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Chapter 10: Making CapitalInvestment Decisions
Faculty of Business AdministrationLakehead University
Spring 2003
May 21, 2003
Outline
10.1 Project Cash Flows: A First Look
10.2 Incremental Cash Flows
10.3 Pro Forma Financial Statements and Project Cash Flows
10.4 More on Project Cash Flow
10.5 Alternative Definitions of Operating Cash Flows
10.6 Applying the Tax Shield Approach
10.7 Special Cases of Cash Flow Analysis
1
10.1 Project Cash Flow: A First Look
Relevant cash flows for a project are those who increase the
overall value of the firm.
Relevant cash flows are calledincremental cash flows.
It may be cumbersome to calculate the future cash flows for the
firm as a whole.
Stand-alone principle: Once the project’s effects on the firm’s
actual cash flows have been determined, it may be simpler to
quantify the incremental cash flows and to consider the project as
a minifirm.
2
10.2 Incremental Cash Flows
• Sunk costsshould not be considered.
• Opportunity costshave to be considered.
• Side effectshave to be considered.
• Net working capitalchanges have to be considered.
• Financing costsare not considered.
• Inflationmust be considered.
• Government intervention, such as CCA, has to be
considered.
3
10.3 Pro Forma Financial Statements
Suppose we believe we can sell 500 cans of crocodile soup per
year at $4.20 per can. Each can costs $2.50 to produce.
Fixed costs are $200 per year and the tax rate is 40%.
The project has a three-year life.
Investments are:
• $900 in equipment, which will depreciate to zero in a
straight line over the project life ($300 per year).
• $200 in net working capital, which will be recovered at the
end of the project.
4
10.3 Pro Forma Financial Statements
Pro forma income statements are
Year
1 2 3
Sales 2,150 2,150 2,150
COGS (1,250) (1,250) (1,250)
Fixed costs (200) (200) (200)
Depreciation (300) (300) (300)
EBIT 400 400 400
Taxes (160) (160) (160)
Net income 240 240 240
5
10.3 Pro Forma Financial Statements
Assets are
Year
0 1 2 3
Net working capital 200 200 200 200
Net fixed assets 900 600 300 0
Total assets 1,100 800 500 200
6
10.3 Pro Forma Financial Statements
As we have seen earlier,
CF(A) = OCF− ∆NWC − NCS,
where
CF(A) ≡ Cash flow from assets;
OCF ≡ Operating cash flow;
∆NWC ≡ Additions to net working capital;
NCS ≡ Net capital spending.
7
10.3 Pro Forma Financial Statements
In the present example,
OCF = EBIT + Depreciation− Taxes
= 400 + 300− 160
= 540
in years 1, 2 and 3.
8
10.3 Pro Forma Financial Statements
Additions to net working capital (∆NWC) and net capital
spending (NCS) are as follows:
Year
0 1 2 3
∆NWC 200 0 0 -200
NCS 900 0 0 0
9
10.3 Pro Forma Financial Statements
Notes:
• Net working capital is recovered at the end of the project.
That is, the value of these assets is transferred to the parent
company or converted to cash.
• Fixed assets could have been sold at market value in year 3.
This is not the case here since we have assumed straight-line
depreciation to zero.
10
10.3 Pro Forma Financial Statements
Cash flows (from assets) are then:
Year
0 1 2 3
OCF 0 540 540 540
∆NWC (200) 0 0 200
NCS (900) 0 0 0
Cash flow (1,100) 540 540 740
11
10.3 Pro Forma Financial Statements
Using a discount of 10%, the net present value of this project is
then
NPV = −1,100 +5401.1
+540
(1.1)2 +740
(1.1)3 = $393.
Net present value is positive but we may want to have a look at
the other measures.
12
10.3 Pro Forma Financial Statements
Payback period= 2.02 years,
Discounted payback period= 2.29 years.
PI =5401.1 + 540
(1.1)2 + 740(1.1)3
1,100= 1.36
AAR = 240900/2+200/4 = 0.46
IRR = 28.26%.
13
10.4 More on Project Cash Flow
• A closer look at net working capital.
