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CHAPTER 10Capital Budgeting
Ch. 9 in the 4th edition 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
Stand-Alone and Mutually Exclusive Projects A stand-alone project has no competing alternatives
The project is judged on its own viability Mutually exclusive projects are involved when selecting
one project excludes selecting the other
Characteristics of Business Projects
Project Cash Flows The first and usually most difficult step in capital
budgeting is reducing projects to a series of cash flows Business projects involve early cash outflows and later
inflows The initial outlay is required to get started
The Cost of Capital A firm’s cost of capital is the average rate it pays its
investors for the use of their money In general a firm can raise money from two sources: debt and
equity If a potential project is expected to generate a return greater
than the cost of the money to finance it, it is a good investment
Capital Budgeting Techniques
There are four basic techniques for determining a project’s financial viability: Payback (determines how many years it takes
to recover a project’s initial cost) Net Present Value (determines by how much
the present value of the project’s inflows exceeds the present value of its outflows)
Internal Rate of Return (determines the rate of return the project earns [internally])
Equivalent annual annuity (EAA)
Capital Budgeting Techniques—Payback
The payback period is the time it takes to recover early cash outflows Shorter paybacks are better
Payback Decision Rules Stand-alone projects
If the payback period < (>) policy maximum accept (reject)
Mutually Exclusive Projects If PaybackA < PaybackB choose Project A
Weaknesses of the Payback Method Ignores the time value of money Ignores the cash flows after the payback period
Relevant Cash Flows
Cash Flow (vs. Accounting Income)
Incremental Cash Flows Partial budget concept
year Project L $
Project S $
0 1
(100) 10
(100) 70
2 3
60 80
50 20
Example Projects
Payback for Project L(Long: Most CFs in out years)
10 8060
0 1 2 3
-100
=
CFt
Cumul -100 -90 -30 50
PaybackL 2 + 30/80 = 2.375 years
0
2.4
Project S (Short: CFs come quickly)
70 2050
0 1 2 3
-100CFt
Cumul -100 -30 20 40
PaybackL 1 + 30/50 = 1.6 years
0
1.6
=
10 8060
0 1 2 3
CFt
Cumul(PV) -100 -90.91 -41.32 18.79
Disc.payback
2 + 41.32/60.11 = 2.7 yrs
Discounted Payback: Uses discountedrather than raw CFs.
PVCFt -100
-100
10%
9.09 49.59 60.11
=
Recover invest + cap costs in 2.7 yrs.
Project L
Capital Budgeting Techniques—Payback: another example Consider the following cash flows
Year
0 1 2 3 4
Cash flow (Ci) ($200,000) $60,000 $60,000 $60,000 $60,000
Cumulative cash flows
($200,000) ($140,000) ($80,000) ($20,000) $40,000
Payback period occurs at 3.33 years.
Year
0 1 2 3 4
Cash flow (Ci) ($200,000) $60,000 $60,000 $60,000 $60,000
Payback period is easily visualized by the cumulative cash flows
Capital Budgeting Techniques—Payback— yet another example
Q: Use the payback period technique to choose between mutually exclusive projects A and B.
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800200C5
800200C4
350400C3
400400C2
400400C1
($1,200)($1,200)C0
Project BProject A
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 Why Use the Payback Method?
It’s quick and easy to apply Serves as a rough screening device Indicates how long to resolve uncertainty
The Present Value Payback Method Involves finding the present value of the
project’s cash flows then calculating the project’s payback
Capital Budgeting Techniques—Net Present Value (NPV)
NPV is the sum of the present values of a project’s cash flows at the cost of capital
outflows
inflows
1 2 n0 1 2 n
C C C C NPV
1+k 1+k 1+kPV
PV
If PVinflows > PVoutflows, NPV > 0
Capital Budgeting Techniques—Net Present Value (NPV)
NPV and Shareholder Wealth A project’s NPV is the net effect that
undertaking a project is expected to have on the firm’s value
A project with an NPV > (<) 0 should increase (decrease) firm value
Since the firm desires to maximize shareholder wealth, it should select the capital spending program with the highest NPV
NPV is the PV of economic profit
Capital Budgeting Techniques—Net Present Value (NPV)
Decision Rules Stand-alone Projects
NPV > 0 accept NPV < 0 reject
Mutually Exclusive Projects NPVA > NPVB choose Project A over B
Capital Budgeting Techniques—Net Present Value (NPV) Example
Q: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken?
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$2,000C2
$1,000C1
($5,000)C0
A: The NPV is found by summing the present value of the cash flows when discounted at the firm’s cost of capital.
Alpha 1 2 3
1,000 2,000 3,000 -5,000 NPV
1.12 1.12 1.12
-5,000 892.90 1,594.40 2,135.40
-5,000 4,622.70
($377.30)
Since Alpha’s NPV<0, it
should not be undertaken.
