−
3.672, FV = 0, and
solve for PMT = EAA = 0.688
≈
$0.69 million.
10-18 a. Using a financial calculator, input the following:
CF
0
= -190000, CF
1
= 87000, N
j
=
3, and I = 14 to solve for NPV
190-3
= $11,981.99
≈
$11,982 (for 3 years).
Adjusted NPV
190-3
= $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
360-6
= $22,256.02
≈
$22,256 (for 6 years).
Both new machines have positive NPVs, hence the old machine should be
replaced.
Further, since its adjusted NPV is greater, choose Model 360-6.
The EAA of machine 190-3 is found by converting its NPV to an equivalent
annual annuity by inputting: N = 3, I/YR = 14, PV =
−
11,981.99, FV = 0, and solve
for PMT = EAA = 5,161.019
≈
$5,161.02.
The EAA of machine 360-6 is found by converting its NPV to an equivalent
annual annuity by inputting: N = 6, I/YR = 14, PV =
−
22,256.02, FV = 0, and solve
for PMT = EAA = 5,723.302
≈
$5,723.30.

Answers and Solutions:
10 - 20
10-19 a.
The project's expected cash flows are as follows (in millions of dollars):
Time
Net Cash Flow
0
($ 4.4)
1
27.7
2
(25.0)
We can construct the following NPV profile:
Discount Rate
NPV
0%
($1,700,000)
9
(29,156)
10
120,661
50
2,955,556
100
3,200,000
200
2,055,556
300
962,500
400
140,000
410
70,204
420
2,367
430
(63,581)
NPV (Mi l l i ons of Dol l ars)
Maxi mum
NPV at 80. 5%
Di scount
Rat e (%)
I RR
1
= 9.2%
I RR
2
= 420%
NPV approaches -$4. 0 as
t he cost of capit al
approaches
∞
3
2
- 4
1
- 2
1 0
- 3
- 1
- 4 . 4
2 0
8 0 . 5
4 2 0

Answers and Solutions:
10- 21
The table above was constructed using a financial calculator with the following
inputs:
CF
0
= -4400000, CF
1
= 27700000, CF
2
= -25000000, and I = discount rate to
solve for the NPV.
b.
If r = 8%, reject the project since NPV < 0.
But if r = 14%, accept the project because
NPV > 0.
c. Other possible projects with multiple rates of return could be nuclear power plants
where disposal of radioactive wastes is required at the end of the project's life, or
leveraged leases where the borrowed funds are repaid at the end of the lease life.
(See Chapter 20 for more information on leases.)
d.
Here is the MIRR for the project when r = 8%:
PV costs = $4,400,000 + $25,000,000/(1.08)
2
= $25,833,470.51.
TV inflows = $27,700,000(1.08)
1
= $29,916,000.00.
Now, MIRR is that discount rate which forces the PV of the TV of $29,916,000 over
2 years to equal $25,833,470.51:
$25,833,470.51 = $29,916,000(PVIF
r,2
).
Inputs
2
-25833470.51
0
29916000
Output
= 7.61
MIRR = 7.61%.
At r = 14%,
Inputs
2
-23636688.21
0
31578000
Output
= 15.58
MIRR = 15.58%.
PV costs = $4,400,000 + $25,000,000/(1.14)
2
= $23,636,688.21.
TV inflows = $27,700,000(1.14)
1
= $31,578,000.
N
I/YR
FV
PMT
PV
N
I/YR
FV
PMT
PV

Answers and Solutions:
10 - 22
Now, MIRR is that discount rate which forces the PV of the TV of $31,578,000 over
2 years to equal $23,636,688.21:
$23,636,688.21 = $31,578,000(PVIF
r,2
).
Yes.
The MIRR method leads to the same conclusion as the NPV method. Reject the
project if r = 8%, which is greater than the corresponding MIRR of 7.61%, and accept
the project if r = 14%, which is less than the corresponding MIRR of 15.58%.
10-20 a. The IRRs of the two alternatives are undefined.
To calculate an IRR, the cash flow
stream must include both cash inflows and outflows.
b.
The PV of costs for the conveyor system is ($911,067), while the PV of costs for the
forklift system is ($838,834).
Thus, the forklift system is expected to be ($838,834) -
($911,067) = $72,233 less costly than the conveyor system, and hence the forklift
trucks should be used.
Financial calculator solution:
Input:
CF
0
= -500000,
CF
1
= -120000, N
j
= 4, CF
2
= -20000, I/YR = 8, NPV
C
= ?
NPV
C
= -911,067.
Input:
CF
0
= -200000,
CF
1
= -160000,
N
1
= 5, I/YR = 8,
NPV
F
= ?
NPV
F
= -
838,834.
10-21 a.
Payback A (cash flows in thousands):
Annual
Period
Cash Flows
Cumulative
0
($25,000)
($25,000)
1
5,000
(20,000)
2
10,000
(10,000)
3
15,000
5,000
4
20,000
25,000
Payback
A
= 2 + $10,000/$15,000 = 2.67 years.