Alternative Investment Rules
(Text reference: Chapter 6)
Topics
data for examples
net present value (NPV) rule
internal rate of return (IRR) rule
payback rule
discounted payback rule
average accounting return (AAR) rule
profitability index (PI) rule
techniques used in practice
AFM 271 - Alternative Investment Rules
Slide 1
Data for Examples
we will consider the following projects:
Project A: cost at (t = 0) = 200,000
period
1
2
3
cash flows
100,000
60,000
110,000
net income
20,000
30,000
20,000
Project B: cost at (t = 0) = 30,000
period
1
2
3
cash flows
20,000
10,000
15,000
net income
6,000
3,000
6,000
Project C: cost at (t = 0) = 200,000
period
1
2
3
cash flows
180,000
60,000
10,000
assume a discount rate of 10% for all three projects
AFM 271 - Alternative Investment Rules
Slide 2
Net Present Value (NPV) Rule
definition: NPV = PVfuture cash flows − cost at t = 0
NPV rule:
for independent projects: accept if NPV ≥ 0
for mutually exclusive projects: accept project with
highest NPV ≥ 0
calculate NPVA :
NPVA = 23,140, NPVB = 7,716
if independent: choose both A and B
if mutually exclusive: choose A
AFM 271 - Alternative Investment Rules
Slide 3
Cont’d
NPV rule analysis:
Advantages
Disadvantages
- based on cash flow
- must forecast all cash flows
- considers all cash flows
- can be hard to estimate discount rate
- discounts cash flows (and incorporates
time value of money)
notes:
accepting positive NPV projects benefits
shareholders by increasing the PV of their wealth
an NPV profile is useful for analyzing the sensitivity
of the NPV to the appropriate discount rate. The
profile plots NPV as a function of the discount rate.
AFM 271 - Alternative Investment Rules
Slide 4
Cont’d
NPV profile
discount rate r
5%
10%
15%
20%
NPVA
44,682
23,140
4,652
(11,343)
15%
20%
NPV
50,000
40,000
30,000
20,000
10,000
0
5%
10%
r
−10,000
AFM 271 - Alternative Investment Rules
Slide 5
Internal Rate of Return (IRR) Rule
definition: IRR is the discount rate which results in NPV = 0
(basic) IRR rule:
for independent projects: accept if IRR ≥ OCC
for mutually exclusive projects: accept project with highest
IRR ≥ OCC (if the projects are the same size)
calculate IRRA :
IRRA = 16.4%, IRRB = 25.2%
if independent: choose both A and B
if mutually exclusive: project sizes differ, so can’t tell
AFM 271 - Alternative Investment Rules
Slide 6
Cont’d
IRR rule analysis:
Advantages
Disadvantages
- better than alternatives such as payback, AAR
- mutually exclusive - scale
- more intuitive than NPV
- mutually exclusive - timing
- coincides with NPV for simple examples
- investing vs. financing
- single number summary of
- multiple IRRs
- comparison to discount rate
project’s profitability
with non-flat term structure
notes:
most important alternative to the NPV approach
IRR ≥ discount rate ⇒ NPV ≥ 0 (in simple cases)
in simple cases, always yields same decision as NPV for
independent projects
trial and error calculation (like yield to maturity for bonds)
AFM 271 - Alternative Investment Rules
Slide 7
Cont’d
IRR problem: mutually exclusive - scale
affects mutually exclusive project decisions only
do you prefer larger $ returns or larger % returns?
calculate incremental IRR:
AFM 271 - Alternative Investment Rules
Slide 8
Cont’d
IRR problem: mutually exclusive - timing
affects mutually exclusive project decisions only
discount rate r
5%
10%
15%
20%
NPVA
44,682
23,140
4,652
(11,343)
NPVC
34,489
20,736
8,466
(2,546)
NPV
50,000
A
40,000
C
30,000
20,000
10,000
0
5%
10%
15%
20%
r
−10,000
AFM 271 - Alternative Investment Rules
Slide 9
Cont’d
IRR problem: mutually exclusive - timing
calculate incremental IRR:
AFM 271 - Alternative Investment Rules
Slide 10
Cont’d
IRR problem: investing/lending vs. financing/borrowing
affects mutually exclusive and independent projects
consider a project D with cash flows exactly the reverse of
project A cash flows (e.g. D = borrowing):
period
0
1
2
3
Project A
-200,000
100,000
60,000
110,000
Project D
200,000
-100,000
-60,000
-110,000
we find:
NPVA = 23,140, NPVD = −23,140
IRRA = 16.4%, IRRD = 16.4%
IRR rule is reversed for financing/borrowing type projects:
for investing/lending, rule is accept if IRR ≥ OCC
for financing/borrowing, rule is accept if IRR ≤ OCC
note: only works if sign of cash flows changes only once
AFM 271 - Alternative Investment Rules
Slide 11
Cont’d
IRR problem: multiple IRRs
affects mutually exclusive and independent projects
consider project E:
period
0
1
2
Project E
-4,000
25,000
-25,000
we find two IRRs, IRRE = 25% and 400% (verify that
each of these discount rates results in NPV = 0)
if sign of cash flows changes n times, there can be n
different IRRs
which IRR is correct?
