Discussion 4
wtfbm69
Ch11-CapitalBudgetingTechniques.pptxChapter 11. Capital Budgeting
1
Capital budgeting deals with investment decisions where
Time is an important element of the decision
Cash flows of investment can be measured
But, there may be some uncertainties
Classification of decisions
Accept or reject
Choose best of a set (mutually exclusive)
Ranking (projects are independent and cash is limited)
Capital budgeting
Independent vs. mutually exclusive projects
Independent projects:
if the cash flows of one are unaffected by the acceptance of the other.
Multiple projects can be chosen.
Mutually exclusive projects:
if the cash flows of one can be adversely impacted by the acceptance of the other.
Only ONE of several potential projects can be chosen
3
Financial managers should accept a project when its perceived benefits exceed perceived costs. In general, value is created when benefits exceed costs.
NPV = Total PV of future CFs - Initial Investment
When firms accept all positive Net Present Value investments, they maximize the value of their shareholders.
Net Present Value (NPV)
Net Present Value (NPV)
Sum of the PVs of all cash inflows and outflows of a project:
Estimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs
Reinvestment assumption
Assumes all cash flows are reinvested at discount rate
Rule
Accept if NPV > 0
Reject if NPV < 0.
Ranking Criteria
Choose the highest NPV
What is Project S’ NPV?
WACC = 10%
Year
CFt
PV of CFt
0
-
100
-
$100.00
1
70
63.64
2
50
41.32
3
20
15.02
NPVS
=
$ 19.98
Excel: =NPV(rate,CF1:CFn) + CF0
Here, CF0 is negative, rate is discount rate or WACC.
6
Rationale for the NPV Method
NPV = PV of inflows – Cost
= Net gain in wealth
If projects are independent, accept if NPV > 0.
If projects are mutually exclusive, accept projects with the highest positive NPV, those that add the most value.
7
IRR is the discount rate that forces PV of inflows equal to cost, and the NPV = 0:
Reinvestment assumption: All future cash flows assumed reinvested at the IRR
Solving for IRR with a financial calculator:
Enter CFs in Cash Flow register.
Press IRR.
Solving for IRR with Excel:
=IRR(CF0:CFn)
Internal Rate of Return (IRR)
8
How is a project’s IRR similar to a bond’s YTM?
They are the same thing.
Think of a bond as a project. The YTM on the bond would be the IRR of the “bond” project.
EXAMPLE: Suppose a 10-year bond with a 9% annual coupon and $1,000 par value sells for $1,134.20.
Solve for IRR = YTM = 7.08%, the annual return for this project/bond.
9
Rules for the IRR Method
For independent projects:
Take all projects with IRR>r*
r*=the opportunity cost of capital or required rate of return
For mutually exclusive projects:
Take the project with the highest IRR, if IRR>r*
10
What is the IRR of the following project?
The IRR does not always exist!
Potential problems with IRR
| Year | 0 | 1 | 2 |
| Project A | 100 | -200 | 150 |
Lending or Borrowing?
Potential problems with IRR
12
Potential problems with IRR
The following cash flow generates NPV=$ 3.3 million at 10%. It has IRRs of (-44%) and +11.6%.
Cash Flows (millions of Australian dollars)
13
When the sign of the cash flows changes more than once, you get multiple rates of return
The IRR does not always unique!
Potential problems with IRR
600
NPV
300
0
-30
-600
Discount Rate
IRR=11.6%
IRR=-44%
14
For cash flows that alternate in sign (i.e. negative, positive, negative), it is not clear whether you are a net borrower or a net lender. Thus, it is not clear whether you would prefer a high or low IRR.
If cash flows have the traditional pattern (one or several negative cash flows followed by only positive cash flows), then the NPV is positive whenever the IRR is greater than the opportunity cost of capital – Thus, the IRR rule usually works.
Potential problems with IRR
| Flows | Number of IRRs | IRR criterion | NPV criterion |
| First cash flow is (-) and all remaining cash flows are (+) | 1 | Accept if IRR>R Reject if IRR<R | Accept if NPV>0 Reject if NPV<0 |
| First cash flows is (+) and all remaining cash flows are (-) | 1 | Accept if IRR<R Reject if IRR>R | Accept if NPV>0 Reject if NPV<0 |
| Some cash flows after first are (+) and some cash flows after first are (-) | Maybe more than 1 | No valid IRR | Accept if NPV>0 Reject if NPV<0 |
General rules
Potential problems with IRR: scale issue
Mutually Exclusive Projects
Mutually exclusive
Only ONE of several potential projects can be chosen
Independent: Accepting/rejecting one project does not affect the decision of the other projects
Scale issues
IRR sometimes ignores the magnitude of the project.
