV is the same in both situations. The real cash flows are discounted at the nominal cost of capital, and real cash flows at the real cost of capital. Problem 19 Discount rate Tax rate General inflation rate

20% 35% 10%

Year

Cost Volume Price Cost per unit

0

1

2

3

4

5

-500,000 20% 10% 15%

10,000 20 10

12,000 22.00 11.50

14,400 24.20 13.23

17,280 26.62 15.21

20,736 29.28 17.49

Revenue Total cost

200,000 100,000

264,000 138,000

348,480 190,440

459,994 262,807

607,192 362,674

Profit  Less: dep.

100,000 100,000

126,000 100,000

158,040 100,000

197,186 100,000

244,518 100,000

0 0

26,000 9,100

58,040 20,314

97,186 34,015

144,518 50,581

0 100,000

16,900 100,000

37,726 100,000

63,171 100,000

93,936 100,000

100,000 0.833 83,333

116,900 0.694 81,181

137,726 0.579 79,703

163,171 0.482 78,690

193,936 0.402 77,939

PBT Tax PAT Add: dep. NCF PVF at 20% PV at 20% NPV IRR

-500,000 1.000 -500,000 -99,155 11.6%

Price increases at general inflation rate while cost increases by a higher rate of inflation. It is assumed that the cost of capital is market determined; hence, it is in nominal terms. Problem 20

Cash outlay Life of project (years) Sales growth: 2-7 years Increase in expenses Initial working capital WC to sales WDV dep. rate Tax rate Opportunity cost of capital Salvage value: 0.20 × 6,000,000 × (1.10)

7

6,000,000 7 10% 10% 500,000 25% 25% 35% 21% 2,338,461

14

Ch. 10: Determining Cash Flows for Investment Analysis

Nominal Cash Flows Year

Cash outlay Sales Op. expenses PBDIT Depreciation Profit/loss Loss carried forward Unrecovered loss Taxable profit Tax PAT  Add : depreciation Funds fr from op operation Initial wo working ca capital Change in WC Release of WC Salvage value NCF PVF, 21% PV NPV IRR

0

1

2

3

4

5

6

7

2,662,000 878,460 1,783,540 474,609 1,308,931 0 0 1,308,931 458,126 850,805 474,609 1,325,414

2,928,200 966,306 1,961,894 355,957 1,605,937 0 0 1,605,937 562,078 1,043,859 355,957 1,399,816

3,221,020 1,062,937 2,158,083 266,968 1,891,116 0 0 1,891,116 661,890 1,229,225 266,968 1,496,193

-60,500

-66,550

-6,000,000 1,200,000 2,000,000 2,200,000 2,420,000 600,000 660,000 726,000 798,600 600,000 1,340,000 1,474,000 1,621,400 1,500,000 1,125,000 843,750 632,813 -900,000 215,000 630,250 988,588 -900,000 -685,000 -54,750 -900,000 -685,000 -54,750 0 0 0 0 933,838 0 0 0 326,843 0 215,000 630,250 661,744 1,500,000 1,125,000 843,750 632,813 1,500,000 1,340,000 1,474,000 1,294,557 -500,000 -300,000

-200,000

-50,000

-55,000

-73,205 1,305,255 2,338,461 -6,500,000 1,200,000 1,140,000 1,424,000 1,239,557 1,264,914 1,333,266 5,066,703 1.000 0.826 0.683 0.564 0.467 0.386 0.319 0.263 -6,500,000 991,736 778,635 803,811 578,262 487,679 424,820 1,334,221 -1,100,836 15.7%

Theoretically, the answer should not change if the analysis is made in terms of real terms. The real cash flows would be discounted at the real cost of capital. However, since flows like deprecation tax shields are always in nominal terms, it is difficult to use real cash flow analysis.

15

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

CASES Case 10.1: Hind Petrochemicals Company This case brings out a number of issues in calculating the relevant cash flows, the discount rate, NPV and IRR. The important points are: (1) relevant depreciation depreciation for tax purposes, (2) irrelevance of allocated overheads, (3) sunk cost (part of survey cost), (4) release of working capital, (5) tax shield treatment of depreciation and salvage value as per the Indian tax system, and (6) ignoring the financing effect in calculating the cash flows.

Cost of refinery Cost of machinery Total capital investment Working capital Total cash outlay

(Rs mn.) 1,550 5,950 7,500 300 7,800

Discount rate

15%

Cash flows 0

Sales  Less:  Wa  Wages and salaries  Se  S elling and distribution costs  Ma  M aterials and consumables  De  Depreciation (WDV)  Co  C orporate office costs  Su  Survey costs Total expenses Profit (loss) before tax Less: tax @ 35% Profit after tax Plus: depreciation CFO Cash outlay Working capital released Salvage value Book value Lost DTS on (SV -BV) Net cash flows NPV at 15% IRR Cumulative casf flows Payback (years)

 

