104
Electricpowered:
NPV
E
= $22,000 + $6,290 [(1/i)(1/(i*(1+i)
n
)]
= $22,000 + $6,290 [(1/0.12)(1/(0.12*(1+0.12)
6
)]
= $22,000 + $6,290(4.1114) = $22,000 + $25,861 = $3,861.
Financial calculator:
Input the appropriate cash flows into the cash flow register, input I
= 12, and then solve for NPV = $3,861.
Financial calculator:
Input the appropriate cash flows into the cash flow register and then
solve for IRR = 18%.
Gaspowered:
NPV
G
= $17,500 + $5,000 [(1/i)(1/(i*(1+i)
n
)]
= $17,500 + $5,000 [(1/0.12)(1/(0.12*(1+0.12)
6
)]
= $17,500 + $5,000(4.1114) = $17,500 + $20,557 = $3,057.
Financial calculator:
Input the appropriate cash flows into the cash flow register, input I
= 12, and then solve for NPV = $3,057.
Financial calculator:
Input the appropriate cash flows into the cash flow register and then
solve for IRR = 17.97% ≈ 18%.
The firm should purchase the electricpowered forklift because it has a higher NPV
than the gaspowered forklift.
The company gets a high rate of return (18% > r = 12%)
on a larger investment.
Answers and Solutions:
10  8
14%
105
Financial calculator solution, NPV:
Project S
Inputs
5
12
3000
0
Output
= 10,814.33
NPV
S
= $10,814.33  $10,000 = $814.33.
Project L
Inputs
5
12
7400
0
Output
= 26,675.34
NPV
L
= $26,675.34  $25,000 = $1,675.34.
Financial calculator solution, IRR:
Input CF
0
= 10000, CF
1
= 3000, N
j
= 5, IRR
S
= ?
IRR
S
= 15.24%.
Input CF
0
= 25000, CF
1
= 7400, N
j
= 5, IRR
L
= ?
IRR
L
= 14.67%.
Financial calculator solution, MIRR:
Project S
Inputs
5
12
0
3000
Output
= 19,058.54
PV costs
S
= $10,000.
FV inflows
S
= $19,058.54.
Inputs
5
10000
0
19058.54
Output
= 13.77
MIRR
S
= 13.77%.
Answers and Solutions:
10  9
N
I
FV
PMT
PV
N
I
FV
PMT
PV
N
I
FV
PMT
PV
N
I
FV
PMT
PV
Project L
Inputs
5
12
0
7400
Output = 47,011.07
PV costs
L
= $25,000.
FV inflows
L
= $47,011.07.
Inputs
5
25000
0
47011.07
Output
= 13.46
MIRR
L
= 13.46%.
PI
S
=
000
,
10
$
33
.
814
,
10
$
= 1.081.
PI
L
=
000
,
25
$
34
.
675
,
26
$
= 1.067.
Thus, NPV
L
> NPV
S
, IRR
S
> IRR
L
, MIRR
S
> MIRR
L
, and PI
S
> PI
L
.
The scale difference
between Projects S and L result in the IRR, MIRR, and PI favoring S over L.
However,
NPV favors Project L, and hence L should be chosen.
Answers and Solutions:
10  10
N
I
FV
PMT
PV
N
I
FV
PMT
PV
106
Project X:
0
1
2
3
4





1,000
100
300
400
700.00
448.00
376.32
140.49
1,664.81
1,000
13.59% = MIRR
X`
$1,000 = $1,664.81/(1 + MIRR
X
)
4
.
Project Y:
0
1
2
3
4






1,000
1,000
100
50
50.00
56.00
125.44
1,404.93
1,636.37
1,000
13.10% = MIRR
Y
$1,000 = $1,636.37/(1 + MIRR
Y
)
4
.
Thus, since MIRR
X
> MIRR
Y
, Project X should be chosen.
Alternative step:
You could calculate NPVs, see that Project X has the higher NPV, and
just calculate MIRR
X
.
NPV
X
= $58.02 and NPV
Y
= $39.94.
107
a.
Purchase price
$
900,000
Installation
165,000
Initial outlay
$1,065,000
CF
0
= 1065000; CF
15
= 350000; I = 14; NPV = ?
NPV = $136,578; IRR = 19.22%.
b.
Ignoring environmental concerns, the project should be undertaken because its NPV
is positive and its IRR is greater than the firm's cost of capital.
c.
Environmental effects could be added by estimating penalties or any other cash
outflows that might be imposed on the firm to help return the land to its previous state
(if possible).
These outflows could be so large as to cause the project to have a
negative NPVin which case the project should not be undertaken.
Answers and Solutions:
10  11
12%
12%
108
a.
b.
IRR
A
= 18.1%; IRR
B
= 24.0%.
c.
At r = 10%, Project A has the greater NPV, specifically $283.34 as compared to
Project B's NPV of $178.60.
Thus, Project A would be selected.
At r = 17%, Project
B has an NPV of $75.95 which is
higher than Project A's NPV of $31.05.
Thus,
choose Project B if r = 17%.