Use CFj on the cash flow
Show on the board
Techniques—Internal Rate of Return (IRR)
A project’s IRR is the return it generates on the investment of its cash outflows For example, if a project has the following cash flows
0 1 2 3
-5,000 1,000 2,000 3,000
Literally the IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow
If you lend yourself the money to make the investment, the IRR is the highest interest rate you could charge and the investment pay off the loan
The “price” of receiving the inflows
outflows
inflows
1 2 n0 1 2 n
C C C: C IRR
1 IRR 1 IRR 1 IRRPV
PV
Techniques—Internal Rate of Return (IRR)
Defining IRR Through the NPV Equation The IRR is the interest rate that makes a project’s NPV
zero
Solve for IRR one equation, one unknown, but usually impossible to
solve with algebra
Projectcost
Techniques—Internal Rate of Return (IRR) Decision Rules
Stand-alone Projects If IRR > cost of capital (or k) accept If IRR < cost of capital (or k) reject
Mutually Exclusive Projects IRRA > IRRB choose Project A over Project B
(but don’t use IRR to rank mutually exclusive projects)
Techniques—Internal Rate of Return (IRR) Calculating IRRs
Finding IRRs usually requires an iterative, trial-and-error technique
Guess at the project’s IRR Calculate the project’s NPV using this interest rate
If NPV is zero, the guessed interest rate is the project’s IRR
If NPV > (<) 0, try a new, higher (lower) interest rate
Techniques—Internal Rate of Return (IRR)—Example
Q: Find the IRR for the following series of cash flows:
If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital is 10%?
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$1,000
C1
($5,000)
C0
$2,000
C2
$3,000
C3
A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate.
1 2 3
1,000 2,000 3,000 -5,000 NPV
1.12 1.12 1.12
-5,000 892.90 1,594.40 2,135.40
-5,000 4,622.70
($377.30)
Since NPV<0, the project’s
IRR must be < 12%.
Techniques—Internal Rate of Return (IRR)—Example
We’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.
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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.$1307
$228
($83)9
($184)10
($377)12%
Calculated NPV
Interest Rate Guess
The exact IRR can be calculated using a financial calculator. The financial calculator uses the iterative process just demonstrated; however it is capable of guessing and recalculating much more quickly.
Okay, if you haven’t already pointed it out by now, there is really no reason to do the trial and error yourself!
Use the CFj calculator function (IRR key)
Cash flows -5000 1000 2000 3000
Techniques—Internal Rate of Return (IRR)
Technical Problems with IRR Multiple Solutions
Unusual projects can have more than one IRR Rarely presents practical difficulties
The number of positive IRRs to a project depends on the number of sign reversals to the project’s cash flows
Normal pattern involves only one sign change
The Reinvestment Assumption IRR method implicitly assumes cash inflows will be reinvested
at the project’s IRR For projects with extremely high IRRs, this is unlikely
When NPV and IRR disagree
Only when comparisons must be made Not stand alone analysis Use the NPV rankings, not the IRR
rankings
NPV Profile
A project’s NPV profile is a graph of its NPV vs. the cost of capital
It crosses the horizontal axis at the IRR
Construct NPV Profiles
Enter CFs in CFLO and find NPVL andNPVS at several discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
-10
0
10
20
30
40
50
60
0 5 10 15 20 23.6
NPV ($)
Discount Rate (%)
IRRL = 18.1%
IRRS = 23.6%
Crossover Point = 8.7%
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
S
L
Mutually Exclusive Projects
k 8.7 k
NPV
%
IRRs
IRRL
L
S
k< 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT k> 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
Crossover rate = 8.7%
Rankings of S and L were consistent because K was 10%
To find the crossover rate:1. Find cash flow differences between
the projects. Project L minus Project S
CashL
(100)
10
60
80
CashS
(100)
70
50
20
Difference0
-601060
2. Enter these differences in CFLOregister, then press IRR. Crossoverrate = 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 projectdominates the other.
Two reasons NPV profiles cross:
1) Size (scale) differences. Smallerproject frees up funds at t = 0 forinvestment. The higher the discountrate, the more valuable these funds,so high k favors small projects.
2) Timing differences. Project with faster payback provides more CF inearly years for reinvestment. If k ishigh, early CF especially good, NPVS
> NPVL.
Reinvestment Rate Assumptions
NPV assumes reinvest at k. IRR assumes reinvest at a rate
greater than the crossover rate. Reinvest at opp. cost, k, is more
realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.
Comparing Projects with Unequal Lives If a significant difference exists between
mutually exclusive projects’ lives, a direct comparison of the projects can be in error
The problem arises using the NPV method Longer lived projects often have higher NPVs Or shorter projects lower net present cost
Must consider if the investments are really a sequence
If not a sequence then NPV is correct.
Comparing Projects with Unequal Lives Two solutions exist
Replacement Chain Method Extends projects until a common time horizon is reached
For example, if mutually exclusive Projects A (with a life of 3 years) and B (with a life of 5 years) are being compared, both projects will be replicated so that they each last 15 years
Equivalent Annual Annuity (EAA) Method Replaces each project with an equivalent annuity (PMT)
that equates to the project’s original NPV That is, annualize the NPV (or net present cost)
Both methods give the same conclusion so I only use EAA
Comparing Projects with Unequal Lives—Example
Q: Which of the two following mutually exclusive projects should a firm purchase?
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Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%)
$750$750$750$750$750$750($2,600)
-
C5
-
C4
$750
C3
Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%)
$750
C1
($1,500)
C0
$750
C2
-
C6
A: The IRR method argues for undertaking the Short-Lived Project while the NPV method argues for the Long-Lived 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—Example
The EAA Method equates each project’s original NPV to an equivalent annual annuity. For the Short-Lived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%); while the Long-Lived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%). Since the Long-Lived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method.
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Review Steps:
1. Create ideas for capital investment
2. Estimate CFs (inflows & outflows).
3. Assess riskiness of CFs.
4. Determine k = WACC (adj. for risk).
5. Find NPV and/or IRR.
6. Accept if NPV > 0 and/or IRR > WACC.
7. If mutually exclusive, take the highest NPV
8. If mutu. excl. & lives differ take highest EAA
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