Strict adherence to the IRR method would further dictate that mutually exclusive projects should be chosen on the basis of the
greater IRR.
In our example, each project has an IRR that exceeds the cost of capital (10%) so both projects should be accepted
if they are independent.
If, however, the projects are mutually exclusive, we would choose Project S because it has the higher
IRR.
Recall that this differs from our conclusion when using the NPV method.
So, we have a conflict between the NPV and the
IRR methods for ranking Projects S and L.
A
B
C
D
E
F
G
H
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113

Figure 10-4. Graph for Multiple IRRs: Project M (Millions of Dollars)
Year =
0
1
2
Project M
-1.60
10
-10
r
=
10%
NPV
=
-$0.774
Note:
r
NPV
0%
-$1.600
10%
-$0.774
25%
$0.000
= IRR #1
=
25%
110%
$0.894
400%
$0.000
= IRR #2
=
400%
500%
-$0.211
Because
of the mathematics involved, it is possible for some (but not all) projects that have more than one change of signs in the
cash flows to have more than one IRR.
If you attempted to find the IRR with such a project using a financial calculator, you
would get an error message.
The procedure for correcting the problem is to store in a guess for the IRR, and then the calculator
will report the IRR that is closest to your guess.
You can then use a different "guess" value, and
you should be able to find the
other IRR.
However, the
nature of the mathematics creates a scenario in which one IRR is quite extraordinary (often, several
hundred percent).
The table shown below calculates Project M's NPV at the rates shown in the left column. These data are plotted to
form the graph shown above.
Notice that NPV = 0 at both 25% and 400%.
Since the definition of the IRR is the rate
at which the NPV = 0, there are two IRRs.
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
500%
-$0.30
-$0.10
$0.10
$0.30
$0.50
$0.70
$0.90
Cost of Capital (%)
NPV (Mil-
lions)
NPV =
−
$1.6 + $10/(1+r) + (
−
$10)/(1+r)
2
IRR #1 = 25%
IRR #2 = 400%
A
B
C
D
E
F
G
H
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168

REINVESTMENT RATE ASSUMPTIONS
MODIFIED INTERNAL RATE OF RETURN, MIRR
Finding the MIRR for Projects S and L
r =
10%
Year =
1
2
3
4
Project S
-10,000
5,000
4,000
3,000
1,000
$3,300
$4,840
$6,655
-10,000
Terminal Value (TV) =
$15,795
12.11%
=RATE(F208,0,B209,F213)
12.11%
=MIRR(B209:F209,B206,B206)
12.11%
Year =
1
2
3
4
Project L
-10,000
1,000
3,000
4,000
6,750
The IRR approach assumes that cash flows can be reinvested at the IRR, but it is more realistic to asssume that cash
flows only can be reinvested at the cost of capital. For this reason, NPV is a better decision criterion than IRR.
The modified internal rate of return is the discount rate that causes a project's cost (or cash outflows) to equal the
present value of the project's terminal value.
The terminal value is defined as the sum of the future values of the
project's cash inflows, compounded at the project's cost of capital.
To find MIRR, calculate the PV of the outflows
and the FV of the inflows, and then find the rate that equates the two.
Alternatively, you can solve using Excel's
MIRR function.
One advantage of using the MIRR, relative to the IRR, is that the MIRR assumes that cash flows received are