17
Potential problems with IRR: scale issue
In this case, can IRR be salvaged?
Look at smaller project
Acceptable? Yes.
So, should you invest extra $$$ for larger project.
Look at incremental CFs: INCREMENTAL IRR
Now, which project is better?
18
Timing Issues
Preferred project depends on the discount rate, not the IRR (mutually exclusive projects)
Potential problems with IRR: timing issue
0 1 2 3
$10,000 $1,000 $1,000
-$10,000
Project A
0 1 2 3
$1,000 $1,000 $12,000
-$10,000
Project B
19
Potential problems with IRR: timing issue
20
20
Potential problems with IRR: timing issue
10.55% = IRR
To find crossover rate: Find INCREMENTAL IRR!
21
The number of years required to recover a project’s cost, or “How long does it take to get our money back?”
Calculated by adding project’s cash inflows to its cost until the cumulative cash flow for the project turns positive.
Payback period
The payback period is the number of years, t*, such that
For independent projects
Accept all projects for which t*<K (where K is the cutoff)
For mutually exclusive projects:
Accept the project with the lowest t* as long as t*<K (where K is the cutoff)
Mutually exclusive: Only ONE of several potential projects can be chosen
Payback period
Payback period
PaybackL = 2 + /
= 2.375 years
30
80
CFt
Cumulative
0
1
2
3
-30
Project L’s Payback Calculation
-100
50
-90
80
-100
60
10
24
Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.
Payback period
25
Strengths and Weaknesses of Payback
Strengths
Provides an indication of a project’s risk and liquidity.
Easy to calculate and understand.
Weaknesses
Ignores the time value of money.
Ignores CFs occurring after the payback period.
26
The discounted payback period is the number of years, t*, such that
For non-mutually excusive projects
Accept all projects for which t*<K
For mutually exclusive projects:
Accept the project with the lowest t* as long as t*<K (where K is the cutoff)
Discounted payback period
Discounted Payback Period
Uses discounted cash flows rather than raw CFs.
Disc PaybackL = 2 + / = 2.7 years;
If our cutoff rule was 2 years, this project would be rejected.
41.32
60.11
CFt
Cumulative
0
1
2
3
-41.32
-100
18.79
-90.91
80
-100
60
10
10%
PV of CFt
-100
9.09
49.59
60.11
28
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IRR
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($4,000.00)
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
$4,000.00
$5,000.00
0%10%20%30%40%
Discount rate
NPV
Project A
Project B
Chart7
| 0 | 0 |
| 0.01 | 0.01 |
| 0.02 | 0.02 |
| 0.03 | 0.03 |
| 0.04 | 0.04 |
| 0.05 | 0.05 |
| 0.06 | 0.06 |
| 0.07 | 0.07 |
| 0.08 | 0.08 |
| 0.09 | 0.09 |
| 0.1 | 0.1 |
| 0.11 | 0.11 |
| 0.12 | 0.12 |
| 0.13 | 0.13 |
| 0.14 | 0.14 |
| 0.15 | 0.15 |
| 0.16 | 0.16 |
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| 0.19 | 0.19 |
| 0.2 | 0.2 |
| 0.21 | 0.21 |
| 0.22 | 0.22 |
| 0.23 | 0.23 |
| 0.24 | 0.24 |
| 0.25 | 0.25 |
| 0.26 | 0.26 |
| 0.27 | 0.27 |
| 0.28 | 0.28 |
| 0.29 | 0.29 |
| 0.3 | 0.3 |
| 0.31 | 0.31 |
