Post on 05-Apr-2018
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Capital budgeting/Investment appraisal
Act Finance
Accruals Cash
Long term decision making
Incremental cash flows
a) NPV (Net present value)
b) Payback Period - calculates how fast the intitial invesment is recovered (time value of money is ig
Discounted payback period
c) IRR (Internal Rate of return)
d) ARR (Accounting rate of return)
Time value of money
a) Inflation
b) Risk / uncertainty
c) Interest rates
Question 1
Is RM 27,778 now different from RM 40,000 in 2 years time, assuming a 20% return on
invetment?
Amount available now 27,778 1
Add: Interest 20% - Year 1 5555.6 (1+r) n
33,334
Add: Interest 20% - Year 2 6666.7 r = Dr
40,000 n = years
Non cash is exluded
sunk costs - e.g. fixed costs
opportunity cost foregone
Year 0 Year 1 Year 2 Year 3 Year 4
RM'000 RM'000 RM'000 RM'000 RM'000
Initial outlay -15
NCF 8 10 5 5
Cash flows -15 8 10 5 5
DF @ 10% 1 0.9091 0.827 0.751 0.683
(15.0) 7.3 8.3 3.8 3.4
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NPV 7.7
Year 0 Year 1 Year 2 Year 3 Year 4
RM'000 RM'000 RM'000 RM'000 RM'000
Initial outlay -15
NCF 8 10 5 5
Cash flows -15 8 10 5 5DF @ 20% 1 0.833 0.69 0.578 0.482
(15.0) 6.7 6.9 2.9 2.4
NPV 3.9
Question 1
Company A has extra cash which is available for investment - RM 1,000,000.
The company is considering four projects to choose from. Only one project will be chosen.
The four projects are as follow Alpha Beta Gamma Delta
Initial investment 400,000 380,000 500,000 420,000
Net cash flow Yr 1 0.892 100,000 80,000 150,000 150,000
Yr 2 0.797 100,000 100,000 150,000 150,000
Yr 3 0.711 100,000 140,000 120,000 120,000
Yr 4 0.636 100,000 150,000 160,000 80,000
Yr 5 0.567 100,000 150,000 200,000 40,000
The cost of capital of Co A is 12%.
Calculate the NPV and decide which project to choose.
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
RM'000 RM'000 RM'000 RM'000 RM'000 RM'000
Investment cost -100
Working capital -30 30
Sales revenue 80 120 144 100 64
VC -40 -50 -48 -30 -32
Contribution foregone -15 -15 -15 -15 -15Fixed costs -8 -8 -8 -8 -8
Net cash flow -130 17 47 73 47 39
DF @ 8% 1 0.926 0.857 0.794 0.735 0.681
PV -130 15.742 40.279 57.962 34.545 26.559
NPV 45.087
1 A B IRR
(1 + r) n 10% 10%
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40% 50%
Payback Period (PBP) 0 0
Year 0 -130
Year 1 -113
Year 2 -66
Year 3 7Year 4
2 years
66/73 0.90410959
PBP = 2.9 years
Payback Period Aplha Beta Gamma Delta
Year 0 -400 -380 -500 -420
Year 1 -300 -300 -350 -270
Year 2 -200 -200 -200 -120
Year 3 -100 -60 -80 0
Year 4 0 90 80
Year 5
PBP 4 years 3.4 years 3.5 years 3 years
Decision: Choose Delta
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Alpha
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Initial outlay -400
Cash Flow 100 100 100 100 100
DF @ 12% 1 0.892 0.797 0.712 0.636 0.567
PV -400 89.2 79.7 71.2 63.6 56.7
NPV -39.6
Decision: Do not accept Project Alpha
Discounted payback period
Payback
Year 0 -400
Yr 0 -400 Year 1 -310.8
Yr 1 -300 Year 2 -231.1
Yr 2 -200 Year 3 -159.9
Yr 3 -100 Year 4 -96.3
Yr 4 0 Year 5 -39.6
Yr 5
DPBP > 5 yrs
Payback is 4 years
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BETA Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Cash Flow -380 80 100 140 150 150
DF @ 12% 1 0.892 0.797 0.712 0.636 0.567
PV -380 71.36 79.7 99.68 95.4 85.05
NPV 51.19
Payback
Yr 0 -380
Yr 1 -300
Yr 2 -200
Yr 3 -60
Yr 4 90 60/150 0.4
Yr 5
Payback is 3.4 years
DPBP
Gamma Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Cash Flow -500 150 150 120 160 200
DF @ 12% 1 0.892 0.797 0.712 0.636 0.567
PV -500 133.8 119.55 85.44 101.76 113.4
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NPV 53.95
Payback
Yr 0 -500
Yr 1 -350Yr 2 -200
Yr 3 -80
Yr 4 80 80/160 0.5
Yr 5
Payback is 3.5 years
delta Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Cash Flow -420 150 150 120 80 40
DF @ 12% 1 0.892 0.797 0.712 0.636 0.567
