Consider the following cash flows:
Cash Flows
Year Project A Project B
0 ($345,000) ($330,000)
1 $100,000
$40,000
2 $100,000
$80,000
3 $100,000 $120,000
4 $100,000 $160,000
5 $100,000 $180,000
6 $100,000 $210,000
1. Calculate the payback period for projects A and
B. Which project should be chosen based on
payback?
2. Calculate the NPV for projects A and B. Which
project should be chosen based on NPV?
Assume a cost of capital of 15 percent.
3. Calculate the IRR for projects A and B. Which
project should be chosen based on IRR? Assume
a cost of capital of 15 percent.
1. Payback Period: Project A = 3.45 years
Project B = 3.5625 years
Choose Project A since it has the shortest payback.
2.
 1

1
NPVA  345, 000  $100, 000 

  $33, 448
6
 0.15 0.15 1.15  
$40, 000 $80, 000 $120, 000 $160, 000



2
3
1.15
1.15
1.15
1.154
$180, 000 $210, 000


5
1.15
1.156
NPVB  $115, 937
NPVB  330, 000 
Since Project B has a higher NPV choose project B.
Multiple IRRs
2. IRRA= 18.54 percent
IRRB= 24.41 percent
Choose Project B.
Consider the following cash flow series:
Year Project A
0 ($45,000)
1
$80,000
2
$15,000
3 ($55,000)
4
$10,000
5
$45,000
6 ($60,000)
1. How many sign changes occur?
2. What is the NPV if the discount rate is 12%?
3. Calculate the IRR(s).
4. Should the project be accepted?
Multiple IRRs
1. There are 4 sign changes
2.
$80,000 $15, 000 $55, 000
NPV = -$45,000 


2
1.12
1.12
1.12 3
$10,000 $45, 000 $60, 000



4
5
1.12
1.12
1.126
NPV  $730
3. The NPV Profile is given below:
10000
5000
%
%
80
%
10
0%
12
0%
14
0%
16
0%
18
0%
20
0%
22
0%
24
0%
26
0%
28
0%
30
0%
32
0%
60
40
20
NPV
0
-5000
%
0
-10000
-15000
-20000
-25000
-30000
Cost of Capital
There are two IRRs. The first is 10.53 percent, and
the second is 58.09 percent. How can we check to
make sure these IRRs are correct?
4. Since the NPV is positive, the project should be
accepted. We really can’t use IRR in this situation.
Conflicts between NPV and IRR when choosing between mutually exclusive projects
Consider the following mutually exclusive projects:
Cash Flows
Year Project A Project B
0 ($335,000) ($330,000)
1
$225,000
$500
2
$112,000
$80,000
3
$87,000
$120,000
4
$10,000
$120,000
5
$12,000
$125,000
6
$2,000
$140,000
The cost of capital is 9 percent.
1. Calculate the NPV and IRR for projects A and B.
2. According to NPV which project should be
chosen?
3. According to IRR which project should be chosen?
4. What is the crossover rate?
Conflicts between NPV and IRR when choosing between mutually exclusive projects
1. NPVA = $48,946; NPVB= $80,185
IRRA = 18.04%; IRRB = 15.10%
2.
3.
4.
NPV Profile
300000
250000
200000
100000
50000
-150000
-200000
Cost of Capital
41%
38%
34%
30%
26%
23%
19%
15%
11%
-100000
8%
-50000
4%
0
0%
NPV
150000
Conflicts between NPV and IRR when choosing between mutually exclusive projects
$225, 000 - $500
1  IRR
$87, 000  $120, 000
NPV = 0 = - $335, 000  $330, 000 

$112, 000 - $80, 000

$10, 000 - $120, 000

1  IRR 
1  IRR 
2
4


1  IRR 
$12, 000  $125, 000
1  IRR 
$2, 000  $140, 000
1  IRR 
3
6
 IRR = 12.88915 percent
How can we check to make sure our answer is
correct?
5