Payback

1
CHAPTER 6 Capital Budgeting Decision Methods

• Payback
• Net present value (NPV)
• Internal rate of return (IRR)
• Modified internal rate of return (MIRR)

2
Steps

• 1. Generate ideas.
• 2. Estimate the CFs (inflows and outflows).
• 3. Assess the riskiness of the CFs.
• 4. Determine the project cost of capital.
• 5. Find NPV, IRR, and/or MIRR.
• 6. Accept if NPV gt 0 and/or IRR gt cost of
  capital.

3
7-
What is the difference between independent and
mutually exclusive projects?

• Projects are independent if the cashflows of one
  are not affected by the acceptance of the other
• Projects are mutually exclusive if acceptance of
  one impacts adversely on the cashflows of the
  other

4
Example of mutually exclusive projects
Bridge vs. boat to get products across a river.
5
7-
What is the difference between normal and
non-normal projects?

• Projects are normal if they have outflows or
  costs in the first year(s) followed by a series
  of inflows
• Projects are non-normal if one or more outflows
  occur after the inflows have begun

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Inflow () or Outflow (-) in year 0 1 2 3 4 5 N
NN - N - - NN - - - N
- - - NN - - - NN
7
Cashflow data we will use for examples
Year 0 1 2 3
L -150 15 90 120
S -150 105 75 30
? L-S 0 -90 15 90
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What is the payback period?

• The expected number of years required to recover
  a projects cost, i.e. how long will it take to
  get our money back?

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Payback for Project L (Long Most CFs in later
years)
CFt Cumulative CF
PaybackL 2 45/120 2.375 years
10
Payback for Project S (Short Most CFs in early
years)
CFt Cumulative CF
PaybackS 1 45/75 1.6 years
11
What is the rationale for the payback period?

• Its a type of breakeven analysis. It tells
  us when the project will break even in a cash
  flow sense.

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Strengths of Payback
1. Indication of a projects risk and
liquidity. 2. Easy to calculate and understand.
Weaknesses

• 1. Ignores time value of money.
• 2. Ignores CFs occurring after payback.

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If maximum acceptable payback is two years, what
is the best decision if L and S are
independent? Mutually exclusive?

• If required payback is 2 years, Project S would
  be accepted and L would not.
• In this situation, it makes no difference whether
  the projects are independent of mutually
  exclusive.

14
Should capital budgeters even look at payback?

• Some firms do calculate payback and give it some
  weight in capital budgeing decisions.
• Its not the primary criterion rather it is used
  as one meausre of a projects liquidity and
  riskiness.

15
NPV is the sum of the PVs of a projects inflows
and outflows.
n

CFt
?
NPV
(1 k)t
t 0
If all costs at t 0, then
CFt
n
- CF0
NPV
?
(1 k)t
t 1
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What is project Ls NPV?
NPVS 29.98
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Calculator Solution
Enter in cash flows for L
CF0
-150 15 90 120 10
CF1
CF2
CF3
28.18 NPVL
NPV
I
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Rationale for NPV method?

• NPV PV inflows - PV costs Net gain in
  wealth
• Accept project if NPV gt 0
• Choose between mutually exclusive projects on the
  basis of higher positive NPV. Adds most to value.

19
Using the NPV method, which project(s) should be
accepted?

• If Projects S and L are independent, accept
  both NPV gt 0.
• If Projects S and L are mutually exclusive,
  accept S because NPVS gt NPVL.

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Would the NPVs change if the cost of capital
changed?
CFt
n
NPV
?
(1k)t
t 0
YES NPV is dependent on k
If k , NPV If k , NPV
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7-
Internal Rate of Return (IRR)

• IRR is the discount rate which forces the NPV to
  equal zero
• (PV of inflows PV of outflows)

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7-
NPV Enter k, solve for NPV
IRR Enter NPV 0, solve for IRR
CFt
n

?
0
(1IRR)t
t 0
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What is Project Ls IRR?
Enter in cash flows for L
CF0
-150 15 90 120
CF1
CF2
23.56
IRR
CF3
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How is a projects IRR related to a bonds YTM?

• They both measure percentage
• rate of return. IRR is to a capital
• project what the YTM is to a bond.
• A bond YTM is its IRR.

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Internal rate of return rationale
If IRR k, then project cashflows are just
sufficient to provide investors their required
rates of return
IRR gt k implies some return is left over to boost
shareholder returns. Example k WACC 10 IRR
15. Profitable.
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IRR acceptance criteria

• If projects are independent,
• accept all projects with IRR gtk
• reject all projects with IRR lt k
• If projects are mutually exclusive,
• accept project with the highest IRR gt k

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Are S and/or L acceptable by IRR?

• If S and L are independent, accept both. IRR gt k
  10.
• If S and L are mutually exclusive, accept S
  because IRRS gt IRRL.

