flows come in from these projects, the firm will either pay them out to investors, or
use them as a substitute for outside capital which costs 10 percent.
Thus, since these
cash flows are expected to save the firm 10 percent, this is their opportunity cost
reinvestment rate.
The IRR method assumes reinvestment at the internal rate of return itself, which
is an incorrect assumption, given a constant expected future cost of capital, and ready
access to capital markets.
Answers and Solutions:
1
0
1
 18
N P V ( M i l l i o n s o f D o l l a r s )
C r o s s o v e r R a t e = 1 1 . 7 %
I R R
A
= 1 5 . 0 3 %
I R R
B
= 2 2 . 2 6 %
A
B
C o s t o f C a p i t a l ( % )
1 2 5
I R R
= 1 1 . 7 %
1 0
1 0 0
7 5
1 5
5 0
2 0
2 5
2 5
 2 5
3 0
 5 0
5
1
0
1
16
Plane A:
Expected life = 5 years; Cost = $100 million; NCF = $30 million; COC =
12%.
Plane B:
Expected life = 10 years; Cost = $132 million; NCF = $25 million; COC =
12%.
0
1
2
3
4
5
6
7
8
9
10
A:











100
30
30
30
30
30
30
30
30
30
30
100
70
Enter these values into the cash flow register:
CF
0
= 100; CF
14
= 30; CF
5
= 70; CF
6
10
= 30.
Then enter I = 12, and press the NPV key to get NPV
A
= 12.764
$12.76
million.
0
1
2
3
4
5
6
7
8
9
10
B:











132
25
25
25
25
25
25
25
25
25
25
Enter these cash flows into the cash flow register, along with the interest rate, and
press the NPV key to get NPV
B
= 9.256 ≈ $9.26 million.
Project A is the better project and will increase the company's value by $12.76
million.
The EAA of plane A is found by first finding the PV: N = 5, I/YR = 12, PMT = 30,
FV = 0; solve for PV = −108.143. The NPV is $108.143 − $100 = $8.143 million. We
convert this to an equivalent annual annuity by inputting: N = 5, I/YR = 12, PV =
−8.143, FV = 0, and solve for PMT = EAA = 2.259 ≈ $2.26 million.
For plane B, we already found the NPV of 9.256. We convert this to an equivalent
annual annuity by inputting: N = 10, I/YR = 12, PV = −9.256, FV = 0, and solve for
PMT = EAA = 1.638 ≈ $1.64 million.
Answers and Solutions:
1
0
1
 19
1
0
1
17
0
1
2
3
4
5
6
7
8
A:









10
4
4
4
4
4
4
4
4
10
6
Machine A's simple NPV is calculated as follows:
Enter CF
0
= 10 and CF
14
= 4.
Then enter I = 10, and press the NPV key to get NPV
A
= $2.679 million.
However,
this does not consider the fact that the project can be repeated again.
Enter these
values into the cash flow register:
CF
0
= 10; CF
13
= 4; CF
4
= 6; CF
58
= 4.
Then
enter I
/YR
= 10, and press the NPV key to get Extended NPV
A
= $4.5096 ≈ $4.51
million.
0
1
2
3
4
5
6
7
8
B:









15
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
Enter these cash flows into the cash flow register, along with the interest rate, and
press the NPV key to get NPV
B
= $3.672 ≈ $3.67 million.
Machine A is the better project and will increase the company's value by $4.51
million.
The EAA of machine A is found by first finding the PV: N = 4, I/YR = 10, PMT =
4, FV = 0; solve for PV = −12.679. The NPV is $12.679 − $10 = $2.679 million. We
convert this to an equivalent annual annuity by inputting: N = 4, I/YR = 10, PV =
−2.679, FV = 0, and solve for PMT = EAA = 0.845 ≈ $0.85 million.
For machine B, we already found the NPV of 3.672. We convert this to an
equivalent annual annuity by inputting: N = 8, I/YR = 10, PV = −3.672, FV = 0, and
solve for PMT = EAA = 0.688 ≈ $0.69 million.
1
0
1
18 a.
Using a financial calculator, input the following:
CF
0
= 190000, CF
1
= 87000, N
j
=
3, and I = 14 to solve for NPV
1903
= $11,981.99 ≈ $11,982 (for 3 years).
Adjusted NPV
1903
= $11,982 + $11,982/(1.14)
3
= $20,070.
Using a financial calculator, input the following:
CF
0
= 360000, CF
1
= 98300, N
j
=
6, and I = 14 to solve for NPV
3606