CHAPTER 9 Capital Budgeting. PV of Cash Flows Payback NPV IRR EAA NPV profiles. Characteristics of Business Projects. Project Types and Risk Capital projects have increasing risk according to whether they are replacements, expansions or new ventures
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1
2
3
CFt
10
60
80
90
Cumul
100
30
50
PaybackL
2 + 30/80 = 2.375 years
Payback for Project L(Long: Most CFs in out years)2.4
100
0
=
1
2
3
70
50
20
CFt
30
Cumul
100
20
40
PaybackL
1 + 30/50 = 1.6 years
Project S (Short: CFs come quickly)1.6
100
0
=
1
2
3
10
60
80
Discounted Payback: Uses discounted
rather than raw CFs.
Project L
10%
CFt
100
9.09
49.59
60.11
PVCFt
100
100
90.91
41.32
18.79
Cumul(PV)
Disc.
payback
2 + 41.32/60.11 = 2.7 yrs
=
Recover invest + cap costs in 2.7 yrs.
Payback period occurs at 3.33 years.
Q: Use the payback period technique to choose between mutually exclusive projects A and B.
Project A
Project B
C0
($1,200)
($1,200)
C1
400
400
C2
400
400
Example
C3
400
350
C4
200
800
C5
200
800
A: Project A’s payback is 3 years as its initial outlay is fully recovered in that time. Project B doesn’t fully recover until sometime in the 4th year. Thus, according to the payback method, Project A is better than B.
Capital Budgeting Techniques—Payback— yet another exampleQ: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken?
C0
($5,000)
C1
$1,000
C2
$2,000
C3
$3,000
Example
A: The NPV is found by summing the present value of the cash flows when discounted at the firm’s cost of capital.
Since Alpha’s NPV<0, it should not be undertaken.
Capital Budgeting Techniques—Net Present Value (NPV) ExampleThe “price” of receiving
the inflows
Project
cost
Q: Find the IRR for the following series of cash flows: considering Alpha has a cost of capital of 12%, should the project be undertaken?
If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital is 10%?
C0
C1
C2
C3
($5,000)
$1,000
$2,000
$3,000
A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate.
Example
Since NPV<0, the project’s IRR must be < 12%.
Techniques—Internal Rate of Return (IRR)—ExampleWe’ll try a different, lower interest rate, say 10%. At 10%, the project’s NPV is ($184). Since the NPV is still less than zero, we need to try a still lower interest rate, say 9%. The following table lists the project’s NPV at different interest rates.
Since NPV becomes positive somewhere between 8% and 9%, the project’s IRR must be between 8% and 9%. If the firm’s cost of capital is 8%, the project is marginal. If the firm’s cost of capital is 10%, the project is not a good idea.
Interest Rate Guess
Calculated NPV
12%
($377)
10
($184)
Example
9
($83)
8
$22
7
$130
The exact IRR can be calculated using a financial calculator. The financial calculator uses the iterative process just demonstrated; however it is capable of guessing and recalculating much more quickly.
Techniques—Internal Rate of Return (IRR)—ExampleEnter CFs in CFLO and find NPVL and
NPVS at several discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
k is really no reason to do the trial and error yourself!
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
NPV ($)
Crossover
Point = 8.7%
S
IRRS = 23.6%
L
Discount Rate (%)
IRRL = 18.1%
Mutually Exclusive Projects is really no reason to do the trial and error yourself!
NPV
k< 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
L
k> 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
S
IRRs
Rankings of S and L were consistent because K was 10%
%
k 8.7 k
IRRL
Crossover
rate = 8.7%
1. Find cash flow differences between
the projects. Project L minus
Project S
CashL
(100)
10
60
80
CashS
(100)
70
50
20
Difference
0
60
10
60
2. Enter these differences in CFLO is really no reason to do the trial and error yourself!
register, then press IRR. Crossover
rate = 8.68, rounded to 8.7%.
3. Can subtract S from L or vice versa,
but better to have first CF negative.
4. If profiles don’t cross, one project
dominates the other.
1) Size (scale) differences. Smaller
project frees up funds at t = 0 for
investment. The higher the discount
rate, the more valuable these funds,
so high k favors small projects.
2) Timing differences. Project with
faster payback provides more CF in
early years for reinvestment. If k is
high, early CF especially good, NPVS
> NPVL.
Q: Which of the two following mutually exclusive projects should a firm purchase?
C0
C1
C2
C3
C4
C5
C6
ShortLived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%)
($1,500)
$750
$750
$750



LongLived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%)
Example
($2,600)
$750
$750
$750
$750
$750
$750
A: The IRR method argues for undertaking the ShortLived Project while the NPV method argues for the LongLived Project. We’ll correct for the unequal life problem by using the EAA Method. Both the EAA and Replacement Chain methods will lead to the same decision.
Comparing Projects with Unequal Lives—ExampleThe EAA Method equates each project’s original NPV to an equivalent annual annuity. For the ShortLived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%); while the LongLived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%). Since the LongLived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method.
Example
Comparing Projects with Unequal Lives—Example