PV -420 133.8 119.55 85.44 50.88 22.68
NPV -7.65
Discounted payback period
Payback
Year 0 -420Yr 0 -420 Year 1 -286.2
Yr 1 -270 Year 2 -166.65
Yr 2 -120 Year 3 -81.21
Yr 3 0 Year 4 -30.33
Yr 4 Year 5 -7.65
Yr 5
DPBP > 5 yrs
Payback is 3 years
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DPBP
Alpha Beta Gamma Delta
NPV -39.6 51.19 53.95 -7.65
Payback
Discounted payback
PaybackBenefits
1. Easy to use
2. Widely in use in practice
Limitations
1. Ignore time value of money
2. Ignores cash flows after payback period
Question 10.4
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
RM mil RM mil RM mil RM mil RM mil RM mil
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Option 1
Property -9 1
Working capital -3 3
Sales revenue 24 30.8 39.6 26.4 10
VC -11.2 -19.6 -25.2 -16.8 -7
FC (exld dep) -0.8 -0.8 -0.8 -0.8 -0.8
Marketing costs -2 -2 -2 -2 -2Opportunity costs -0.1 -0.1 -0.1 -0.1 -0.1
-12 9.9 8.3 11.5 6.7 4.1
DF@ 10% 1 0.909 0.826 0.751 0.683 0.621
PV -12 8.9991 6.8558 8.6365 4.5761 2.5461
NPV 19.6
Workings
Fixed cost 2.4
Depreciation per year = 9 - 1 1.6
5
FC (exld dep) 2.4 - 1.6 = 0.8
Option 2 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
RM mil RM mil RM mil RM mil RM mil RM mil
Royalties 0 4.4 7.7 9.9 6.6 2.8
DF@ 10% 1 0.909 0.826 0.751 0.683 0.621
PV 0 3.9996 6.3602 7.4349 4.5078 1.7388
NPV 24.0
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
RM mil RM mil RM mil RM mil RM mil RM mil
Option 3
Installments 12 12
DF@ 10% 1 0.826
PV 12 9.912
NPV 21.9
Payback
Internal Rate of Return (IRR)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
RM mil RM mil RM mil RM mil RM mil RM mil
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Option 1
Property -9 1
Working capital -3 3
Sales revenue 24 30.8 39.6 26.4 10
VC -11.2 -19.6 -25.2 -16.8 -7
FC (exld dep) -0.8 -0.8 -0.8 -0.8 -0.8
Marketing costs -2 -2 -2 -2 -2Opportunity costs -0.1 -0.1 -0.1 -0.1 -0.1
-12 9.9 8.3 11.5 6.7 4.1
DF@ 20% 1 0.833 0.694 0.579 0.482 0.402
PV -12 8.2467 5.7602 6.6585 3.2294 1.6482
NPV 13.5
Internal Rate of Return (IRR)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
RM mil RM mil RM mil RM mil RM mil RM mil
Option 1
Property -9 1
Working capital -3 3
Sales revenue 24 30.8 39.6 26.4 10
VC -11.2 -19.6 -25.2 -16.8 -7
FC (exld dep) -0.8 -0.8 -0.8 -0.8 -0.8
Marketing costs -2 -2 -2 -2 -2
Opportunity costs -0.1 -0.1 -0.1 -0.1 -0.1
-12 9.9 8.3 11.5 6.7 4.1
DF@ 30% 1 0.769 0.592 0.455 0.35 0.269PV -12 7.6131 4.9136 5.2325 2.345 1.1029
NPV 9.2
Internal Rate of Return (IRR)
Year 5
RM mil RM mil RM mil RM mil RM mil RM mil
Option 1
Property -9 1
Working capital -3 3
Sales revenue 24 30.8 39.6 26.4 10VC -11.2 -19.6 -25.2 -16.8 -7
FC (exld dep) -0.8 -0.8 -0.8 -0.8 -0.8
Marketing costs -2 -2 -2 -2 -2
Opportunity costs -0.1 -0.1 -0.1 -0.1 -0.1
-12 9.9 8.3 11.5 6.7 4.1
DF@ 40% 1 0.714 0.51 0.364 0.26 0.186
PV -12 7.0686 4.233 4.186 1.742 0.7626
NPV 5.9922
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New example
Year 0 Year 1 Year 2 Year 3 Year 4
PPE -600
Cash inflow 500 600 500 700
Cash outflow -200 -400 -400 -500
-600 300 200 100 200DF @ 10% 1 0.909 0.826 0.751 0.683
PV -600 272.7 165.2 75.1 136.6
NPV 49.6
Year 0 Year 1 Year 2 Year 3 Year 4
PPE -600
Cash inflow 500 600 500 700
Cash outflow -200 -400 -400 -500
-600 300 200 100 200
DF @ 20% 1 0.833 0.694 0.579 0.482
PV -600 249.9 138.8 57.9 96.4
NPV -57
IRR = A + (B-A) X a
(a - b)
A = + DF 0.1 + (0.2 - 0.1) X 49.6
B = - DF (49.6 + 57a = + NPV
b = - NPV
Accounting rate of return (ARR)
ARR = Average annual profit X 100
Average investment to earn that profit
Average investment = Cost of Investment + Disposal value
2
Question
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Chaotic Industries is considering an investment in a fleet of ten delivery vans to take its
products to customers. The vans cost RM 15,000 each to buy, payable immediately. The
annual running costs are expected to total RM 20,000 for each van (including driver's salary).