1

2

3

4

5,730 1,450 760 180 1,875 100 15 4,380 1,350 473 878 1,875 2,753

5,930 1,500 770 270 1,406 100 4,046 1,884 659 1,224 1,406 2,631

5,870 1,850 1,080 290 1,055 100 4,375 1,495 523 972 1,055 2,027

3,790 1,030 530 200 791 100 2,651 1,139 399 740 791 1,531

(Rs mn.) 5 4,500 1,210 650 230 593 100 2,783 1,717 601 1,116 593 1,709

300 3,600 1,780 -430 5,179

-7,800

-7,800 1,365 22%

2,753

2,631

2,027

1,531

-7,800

-5,048

-2,417

-390

1,141 3.25

6,320

Note: (1) (1) Onl Only Rs 15 millio llion n of surv survey ey cost ost is rle rlevant. ant. (2) (2) All corp corpo orat rate off office ice costs osts are not not rele relev vant for for the the proj projec ect; t; Rs 100 100 mill millio ion n cost costss rela relate te to the the proj projec ect. t. (3) (3) Inte Intere rest st is a fina financ ncin ing g cost cost.. Free Free cash cash flow flowss are are calc calcul ulat ated ed,, ignoring the interest ch

16

Ch. 10: Determining Cash Flows for Investment Analysis

Case 10.2: Pure Drinks Company Like Hind Petrochemicals case, this case high lights the relevant cash flows. It introduces the concept of opportunity cost of using existing facilities. Further, it also introduces the adjustment of inflation.  Inflation rate assum assumed ed zero zero

Number of sachets Price Variable costs: Material Labour Overhead Fixed costs (Rs million) Allocated fixed costs (Rs million) Working capital ratio Tax rate Real discount rate Inflation rate Nominal discount rate Tax rate

900,000 (Rs) 65.0 15.0 6.5 3.5 5.0 0.5 6.8 26% 35% 8.65% 0% 8.65% 35%

Cost of processing facilities (Rs million) Life (years) SL depreciation Salvage value (Rs million)

200 5 40 100

Current building opportunity cost (Rs mn) Building opportunity cost af after 5 years(Rs mn mn) PV of bu build ilding ing co cost af after ter 5 years: 200 200/( /(1 1.0865)5

100 200 132

17

I. M. Pandey, Financial Management, 9 th Edition, New Delhi: Vikas.

0 Revenue Variable costs Material Labour Overhead Total Fixed costs Total cost EBDIT Depreciation EBIT Less: Tax Post-tax earnings Plus: depreciation Cash flow from operations Change in working capital Free cash flows Cost of processing facilities Cost of building Salvage value Less: Tax on (SV - BV) Net cash flows NPV NPV if WC ratio is 30%

1

-15.21 -15.21 -200 -132

-347.30 -125.84 -126.63

2

3

4

(Rs lakh) 5

58.50

58.50

58.50

58.50

58.50

5.85 3.15 4.50 13.5 0.50 14.00 44.50 40.00 4.50 1.58 2.93 40.00 42.93 0.00 42.93

5.85 3.15 4.50 13.5 0.50 14.00 44.50 40.00 4.50 1.58 2.93 40.00 42.93 0.00 42.93

5.85 3.15 4.50 13.5 0.50 14.00 44.50 40.00 4.50 1.58 2.93 40.00 42.93 0.00 42.93

5.85 3.15 4.50 13.5 0.50 14.00 44.50 40.00 4.50 1.58 2.93 40.00 42.93 0.00 42.93

5.85 3.15 4.50 13.5 0.50 14.00 44.50 40.00 4.50 1.58 2.93 40.00 42.93 15.21 58.14

42.93

100 -35 123.14

42.93

42.93

42.93

Note: Note: (1) Rs 5 million survey cost is sunl cost. Hence, it is ignored. (2) The corporate office fixed costs are irrelevant for the project. Inflation adjustment: Number of sachets

Price Variable costs: Material Labour Overhead Fixed costs (Rs million) Working capital ratio Tax rate Real discount rate General inflation rate Nominal discount rate Tax rate Cost of processing facilities Life SL depreciation Salvage value Current building opportunity cost (Rs mn) Building opportunity cost af after 5 years(Rs mn mn) PV of building cost after 5 years: 200/(1.13)5

900,000 (Rs) Inflation 65.0 4% 6. 5 3. 5 5. 0 0. 5 26% 35% 8.65%

3% 5% 5%

4% 13% 35% 200 5 40 100 100 200 109

18

Ch. 10: Determining Cash Flows for Investment Analysis

(Rs lakh) 0

Revenue Variable costs Material Labour Overhead Total Fixed costs Total cost EBDIT Depreciation EBIT Less: Tax Post-tax earnings Plus: depreciation Cash flow from operations Change in working capital Free cash flows Cost of processing facilities Cost of building Salvage value Less: Tax on (SV - BV) Net cash flows NPV NPV if WC ratio 30%

-15.82 -15.82 -200 -109

-324.39 -118.40 -199.59

Note: (1)

1

2

3

4

5

60.84

63.27

65.80

68.44

71.17

6.03 3.31 4.73 14.1 0.52 14.58 46.26 40.00 6.26 2.19 4.07 40.00 44.07 -0.63 43.44

6.21 3.47 4.96 14.6 0.54 15.18 48.09 40.00 8.09 2.83 5.26 40.00 45.26 -0.66 44.60

6.39 3.65 5.21 15.2 0.56 15.81 49.99 40.00 9.99 3.50 6.50 40.00 46.50 -0.68 45.81

6.58 3.83 5.47 15.9 0.58 16.47 51.97 40.00 11.97 4.19 7.78 40.00 47.78 -0.71 47.07

6.78 4.02 5.74 16.5 0.61 17.15 54.02 40.00 14.02 4.91 9.11 40.00 49.11 18.51 67.62

47.07

100 -35 132.62

43.44

44.60

45.81

Rs 5 million survey cost is sunl cost. Hence, it is ignored. (2) The corporate office fixed costs are irrelevant for the project.

19