Chapter 7
Capital Budgeting & NPV
Recall: Value of an Asset = PV(Future CFs)
Note:
CF g accounting income (earnings)
Examples:

Value of a Project = PV(future CFs generated by project)

Value of Firm’s Equity = PV(dividends) g PV(earnings)

Capital Investment g Depreciation
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 For the NPV of a project - use only Incremental CF
 Is a CF incremental?
 YES - if occurs as a result of accepting the project
 No - if occurs independent of the decision
 Example: Determine which is an incremental CF:


a marketing survey done 2 years ago
R&D expenses spent last year
Sunk Costs are NOT Incremental CF


apparently, the machine required for the new project is found in the
company’s warehouse
the company already owns the office building for the new project
Opportunity Costs ARE Incremental CF

buyers of the GMC’s new truck, are potential buyers

of GMC’s SUV
advertising of the new product will increase the sales of an older product
wage increase resulting from a labour shortage due to accepting the project

Side Effects ARE Incremental CF
2
The Appropriate Discount Rate
The Fisher Relation:
Nominal Rate (rn) Vs. Real Rate (rr):
(1+ rn) = (1+ rr)(1+p)
where p is the inflation rate
What rate should we use?


Nominal CFs should be discounted with rn
Real CFs should be discounted with rr
Risk and discount rates:
higher risk CFs require a higher return
3
Inflation
 Your time-0 endowment is: $2,000,000
 You can invest at a nominal rate of rn=5% p.a.
 At time-0, the cheapest house in Beverly-Hills costs $2,000,000
 Real-estate prices are expected to grow at p=10% p.a.
 Can you afford buying a house in Beverly-Hills next year?
 At time-1


your money grows to: $2,000,000 (1.05) = $2,100,000
The cheapest house in B.H. will cost: $2,000,000 (1.10) = $2,200,000
 Conclusion: the real value of your money has depreciated
4
Inflation
 The Fisher Relation:
(1+ rn) = (1+ rr)(1+p)
Your real rate is:
rr = [(1+ rn)/(1+p)] - 1
= [(1.05)/(1.10)] - 1
= - 4.55%
 Real CF (Ct,r) vs. Nominal CF (Ct,n):
Ct,n = Ct,r (1+p)t
In our example: t=1, p =0.10, C1,n = $2,200,000 (actual cost), and
Ct,r = Ct,n/(1+p)t
= [$2,200,000 / 1.101]
= $2,000,000 (time-0 value)
 What rate should we use?
 Ct,n should be discounted with rn:
PV = [$2,200,000 / (1+0.05)1] = $2,095,238.10

Ct,r should be discounted with rr:
PV = [$2,000,000 / (1 - 0.0455)1] = $2,095,238.10
5
Calculating the Net Operating Cash Flow (NOCF)
 Recall:
CF g accounting income
 We are interested in the PV of Net (after-tax) Operating
CF (NOCF):
NOCF =
R
E
- Taxes
(1)
Revenues
where,
Operating
Costs
Taxes = [R - E - D]Tc
Plug (2) into (1):
NOCF = R - E - Tc[R - E - D]
= (R - E)(1- Tc)
+
(2)
TcD
6
EBDT(1- Tc)
Tax Shield of D
Calculating NOCF - An Example
Income
Statement
100
70
Without
Depreciation (D)
100
70
EBDT
Depreciation (D)
30
10
30
0
30
0
EBT
Taxes (@40%)
20
8
30
12
30
8
NI
12
18
Revenues
Expenses
CF-based
(with D)
100
70
Pay less taxes ($4)
22