The vans are expected to operate successfully for six years, at the end of which period they
will have to be sold, with disposals proceeds expected to be RM 3000 a van. At present the
business uses a commerical carrier for all of its deliveries. It is expected that this carrier will
charge a total of RM 230,000 each year for the next six years to undertake the deliveries.
What is the ARR of buying the vans?
Cost of van = 15,000 X 10 150,000
Running costs 20,000 X 10 200,000
Cost of hiring carrier 230,000
Annual savings 30,000
Cash outflow and inflow RM'000
Immediately Cost of vans (10 X 15) -150
1 years time Net savings before depreciation 30
2 years time Net savings before depreciation 30
3 years time Net savings before depreciation 30
4 years time Net savings before depreciation 30
5 years time Net savings before depreciation 30
6 years time Net savings before depreciation 30
6 years time Disposal proceeds from the vans 30
(10 X 3)
Depreciation per year (straight line) 150,000 - 30,000 200006
Thus average annual savings after depreciation = 30,000 - 20,000 = 10,000
Average investment = 150,000 + 30,000 90,000
2
ARR 10,000 X 100 11.10%
90,000
Inflation
Real rate does not incorporate inflation RR
Monetary rate incorporates inflation MR 13.40%
Inflation rate IR 5%
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RR = (1 + MR) 1 + 0.134 -1
(1 + IR) -1 1 + 0.05
MR = (1 + RR) (1 + IR) - 1
A company is condering investing in a project which requires an intital investment of RM 150,000.
The cash flows during years 1 - 3 are expected to be RM 55,000 per year. The company's
monetary cost of capital is 10% and inflation is expected to be 6% during the life of the project.
Calculate the NPV of the project using the MR
Step 1 - Incorporate the Inflation into the cash flows
Year
1 55,000 X 1.06 58300
2 58,300 X 1.06 61798
3 61,798 X 1.06 65506
Yr 0 Yr 1 Yr 2 Yr 3
IO -150000
CF 58300 61798 65506
-150000 58300 61798 65505.88
DF @ 10% 1 0.9091 0.826 0.751
PV -150000 53000.53 51045.148 49194.92NPV 3240.59388
Calculate the NPV of the project using the RR
RR = (1 + 0.1) -1 3.80%
( 1 + 0.06)
Yr 0 Yr 1 Yr 2 Yr 3
IO -150000
CF 55000 55000 55000-150000 55000 55000 55000
DF @ 10% 1 0.963 0.928 0.894
PV -150000 52965 51040 49170
NPV 3175
The effect of taxation
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Tax rate = 25% outflow
Cash outflow current year (50%)
following year (50%)
Tax savings on assets (depreciation)
Net book value = Tax written down value (WDV)
Depreciation = Capital allowance = Writing down allowance (WDA) 25%
Reducing balance
The management of a company are making a decision on whether or not to purchase a new of plant
and machinery which costs RM 100,000. The new machine will generate a net cash flow
of RM 30,000 per year for 4 years. At the end of the 4th year it will be sold for RM 20,000.
The company's cost of capital is 5%. Writing down allowance are 25% reducing balance
and corporate tax rate is 30%.
Calculate NPV
WDV Asset cost 30% tax saved Yr 1 Yr 2 Yr 3
Year 100,000
1 WDA (25%) 25000 7500 3750 3750WDV 75,000
2 WDA (25%) 18750 5625 2812.5 2812.5
56,250 6562.5
3 WDA (25%) 14062.5 4218.75 2109.375
42,188 4921.875
Disposal 20,000
Balancing allowance 22,188 6656.25
Balancing charge
Calculation Yr 1 Yr 2
Year 1 profit 30,000 X 30% 9,000 4500 4500
Year 2 profit 30,000 X 30% 9,000 4500 4500
9000
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Yr 0 Yr 1 Yr 2 Yr 3 Yr 4 Yr 5
IO -100,000 20,000
Tax saved 3750 6562.5 4921.875 5437.5 3328.125
Profit/CF 30,000 30,000 30,000 30,000
Tax -4500 -9000 -9000 -9000 -4500
-100,000 29,250 27,563 25,922 46,438 -1,172
DF @ 5% 1 0.952 0.907 0.864 0.823 0.784-100000 27846 24999.1875 22396.5 38218.06 -918.75
NPV 12,541
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nored)
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Discounted payback period
Year 0 -380
Year 1 -308.64
Year 2 -228.94
Year 3 -129.26
Year 4 -33.86
Year 5 51.19
0.40
4.4 yrs
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Year 0 -500
Year 1 -366.2
Year 2 -246.65
Year 3 -161.21Year 4 -59.45
Year 5 53.95
0.5
DPBP 4.5 yrs
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28.5
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14.70%
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8%
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Yr 4 Yr 5
2109.375
3328.125 3328.125
5437.5