28
Are IRRs affected by changes in the cost of
capital?

• NO. IRRs are independent of the cost of capital.
• However, the acceptability of projects could
  change.

29
Construct the Projects NPV Profiles
Enter CFs in CFLO and find NPVL and NPVS at
several discount rates k NPVL NPVS 0 75 60
5 50 44 10 28 30 15 10 18 20
- 6 7
30
k NPVL NPVS 0 75 60 5 50 44 10 28
30 15 10 18 20 - 6 7
NPV 80 60 40 20
Crossover point 8.7
IRRL 18.1
IRRS 23.6
0 5 10 15 20 25 k
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NPV and IRR always lead to the same accept/reject
decision for any independent project.
IRR lt k and NPV lt 0
IRR gt k and NPV gt 0
NPV
ACCEPT
REJECT

IRR
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Mutually Exclusive Projects
NPV 80 60 40 20
L
k lt 8.7 NPVL gt NPVS IRRSgt IRRL CONFLICT k gt
8.7 NPVSgt NPVL IRRS gt IRRL NO CONFLICT
IRRL
S
IRRS
0 8.7 15 20 25 k
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How do you find the crossover rate?

• Find the CF differences between the projects.
• Enter the differences in CFLO, then press IRR.
  Crossover rate 8.68.
• Can subtract S from L or vice versa, but better
  to have first CF negative.
• If profiles do not cross, one project dominates
  the other.

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Why do NPV profiles cross?

• Timing differences A project with faster
  payback provides more CF in early years for
  reinvestment. If k is high, early CF is
  especially good and NPVS gt NPVL.
• Size (scale) differences Smaller project frees
  up funds at t 0 for investment. The higher the
  opportunity cost, the more valuable these funds
  are. High k favors small projects.

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Reinvestment rate assumptions

• NPV assumes reinvestment at k (opportunity cost
  of capital).
• IRR assumes reinvestment at IRR.
• Reinvestment at opportunity cost, k, is more
  realistic, so NPV method is best. NPV should be
  used to choose between mutually excusive projects.

36
Managers like rates- they can visualize IRR
better than NPV. Can we give them a better IRR?

• YES. MIRR is the discount rate which causes the
  PV of a projects terminal value (TV) to equal
  the PV of its costs. Since TV is found by
  compounding inflows at the opportunity cost of
  capital,
• MIRR assumes cash inflows are reinvested at k

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MIRR for Project L (k 10)
0
1
2
3
10
-150
15
90
120
10
237.15
TV of inflows
PV of outflows
237.15 (1MIRR)3
MIRRL 16.5 MIRRS 16.9
150
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Calculator Solution

• First enter CFs for t 1-3 and solve for PV of
  inflows 178.17
• Calculate FV of inflowsPV -178.17 n 3, I
  10 FV 237.15
• Calculate MIRRFV 237.15 PV -150 N 3
  I 16.5 MIRRL

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Why use MIRR vs. IRR?

• MIRR correctly assumes reinvestment at the
  opportunity cost of capital.
• MIRR also avoids problems with nonnormal
  projects.
• Managers like rate of return comparisons and MIRR
  is better for this than IRR.

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Is MIRR better than NPV?

• NO. MIRR does not always lead to the same
  decision as NPV for mutually exclusive projects.
  In particular, small projects often have a higher
  MIRR, but a lower NPV than larger projects.
• NPV remains the conceptually best decision rule.

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The Pavilion Project Find NPV and IRR
Year 0 1 2
CF -400,000 2,500,000 -2,500,000
k 10
Enter CFs in CFLO, enter I 10 NPV
-193.39 IRR ERROR. WHY?
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We got IRR ERROR because there are 2 IRRs.
Nonnormal CFs- two sign changes.
NPV Profile
225
100 400
-400
IRR1 25
IRR2 400
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Logic of Multiple IRRs

• At very low discount rates, the PV of CF2 is
  large negative, so NPV lt 0.
• At very high discount rates, the PV of CF1 and
  CF2 are both low, so CF0 dominates and again NPV
  lt 0.
• In between, the discount rate hits CF2 harder
  than CF1, so NPV gt 0, resulting in 2 IRRs.

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Could find IRR with HP-10B calculator as follows

• Enter CFs as before.
• Enter a guess as to IRR by storing the guess.
  Try 1010 STOIRR 25 lower IRR.
• Now guess large IRR, say 200200 STOIRR
  400 upper IRR.

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When there are nonnormal CFs and more than one
IRR, use MIRR.
0 1 2
-400,000 2,500,000 -2,500,000
PV outflows _at_ 10 -2,466,115.70 PV inflows _at_
10 2,750,000.00 MIRR 5.6
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Accept Project P?

• NO. Reject it because
• MIRR 5.6 lt k 10
• Also, if MIRR lt k, NPV will be
• negative NPV -193,388.43