Tax-Shield of CCA: Tc % D =

NOCF=(R - E)(1- Tc)+TcD=EBDT(1- Tc)+TcD=30(1- 0.4)+0.4%10= $22

Conclusion: CCA Tax-Shield is equivalent to cash inflow
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= $4
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Capital Cost Allowance (CCA)
 Revenue Canada’s rules of depreciating assets for tax purposes
 Assign every asset to its asset class (pool)
 Find its maximum CCA rate
e.g. Brick buildings (acquired after 1987): d = 4%
Electrical equipment & aircraft: d = 25%
 Revenue Canada’s ‘50% rule’:
CCA for the first year = d [installed cost / 2]
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CCA - The U-Air Case
Initial Facts:
 U-Air is considering the addition of 4 new planes to its fleet, at a cost of
$10 M each. (ready to fly), for a new line to the Bahamas
 Expected life of an airplane is 30 years
 U-Air is expected to sell the airplanes for $3,691,406.25 each in 4 years
 Calculate the expected CCA schedule for this purchase for the next 4 years
Year
Beginning
UCC
CCA
Ending
UCC
CCA Tax Shield
(TcCCA)
1
2
3
4
.
.
.
.
.
.
.
.
.
.
.
.
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Investing in Net Working Capital (NWC)
An investment in NWC, represents an increase in the NWC
allocated to the project:

purchasing of raw materials and inventory

keeping cash reserves for unexpected expenses

an increase in accounts receivable

a decrease in accounts payable and taxes payable
NWC - The U-Air Case:
U-Air managers predict the following requirement for NWC generated
by the Bahamas project:
Year
0
1
2
3
4
NWC
1,600 K
2,400
3,000
2,200
0
Changes in NWC
+1,600 K
+ 800
+ 600
- 800
- 2,200
Cash Flow from NWC
- 1,600 K
- 800
- 600
+ 800
+2,200
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Calculating Net Working Capital (NWC)
Inventory
Cash
Accounts Receivable
Accounts Payable
Taxes Payable
Year 0
$600,000
$1,000,000
$1,300,000
$1,100,000
$200,000
Year 1
$850,000
$1,550,000
$1,900,000
$1,600,000
$300,000
Year 2
$1,050,000
$1,950,000
$2,300,000
$2,000,000
$300,000
Jacoby, Stangeland and Wajeeh, 2000
Year 3
Year 4
$800,000
$0
$1,400,000
$0
$1,650,000
$0
$1,450,000
$0
$200,000
$0
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Capital Budgeting: The U-Air Case
Facts
 Costs of test marketing (already spent)
$2,000 K
 Current (time-0) market value of 4 airplanes
$40,000 K
 Number of round-trip tickets per year during 4-year life
of the project: (16,000, 24,000, 30,000, 22,000)
 Ticket price
$2 K
 Operating costs per ticket
$1 K
 Number of round-trip tickets per year (during next 4 years)
lost in sales of U-Air’s other Caribbean lines:
(100, 200, 400, 300) with the same ticket price and variable cost
 Cash flows from investment in NWC: (-$1,600 K, -800, -600, +800, +2,200)
 U-Air already owns a terminal which can be used for the Bahamas project.
Renting a similar terminal would cost U-Air $10,000 K per year
 U-Air will sell the airplanes after 4 years for $3,691.40625 K each
 r =10%, and Tc = 40%.
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The Worksheet for Cash Flows of U-Air’s Bahamas Project
($ thousands) (All cash flows occur at the end of the year.)
I. Income
Year 0 Year 1 Year 2
CF from Ticket Sales
Ticket Sales Revenues
Sales - Side effects
Year 3
Year 4
32,000 48,000 60,000 44,000
(200) (400) (800) (600)
31,800 47,600 59,200 43,400
Operating costs
Fixed costs (Opportunity cost)
Variable costs
V. costs - Side effects
EBDT
EBDT(1- Tc)*
0
10,000
16,000
(100)
(25,900)
5,900
3,540
10,000
24,000
10,000
30,000
(200)
10,000
22,000
(400) (300)
(33,800) (39,600) (31,700)
13,800 19,600 11,700
8,280 11,760
7,020
* Calculated with Tc = 40%.
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Case – Part 1 - Q1 & Q2
The Worksheet for Cash Flows of U-Air’s Bahamas Project (Cont’d)
($ thousands) (All cash flows occur at the end of the year.)
Airplanes
Change in NWC
Total investment
cash flow (ICF)
II. Investments
Year 0 Year 1 Year 2 Year 3 Year 4
(40,000)
14,765.625
(1,600) (800)
(600)
800
2,200
(41,600)
(800)
(600)
800
16,965.625
Calculating the NPV of the Project (@ r = 10%)
PV of EBDT(1- Tc)
PV of ICF
PV of CCA Tax-Shield
23,691.37
(30,634.34)
8,027.63
NPV of the Bahamas Project
1,084.66
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The PV of CCA Tax Shield
 If U-Air never sells the airplanes, then the CCA tax shield will be a growing perpetuity with a
negative growth rate, and the twist of Revenue Canada’s ‘50% rule’
 Since U-Air will sell the airplanes in 4 years (for $3,691,406.25 each), to calculate the PV of
CCA tax shield, we use the growing perpetuity formula, adjusted for Revenue Canada’s ‘50%
rule’ and the sale of the airplanes.
 In this course, we deal with the simplest case where there are no capital gains and the asset pool
is not terminated after the sale (“The total value of U-Air’s class-9 asset pool is not expected to
be below a level of $350 million over the next four years.”)
 The PV of CCA tax shield is given by:
PVCCATax Shield
C  d  Tc 1  0.5r  S  d  Tc
1