solution:
with changing signs, ignore IRR and use NPV
AFM 271 - Alternative Investment Rules
Slide 12
Cont’d
IRR problem: non-flat term structure
affects mutually exclusive and independent projects
a non-flat term structure implies that discount rates vary
depending on the timing of future cash flows
recall
T
Ct
t
t=0 (1 + rt )
NPV = ∑
can be hard to compare IRR to the entire term structure of
interest rates
example: two year project, IRR = 5%, r1 = 4%, r2 = 6%
solution:
if term structure of interest rates is important, ignore IRR
and use NPV
AFM 271 - Alternative Investment Rules
Slide 13
Payback Rule
definition: the payback period is the time required for an
investment to recover its cost
payback rule:
for independent projects: accept if payback ≤ threshold
for mutually exclusive projects: accept project with shortest
payback ≤ threshold
calculate payback for Project A:
paybackA = 2.36 periods, paybackB = 2 periods
if independent: choose B only
if mutually exclusive: choose B only
AFM 271 - Alternative Investment Rules
Slide 14
Cont’d
payback rule analysis:
Advantages
Disadvantages
- simple rule (easy to use)
- ignores time value of money
- may be important for firms
- ignores cash flows after threshold
with liquidity problems
- ignores risk differences
between projects
- arbitrary payback threshold
notes:
gives the number of years to recover investment cost
becomes unreliable as time value of money
becomes more important (i.e. larger number of
periods, larger discount rate)
AFM 271 - Alternative Investment Rules
Slide 15
Discounted Payback Rule
definition: the discounted payback period is the time required
for an investment to recover its cost, after discounting the
project cash flows
discounted payback rule:
for independent projects: accept if discounted payback ≤
threshold
for mutually exclusive projects: accept project with shortest
discounted payback ≤ threshold
calculate discounted payback for Project A:
AFM 271 - Alternative Investment Rules
Slide 16
Cont’d
discounted payback for A = 2.72 periods, for B = 2.32 periods
if independent: choose neither
if mutually exclusive: choose neither
discounted payback period rule analysis:
Advantages
Disadvantages
- simple rule (easy to use)
- arbitrary payback threshold
- useful for firms
- ignores cash flows after threshold
with liquidity problems
- considers timing of cash flows
notes:
- ignores some risk differences
between projects
- can be hard to estimate discount rate
discounted payback period > payback period
if we have already discounted all cash flows, just use NPV
AFM 271 - Alternative Investment Rules
Slide 17
Average Accounting Return (AAR) Rule
definition: AAR is average project earnings after taxes and
depreciation, divided by average book value of investment
during its life
AAR rule:
for independent projects: accept project if AAR ≥ threshold
mutually exclusive projects: accept project with highest
AAR ≥ threshold
calculate AAR for Project A:
AFM 271 - Alternative Investment Rules
Slide 18
Cont’d
AARA = 23.3%, AARB = 33.3%
if independent: choose both A and B
if mutually exclusive: choose B
average accounting return (AAR) rule analysis:
Advantages
Disadvantages
- simple rule (easy to use)
- does not use cash flows
- sensitive to accounting methods
and estimates
- ignores timing of cash flows
- arbitrary threshold rate
- ignores risk differences
between projects
AFM 271 - Alternative Investment Rules
Slide 19
Profitability Index (PI) Rule
definition: PI =
PV of cash flows after initial investment
initial investment
PI rule:
for independent projects: accept if PI ≥ 1
for mutually exclusive projects: accept project with highest
PI ≥ 1 (if they are the same size)
calculate PI for Project A:
PIA = 1.12, PIB = 1.26
if independent: choose both A and B
if mutually exclusive: project sizes differ, so can’t tell
AFM 271 - Alternative Investment Rules
Slide 20
Cont’d
PI problem: mutually exclusive - scale
affects mutually exclusive project decisions only
calculate incremental PI:
AFM 271 - Alternative Investment Rules
Slide 21
Cont’d
profitability index (PI) rule analysis:
Advantages
Disadvantages
- reflects time value of money
- mutually exclusive - ignores scale
- considers all cash flows
- can be hard to estimate discount rate
notes:
if PI > 1, then NPV > 0!
can overcome the “scale problem” by looking at PI of
incremental cash flows
useful when there is capital rationing (i.e. insufficient
capital to undertake all desirable projects)
rank projects according to PIs, and invest in
projects with highest PIs until all capital is used
NPV rule is just as easy to use as PI (and doesn’t
suffer from scale problems)
AFM 271 - Alternative Investment Rules
Slide 22
Techniques Used in Practice
see text pp. 177-178
based on a 1995 survey of CFOs of large Canadian
industrial firms, discounted cash flow methods (IRR,
NPV) are the most popular methods
payback is also quite popular
most firms use NPV or IRR along with payback or AAR
payback is most popular among small firms and for
firms with CEOs who do not have an MBA
firms in industries where cash flows are easier to
forecast are more likely to use IRR or NPV
AFM 271 - Alternative Investment Rules
Slide 23