Capital Budgeting - University of Manitoba
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Transcript Capital Budgeting - University of Manitoba
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
Jacoby, Stangeland and Wajeeh, 2000
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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
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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
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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
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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
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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
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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
Jacoby, Stangeland and Wajeeh, 2000
= $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 $3,691.40625 K each
r =10%, and Tc = 40%.
Jacoby, Stangeland and Wajeeh, 2000
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The Worksheet for Cash Flows of U-Air’s Bahamas Project
($ 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
Jacoby, Stangeland and Wajeeh, 2000
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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:
PVCCA Tax Shield
C d Tc 1 0.5r S d Tc
1
rd
1 r
rd
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
1.14
$8,027 .63 K
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
Jacoby, Stangeland and Wajeeh, 2000
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