rd
1 r
rd
1  r n
40,000  0.25  0.4 1.05 14,765.625  0.25  0.4
1




0.1  0.25
1 .1
0.1  0.25
1.14
 $8,027 .63K
Where:
S = Min[sale value of assets, original price of assets]
= Min[$14,765,625.25, $40,000,000]= $14,765,625.25
C = the original price of the assets = $40,000K
d = 25% for Electrical equipmentJacoby,
& aircraft.
Stangeland and Wajeeh, 2000
n = the time when assets are sold = 4 years
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Total Project Cash Flow Approach
($ thousands) (All cash flows occur at the end of the year.)
EBDT(1- Tc)
Year 0
0
Total investment
cash flow (ICF)
(41,600)
(800)
(600)
800
16,965.625
Total Project CF
(Excluding CCA Tax-Shield)
(41,600) 2,740
7,680
12,560
23,985.625
5,000
2,000
8,750
3,500
(41,600) 4,740
11,180
CCA Tax-Shield s:
Annual CCA
Annual Tax-Shield (TcCCA)
Total Project Cash Flow:
Year 1
3,540
Year 2
8,280
Year 3
11,760
Year 4
7,020
6,562.5 4,921.875
2,625
1,968.75
15,185
25,954.375
Calculating the NPV of the Project (@ r = 10%)
NPV of the Bahamas Project:
1,084.66
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Case – Part 1 – Q3
The Worksheet for REAL Cash Flows of U-Air’s Bahamas Project
Nominal CF’s
($ thousands) (All cash flows occur at the end of the year.)
Year 0 Year 1
EBDT(1- Tc)
Investment CF (ICF)


0
3,540
(41,600) (800)
Year 2
Year 3
Year 4
8,280 11,760 7,020
(600) 800 16,965.625
We have an annual inflation rate of: p = 4%
We convert nominal CFs to real CFs, with: Ct,r = Ct,n / (1+p)t
Real CF’s
Year 0
Year 1
Year 2
EBDT(1- Tc)
0
3,403.85 7,655.33
Investment CF (ICF) (41,600.00) (769.23) (554.73)
Jacoby, Stangeland and Wajeeh, 2000
Year 3
Year 4
10,454.60 6,000.73
711.20 14,502.29
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The Worksheet for REAL Cash Flows of U-Air’s Bahamas Project (Cont’d)
We calculate the NPV of the REAL CFs of the Project with the real rate:
Fisher Relation: rr = [(1+ rn)/(1+p)] - 1= [(1.10)/(1.04)] - 1= 5.769231%
The NPV of the Project:
PV of EBDT(1- Tc)
PV of ICF
23,691.37
(30,634.34)
PV of CCA Tax-Shield*
8,027.63
NPV of the Bahamas Project
1,084.66
Same as calculated
with the nominal CF
* CCA Tax-Shield
is a stream of
nominal CF =>
calculate NPV with
the nominal rate
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