| 0.32 | 0.32 |
| 0.33 | 0.33 |
| 0.34 | 0.34 |
| 0.35 | 0.35 |
| 0.36 | 0.36 |
| 0.37 | 0.37 |
| 0.38 | 0.38 |
| 0.39 | 0.39 |
| 0.4 | 0.4 |
Sheet1
| 0 | 1 | 2 | 3 | ||
| $ (10,000.00) | $ 10,000.00 | $ 1,000.00 | $ 1,000.00 | A | |
| $ (10,000.00) | $ 1,000.00 | $ 1,000.00 | $ 12,000.00 | B | |
| 16.04% | IRR A | ||||
| 12.94% | IRR B | ||||
| Discount Rate | Project A | Project B | |||
| 0% | $2,000.00 | $4,000.00 | |||
| 1% | $1,833.54 | $3,581.66 | |||
| 2% | $1,673.93 | $3,185.71 | |||
| 3% | $1,520.85 | $2,810.84 | |||
| 4% | $1,373.98 | $2,455.82 | |||
| 5% | $1,233.03 | $2,119.49 | |||
| 6% | $1,097.72 | $1,800.78 | |||
| 7% | $967.79 | $1,498.68 | |||
| 8% | $842.99 | $1,212.27 | |||
| 9% | $723.10 | $940.65 | |||
| 10% | $607.88 | $683.01 | |||
| 11% | $497.14 | $438.58 | |||
| 12% | $390.67 | $206.62 | |||
| 13% | $288.28 | ($13.54) | |||
| 14% | $189.80 | ($222.53) | |||
| 15% | $95.05 | ($420.95) | |||
| 16% | $3.89 | ($609.38) | |||
| 17% | ($83.85) | ($788.32) | |||
| 18% | ($168.31) | ($958.29) | |||
| 19% | ($249.63) | ($1,119.76) | |||
| 20% | ($327.93) | ($1,273.15) | |||
| 21% | ($403.35) | ($1,418.89) | |||
| 22% | ($475.99) | ($1,557.36) | |||
| 23% | ($545.98) | ($1,688.95) | |||
| 24% | ($613.41) | ($1,813.98) | |||
| 25% | ($678.40) | ($1,932.80) | |||
| 26% | ($741.04) | ($2,045.71) | |||
| 27% | ($801.41) | ($2,153.01) | |||
| 28% | ($859.62) | ($2,254.96) | |||
| 29% | ($915.74) | ($2,351.84) | |||
| 30% | ($969.85) | ($2,443.89) | |||
| 31% | ($1,022.04) | ($2,531.35) | |||
| 32% | ($1,072.37) | ($2,614.42) | |||
| 33% | ($1,120.92) | ($2,693.34) | |||
| 34% | ($1,167.75) | ($2,768.28) | |||
| 35% | ($1,212.93) | ($2,839.45) | |||
| 36% | ($1,256.51) | ($2,907.02) | |||
| 37% | ($1,298.57) | ($2,971.15) | |||
| 38% | ($1,339.14) | ($3,032.01) | |||
| 39% | ($1,378.30) | ($3,089.76) | |||
| 40% | ($1,416.08) | ($3,144.52) | |||
| Discount Rate | NPV | ||||
| 0% | $2,000.00 | ||||
| 4% | $1,373.98 | ||||
| 8% | $842.99 | ||||
| 12% | $390.67 | ||||
| 16% | $3.89 | ||||
| 20% | ($327.93) | ||||
| 24% | ($613.41) | ||||
| 28% | ($859.62) | ||||
| 32% | ($1,072.37) | ||||
| 36% | ($1,256.51) | ||||
| 40% | ($1,416.08) | ||||
| 44% | ($1,554.45) | ||||
| 48% | ($1,674.48) | ||||
| 52% | ($1,778.60) | ||||
| 56% | ($1,868.86) | ||||
| 60% | ($1,947.02) | ||||
| 64% | ($2,014.59) | ||||
| 17% | ($83.85) | ||||
| 18% | ($168.31) | ||||
| 19% | ($249.63) | ||||
| 20% | ($327.93) | ||||
| 21% | ($403.35) | ||||
| 22% | ($475.99) | ||||
| 23% | ($545.98) | ||||
| 24% | ($613.41) | ||||
| 25% | ($678.40) | ||||
| 26% | ($741.04) | ||||
| 27% | ($801.41) | ||||
| 28% | ($859.62) | ||||
| 29% | ($915.74) | ||||
| 30% | ($969.85) | ||||
| 31% | ($1,022.04) | ||||
| 32% | ($1,072.37) | ||||
| 33% | ($1,120.92) | ||||
| 34% | ($1,167.75) | ||||
| 35% | ($1,212.93) | ||||
| 36% | ($1,256.51) | ||||
| 37% | ($1,298.57) | ||||
| 38% | ($1,339.14) | ||||
| 39% | ($1,378.30) | ||||
| 40% | ($1,416.08) |
Sheet1
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
