R cf r cf cf npv 1 1 1 2 2 1 1 0 16 866 14 1 000 2 14

r
CF
r
CF
CF NPV
) 1 (
...
) 1 ( ) 1 ( 2
2
1
1
0
+
+ +
+
+
+
+ =
16 . 866 $
%) 14 1 (
000 , 2 $
%) 14 1 (
000 , 2 $
%) 14 1 (
000 , 2 $
%) 14 1 (
000 , 2 $
%) 14 1 (
000 , 2 $
000 , 6 $
5 4 3 2 1
=
+
+
+
+
+
+
+
+
+
+ - =
0
) 1 (
...
) 1 ( ) 1 (
2
2
1
1
0
=
+
+ +
+
+
+
+ =
N
N
IRR
CF
IRR
CF
IRR
CF
CF NPV

 IRR = 19.86%
Using Excel, MIRR = 17.12%
Period Cash flow Cumulative (A)
0 -$6,000 -$6,000
1 $2,000 -$4,000
2 $2,000 -$2,000
3 $2,000 $0
4 $2,000 $2,000
5 $2,000 $4,000
Payback
Discounted payback
Project B
Period Cash flow Discounted Cash
flow
Cumulative
discounted CF
0 -$6,000 -$6,000 -$6,000
1 $2,000 $1,754 -$4,246
2 $2,000 $1,539 -$2,707
3 $2,000 $1,350 -$1,357
4 $2,000 $1,184 -$173
5 $2,000 $1,039 $866
0
) 1 (
000 , 2 $
) 1 (
000 , 2 $
) 1 (
000 , 2 $
) 1 (
000 , 2 $
) 1 (
000 , 2 $
000 , 6 $
5 4 3 2 1
=
+
+
+
+
+
+
+
+
+
+ - =
IRR IRR IRR IRR IRR
NPV
years S 3
000 , 2 $
000 , 2 $
2 = + =
N
N
r
CF
r
CF
r
CF
CF NPV
) 1 (
...
) 1 ( ) 1 ( 2
2
1
1
0
+
+ +
+
+
+
+ =
25 . 225 , 1 $
%) 14 1 (
600 , 5 $
%) 14 1 (
600 , 5 $
%) 14 1 (
600 , 5 $
%) 14 1 (
600 , 5 $
%) 14 1 (
600 , 5 $
000 , 18 $
5 4 3 2 1
=
+
+
+
+
+
+
+
+
+
+ - =
years S 2 . 4
039 , 1 $
173 $
4 = + =
0
) 1 (
...
) 1 ( ) 1 ( 2
2
1
1
0
=
+
+ +
+
+
+
+ =
N
N
IRR
CF
IRR
CF
IRR
CF
CF NPV

 IRR = 16.80%
Using Excel, MIRR = 15.51%
Period Cash flow Cumulative
0 -$18,000 -$18,000
1 $5,600 -$12,400
2 $5,600 -$6,800
3 $5,600 -$1,200
4 $5,600 $4,400
5 $5,600 $10,000
Payback
Period Cash Flow Discounted Cash
Flow
Cumulative
Discounted CF
0 -$18,000 -$18,000 -$18,000
1 $5,600 $4,912 -$13,088
2 $5,600 $4,309 -$8,779
3 $5,600 $3,780 -$4,999
4 $5,600 $3,316 -$1,683
5 $5,600 $2,908 $1,225
Discounted payback
b. Assuming the project are independent, I would recommend 2
projects.
c. If the projects are mutually exclusive, I would recommend project B
because NPV
A
<NPV
B
.
d. The projects have the same cash flow timing pattern. There is a
conflict between NPV and IRR because NPV = IRR = 0.
11.8/ CAPITAL BUDGETING CRITERIA: ETHICAL CONSIDERATIONS A mining
company is considering a new project. Because the mine has received a permit, the
0
) 1 (
600 , 5 $
) 1 (
600 , 5 $
) 1 (
600 , 5 $
) 1 (
600 , 5 $
) 1 (
600 , 5 $
000 , 18 $
5 4 3 2 1
=
+
+
+
+
+
+
+
+
+
+ - =
IRR IRR IRR IRR IRR
NPV
years S 21 . 3
600 , 5 $
200 , 1 $
3 = + =
years S 58 . 4
908 , 2 $
683 , 1 $
4 = + =

project would be legal; but it would cause significant harm to a nearby river. The firm
could spend an additional $10 million at Year 0 to mitigate the environmental problem,
but it would not be required to do so. Developing the mine (without mitigation) would
cost $60 million, and the expected net cash inflows would be $20 million per year for 5
years. If the firm does invest in mitigation, the annual inflows would be $21 million. The
risk-adjusted WACC is 12%.
a. Calculate the NPV and IRR with and without mitigation.