Crossover rate
Crossover rate is the discount rate
that makes the NPVs of two
projects equal
How to find the crossover rate?
Compute the (B-A or A-B) cash flows
and find IRR of (B-A or A-B)
50

Find IRR of (B-A)
51
Yea
r
Project
A
Project B
B-A
0
-$100
-$100
$0
1
50
20
-$30
2
40
40
$0
3
40
50
$10
4
30
60
$30
IRR
24%
21%
11.1%
Crossover rate

Question
- Crossover rate
You are comparing two mutually exclusive projects.
The crossover point is 12.3 percent. You have
determined that you should accept project A if the
required return is 13.1 percent. This implies you
should:
A.
always accept project A.
B.
be indifferent to the projects at any discount rate above
13.1 percent.
C.
always accept project A if the required return exceeds
the crossover rate.
D.
accept project B only when the required return is equal
to the crossover rate.
E.
accept project B if the required return is less than 13.1
percent.
52

IRR: advantages &
disadvantages
Advantages
Disadvantages
Closely related to NPV,
often leading to
identical decisions
May result in multiple
answers
Easy to understand
and communicate
May lead to incorrect
decisions in
comparisons of
mutually exclusive
investments
53

NPV, IRR, PI problem
A firm is considering a project
that costs $1,200 and generates
cash flows of $500 in the first
year, $600 in the second year
and $700 in the third year.
Compute the NPV, IRR and PI of
this project. The appropriate
discount rate is 10 percent.
54

Yr 0
Yr1
Yr2
Yr3
-1200
500
600
700
Conventional cash flows
Not a case of mutually exclusive
events (no other event you need
to consider)
NPV, PI, and IRR give the same
answer
55

1) NPV=(500/1.1+600/1.1
2
+700/1.1
3
)-1200=
276.33 (>0)
=>
Accept the project
Or using a financial calculator
CF0=-1200; C01=500; F01=1; C02=600; F02=1;
C02=700; C03=1; NPV (I=10); CPT
NPV= 276.33
2) IRR
Using a financial calculator
CF0= -1200; C01=500; F01=1; C02=600; F02=1;
C02=700; C03=1; IRR CPT
IRR=21.92%
(at IRR, NPV=0)
Accept
the project since IRR(=21.92%) > required
return(=10%)
3) PI
PI = PV of cash inflows/PV of cash outflows
= (500/1.1+600/1.1
2
+700/1.1
3
)/1200
= 1476.33/1200=
1.23
Accept the project since PI is greater than 1.
56

Payback period
Amount of time required to
generate cash flows sufficient to
recover initial cost
Payback Rule:
Accept a project if its payback period
is less than some prespecified
number of years (“cutoff point”)
57

Payback problem
Compute payback period for the
following projects
Year
A
B
C
0
-$9,000
-$11,000
-$200
1
2,000
2,000
100
2
3,000
3,000
100
3
4,000
4,000
-200
4
5,000
5,000
200
5
6,000
6,000
C=2 yrs or 4 yrs? Both are correct ; ambiguous answers in
this case
58
B=3yr+2000/5000=3.4 yrs
=3yrs
(since
-9000+2000+3000+4000=0)

Payback does not consider cash
flows after cutoff date
Your firm has two projects: Long and
Short. The discount rate is 15% and
the cutoff point is 2 years.
Year
Long
Short
0
-$250
-$250
1
100
100
2
100
200
3
100
0
4
100
0
Payback period
(yrs)
2.5
1.75
NPV
$35.50
-$11.81
59
•
Payback period rule: Choose
Short
•
NPV rule: Choose
Long