• Depreciation and Capital Cost Allowance
14
Depreciation and Capital Cost Allowance
Depreciation is a non-cash expense that reduces the pre-tax
income.
The depreciation rate that effectively affects the amount of taxes
paid by the firm is the CCA rate.
The CCA depreciation may differ from the accounting
depreciation.
Thus the CCA depreciation should be used in cash flow
calculations instead of the accounting depreciation.
15
Depreciation and Capital Cost Allowance
Suppose Brutus, Inc., has a 5-year project where sales are
expected to be as follows:
Year Sales (in $)
1 480
2 660
3 810
4 750
5 720
16
Depreciation and Capital Cost Allowance
The equipment purchased at the beginning of the project costs
$500, and the CCA rate associate with it is 20%. This gives
Year Beg. UCC CCA End. UCC
1 500 50 450
2 450 90 360
3 360 72 288
4 288 58 230
5 230 46 184
17
Depreciation and Capital Cost Allowance
Suppose also that
• variable costs are 1/3 of sales;
• fixed costs are $20 per year;
• tax rate is 36%;
• net working capital is $60 at time 0 and 20% of sales
thereafter.
• salvage value of fixed assets is $180.
18
Depreciation and Capital Cost Allowance
Brutus’ pro forma income statements are
Year
1 2 3 4 5
Sales 480 660 810 750 720
Var. costs (160) (220) (270) (250) (240)
Fixed costs (20) (20) (20) (20) (20)
Depreciation (CCA) (50) (90) (72) (58) (46)
EBIT 250 330 448 422 414
Taxes (90) (119) (161) (152) (149)
Net income 160 211 287 270 265
19
Depreciation and Capital Cost Allowance
On the asset side, we haveYear
0 1 2 3 4 5
Net working capital 60 96 132 162 150 144
(a) Change in NWC 60 36 36 30 (12) (6)
(b) NWC recovery 144
∆NWC ((a)-(b)) 60 36 36 30 (12) (150)
Net capital spending 500 (180)
20
Depreciation and Capital Cost Allowance
Operating cash flows are
Year
0 1 2 3 4 5
EBIT 0 250 330 448 422 414
CCA 0 50 90 72 58 46
Taxes (0) (90) (119) (161) (152) (149)
OCF 0 210 301 359 328 311
21
Depreciation and Capital Cost Allowance
Cash flows are
Year
0 1 2 3 4 5
OCF 0 210 301 359 328 311
∆NWC 60 36 36 30 −12 −150
NCS 500 −180
CF −560 174 265 329 340 641
22
Depreciation and Capital Cost Allowance
At a discount rate of 15%, the net present value of this project is
NPV = −560 +1751.15
+265
(1.15)2 +329
(1.15)3 +340
(1.15)4 +641
(1.15)5
= $521.
The IRR is 42% and the payback period is 2.37 years.
Are we missing something?
23
Depreciation and Capital Cost Allowance
Regarding CCA, what happens when an asset is sold?
When the asset is sold for less than its UCC, the difference
depreciates forever (if the asset pool is not terminated).
When the asset is sold for more than its UCC, the difference is
subtracted from the value of the asset pool.
In the Brutus example, the assets are sold for less than the UCC,
and thus there will be further tax savings coming from the
project.
24
Depreciation and Capital Cost Allowance
In the Brutus example, the equipment’s UCC after 5 years is
expected to be $184 but the market value is expected to be $180.
The difference, 184−180= 4, is then expected to depreciate
forever, thus inducing tax savings into perpetuity.
25
Depreciation and Capital Cost Allowance
Let Tc denote the firm’s tax rate (36% in this case) and letd
denote the CCA rate (20% in this case). The tax savings arising
from year 6 on are then
Tc×d×4 in year 6,
Tc×d× (1−d)4 in year 7,
Tc×d× (1−d)24 in year 8,
Tc×d× (1−d)34 in year 9,...
26
Depreciation and Capital Cost Allowance
As of year 5, the present value of this perpetuity is
PV5 =4dTc
1+ r+
(1−d)4dTc
(1+ r)2 +(1−d)24dTc
(1+ r)3 +(1−d)34dTc
(1+ r)4 + . . .