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| 0 | 0 |
| 0 | 0 |
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| 0 | 0 |
| 0 | 0 |
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| 0 | 0 |
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| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
Sheet2
Sheet3
YearProject AProject BProject A-B Project B-A
0($10,000)($10,000)$0$0
1$10,000$1,000$9,000($9,000)
2$1,000$1,000$0$0
3$1,000$12,000($11,000)$11,000
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
0%5%10%15%20%
Discount rate
NPV
A-B
B-A
Sheet1
| Year | Project A | Project B | Project A-B | Project B-A |
| 0 | ($10,000) | ($10,000) | $0 | $0 |
| 1 | $10,000 | $1,000 | $9,000 | ($9,000) |
| 2 | $1,000 | $1,000 | $0 | $0 |
| 3 | $1,000 | $12,000 | ($11,000) | $11,000 |
| 10.55% | ||||
| Discount rtae | A-B | B-A | ||
| 0% | ($2,000.00) | |||
| 1% | ($1,748.12) | |||
| 2% | ($1,511.78) | |||
| 3% | ($1,289.99) | |||
| 4% | ($1,081.84) | |||
| 5% | ($886.46) | |||
| 6% | ($703.06) | |||
| 7% | ($530.90) | |||
| 8% | ($369.28) | |||
| 9% | ($217.56) | |||
| 10% | ($75.13) | |||
| 11% | $58.56 | |||
| 12% | $184.05 | |||
| 13% | $301.81 | |||
| 14% | $412.32 | |||
| 15% | $516.01 | |||
| 16% | $613.26 | |||
| 17% | $704.47 | |||
| 18% | $789.98 | |||
| 19% | $870.13 | |||
| 20% | $945.22 |
Sheet1
Sheet2
Sheet3
Chart2
| 0 | 0 |
| 0.01 | 0.01 |
| 0.02 | 0.02 |
| 0.03 | 0.03 |
| 0.04 | 0.04 |
| 0.05 | 0.05 |
| 0.06 | 0.06 |
| 0.07 | 0.07 |
| 0.08 | 0.08 |
| 0.09 | 0.09 |
| 0.1 | 0.1 |
| 0.11 | 0.11 |
| 0.12 | 0.12 |
| 0.13 | 0.13 |
| 0.14 | 0.14 |
| 0.15 | 0.15 |
| 0.16 | 0.16 |
| 0.17 | 0.17 |
| 0.18 | 0.18 |
| 0.19 | 0.19 |
| 0.2 | 0.2 |
Sheet1
| Year | Project A | Project B | Project A-B | Project B-A |
| 0 | ($10,000) | ($10,000) | $0 | $0 |
| 1 | $10,000 | $1,000 | $9,000 | ($9,000) |
| 2 | $1,000 | $1,000 | $0 | $0 |
| 3 | $1,000 | $12,000 | ($11,000) | $11,000 |
| 10.55% | ||||
| Discount rtae | A-B | B-A | ||
| 0% | ($2,000.00) | $2,000.00 | ||
| 1% | ($1,748.12) | $1,748.12 | ||
| 2% | ($1,511.78) | $1,511.78 | ||
| 3% | ($1,289.99) | $1,289.99 | ||
| 4% | ($1,081.84) | $1,081.84 | ||
| 5% | ($886.46) | $886.46 | ||
| 6% | ($703.06) | $703.06 | ||
| 7% | ($530.90) | $530.90 | ||
| 8% | ($369.28) | $369.28 | ||
| 9% | ($217.56) | $217.56 | ||
| 10% | ($75.13) | $75.13 | ||
| 11% | $58.56 | ($58.56) | ||
| 12% | $184.05 | ($184.05) | ||
| 13% | $301.81 | ($301.81) | ||
| 14% | $412.32 | ($412.32) | ||
| 15% | $516.01 | ($516.01) | ||
| 16% | $613.26 | ($613.26) | ||
| 17% | $704.47 | ($704.47) | ||
| 18% | $789.98 | ($789.98) | ||
| 19% | $870.13 | ($870.13) | ||
| 20% | $945.22 | ($945.22) |
Sheet1
| 0 | 0 |
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Sheet2
Sheet3
å
=
=
*
0
0
t
t
t
CF
050018002000-C
018005002000-B
50005005002000-A
10% @NPV
Period
Payback
CCCCProject
3210
å
=
=
+
*
0
0
)
1
(
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t
t
t
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