11-23 a.
Project A:
Using a financial calculator, enter the following data:
CF
0
= -30; CF
1
= 5; CF
2
= 10; CF
3
= 15; CF
4
= 20; I/YR = 10; and solve for NPV
A
= $7.74;
IRR
A
= 19.19%.
Calculate MIRR
A
at WACC = 10%:
Step 1: Calculate the NPV of the uneven cash flow stream, so its FV can then be calculated.
With a financial calculator, enter the cash flow stream into the cash flow registers, then
enter I/YR = 10, and solve for NPV = $37.739.
Step 2: Calculate the FV of the cash flow stream as follows:
Enter N = 4, I/YR = 10, PV = -37.739, and PMT = 0 to solve for FV = $55.255.
Step 3: Calculate MIRR
A
as follows:
Enter N = 4, PV = -30, PMT = 0, and FV = 55.255 to solve for I/YR = 16.50%.
Payback A (cash flows in millions):
Annual
Period
Cash Flows
Cumulative
0
($30)
($30)
1
5
(25)
2
10
(15)
3
15
0
4
20
20
Payback
A
= 3 years.
Discounted Payback A (cash flows in millions):
Annual
Discounted @10%
Cumulative
Period
Cash Flows
Cash Flows
Cash Flows
0
($30)
($30.00)
($30.00)
1
5
4.55
(25.45)
2
10
8.26
(17.19)
3
15
11.27
(5.92)
4
20
13.66
7.74
Discounted Payback
A
= 3 + $5.92/$13.66 = 3.43 years.

284
Comprehensive/Spreadsheet Problem
Chapter 11:
The Basics of Capital Budgeting
Project B:
Using a financial calculator, enter the following data:
CF
0
= -30; CF
1
= 20; CF
2
= 10; CF
3
= 8; CF
4
= 6; I/YR = 10; and solve for NPV
B
= $6.55; IRR
B
= 22.52%.
Calculate MIRR
B
at WACC = 10%:
Step 1: Calculate the NPV of the uneven cash flow stream, so its FV can then be calculated.
With a financial calculator, enter the cash flow stream into the cash flow registers, then
enter I/YR = 10, and solve for NPV = $36.55.
Step 2: Calculate the FV of the cash flow stream as follows:
Enter N = 4, I/YR = 10, PV = -36.55, and PMT = 0 to solve for FV = $53.52.
Step 3: Calculate MIRR
B
as follows:
Enter N = 4, PV = -30, PMT = 0, and FV = 53.52 to solve for I/YR = 15.57%.
Payback B (cash flows in millions):
Annual
Period
Cash Flows
Cumulative
0
($30)
($30)
1
20
(10)
2
10
0
3
8
8
4
6
14
Payback
B
= 2 years.
Discounted Payback B (cash flows in millions):
Annual
Discounted @10%
Cumulative
Period
Cash Flows
Cash Flows
Cash Flows
0
($30)
($30.00)
($30.00)
1
20
18.18
(11.82)
2
10
8.26
(3.56)
3
8
6.01
(2.45)
4
6
4.10
6.55
Discounted Payback
B
= 2 + $3.56/$6.01 = 2.59 years.
Summary:
Project A
Project B
NPV
$7.74
$6.55
IRR
19.19%
22.52%
MIRR
16.50%
15.57%
Payback
3 years
2 years
Discounted Payback
3.43 years
2.59 years
b.
If the two projects are independent, both projects will be accepted because their NPVs are
greater than zero.
c.
If the two projects are mutually exclusive, at WACC = 10% Project A should be chosen since
NPV
A
> NPV
B
.

Chapter 11:
The Basics of Capital Budgeting
Comprehensive/Spreadsheet Problem
285
d.
WACC
NPV
A
NPV
B
0%
$20.00
$14.00
5
13.24
9.96
10
7.74
6.55
15
3.21
3.64
19.19
0
1.52
20
(0.56)
1.13
22.52
(2.23)
0
-5
0
5
10
15
20
25
0%
5%
10%
15%
20%
25%
WACC (%)
NPV
($)
Project A
Project B
e.
At WACC = 5% and the two projects are mutually exclusive, NPV
A
> NPV
B
so choose Project A.
This doesn’t change our recommendation.
At WACC = 15% and the two projects are mutually
exclusive, NPV
B
> NPV
A
so choose Project B.
This does change our recommendation.
Both of
these decisions can be made from looking at the NPV profile in part d.
f.
The crossover rate is the cost of capital at which the NPV profiles of two projects cross and,
thus, at which the projects’ NPVs are equal.
At a cost of capital less than the crossover rate
there is a conflict between NPV and IRR but at a cost of capital greater than the crossover rate
there is no conflict between NPV and IRR.