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