= 4dTc
(1
1+ r+
1−d(1+ r)2 +
(1−d)2
(1+ r)3 + . . .
)= 4dTc×
1r− (−d)
=4dTc
r +d,
and thus the project’s NPV should also include
4dTc
(r +d)(1+ r)5 =4×0.36×0.20
(0.15+0.20)(1.15)5 = $0.41.
27
Depreciation and Capital Cost Allowance
To take into account all the tax savings arising from the purchase
of assets for new projects, we will calculate OCF differently.
This method will be called thetax shield approach.
28
10.5 Alternative Definitions of Operating Cash Flow
Let
S ≡ Sales,
C ≡ Operating costs,
D ≡ Depreciation for tax purposes,
Tc ≡ Corporate tax rate.
Then
EBIT = S−C−D and Taxes= Tc(S−C−D).
29
10.5 Alternative Definitions of Operating Cash Flow
Therefore,
OCF = EBIT + D − Tc(S−C−D)
= S−C−D + D − Tc(S−C−D)
= (1−Tc)(S−C) + TcD.
This way of calculating operating cash flow is called thetax
shield approach.
30
10.6 The Tax Shield Approach
Each year, cash flow from assets is
CF = OCF− ∆NWC − NCS
= (1−Tc)(S−C) + TcD − ∆NWC − NCS
= (1−Tc)(S−C) − ∆NWC − NCS + TcD.
The problem can be simplified by treating depreciationseparately from OCF. That is, NPV can be calculated as
NPV = PV of (1−Tc)(S−C) − PV of ∆NWC − PV of NCS
+ PV of CCA tax shield.
31
10.6 The Tax Shield Approach
What is PV of CCA tax shield (CCATS)?
Let
A ≡ value of assets initially purchased,
S ≡ salvage value of these assets at the end of the project,
Tc ≡ Corporate tax rate.
d ≡ CCA rate,
k ≡ discount rate,
n ≡ asset life.
32
10.6 The Tax Shield Approach
PV of CCATS
As we have seen in Chapter 2, CCA depreciation is
0.5dA in year 1,
0.5d(1−d)A + 0.5dA in year 2,
0.5d(1−d)2A + 0.5d(1−d)A in year 3,...
33
10.6 The Tax Shield Approach
PV of CCATS
The tax shield arising fromA is then
0.5TcdA in year 1,
0.5Tcd(1−d)A + 0.5TcdA in year 2,
0.5Tcd(1−d)2A + 0.5Tcd(1−d)A in year 3,...
34
10.6 The Tax Shield Approach
PV of CCATS
If these assets are never sold, the present value of this tax shieldis
PVCCATS =0.5TcdA
k+d+
0.5TcdA(1+k)(k+d)
=0.5TcdA
k+d×
(1+
11+k
)=
0.5TcdAk+d
×(
1+k+11+k
)=
0.5TcdAk+d
×(
2+k1+k
)=
TcdAk+d
× 1+0.5k1+k
35
10.6 The Tax Shield Approach
PV of CCATS
When the assets are sold, their market value (S) is subtracted
from the asset pool. That is,Swon’t depreciate forever.
As of timen, the present value of the tax savings attributed toS is
TcdSk+d
,
and thus
PVCCATS =TcdA(1+0.5k)(k+d)(1+k)
− TcdS(k+d)(1+k)n .
36
10.6 The Tax Shield Approach
In the Brutus example,
Year
0 1 2 3 4 5
(1−Tc)(S−C) 0 192 269 333 307 294
∆NWC 60 36 36 30 −12 −150
NCS 500 −180
PV of (1−Tc)(S−C) = 911,
PV of ∆NWC = 57,
PV of NCS = 411,
37
10.6 The Tax Shield Approach
and
PVCCATS =TcdA(1+0.5k)(k+d)(1+k)
− TcdS(k+d)(1+k)n
=0.36×0.20×500×1.075
0.35×1.15− 0.36×0.20×180
0.35(1.15)5
= 78.
Therefore,
NPV = 911− 57 − 411 + 78 = $521.
38