Agriculture Reference
In-Depth Information
Internal rate of return
The same equation used to calculate the net present value of an investment can be used to
determine the
internal rate of return (IRR)
for the investment. The internal rate of return
is called by various names: discounted rate of return, marginal effi ciency of capital, yield,
etc. However, it is essentially the discount rate that equates the net present value of the pro-
jected net cash fl ows to zero.
To calculate the internal rate of return for an investment, set up the net present value
model as outlined above. Determine the projected cash fl ows and set the net present value to
zero, then solve for i as shown below:
P
1i
P
P
V
1
P
2
NPV($0)
= −
P
INV
+
+
++
+
(1
(1
2
…
N
N
i
)
i)
(
1
i
)
+
+
+
The discount rate that satisfi es this equation is the internal rate of return.
To illustrate this method, let's fi nd the internal rate of return for an investment that
requires a $1,000 initial investment and yields a $1,200 cash payment one year in the future.
The IRR model is set up as shown below:
1 200
1
,
01000
+
,
i
+
Solving the equation for i results in the following:
1 200
1 000
i
,
1
12
+=
=
.
,
i
02
=
So, the IRR for this investment is 20 percent.
When the planning horizon exceeds one year, the procedure is essentially a trial-and-error
approach to determine the discount rate that will yield a zero net present value. Today,
spreadsheets are used to determine the IRR given the complexity of the calculation.
Investments can be ranked and accepted or rejected on the basis of their internal rates of
return. The ranking is based on the relative sizes of the internal rates of returns, with the
largest being the most favored. The acceptance of each investment depends upon the com-
parison of its internal rate of return with the investor's required rate of return. Acceptability
is based on the following decision rules:
•
If the internal rate of return exceeds the required rate of return, accept the investment.
•
If the internal rate of return equals the required rate of return, be indifferent.
•
If the internal rate of return is less than the required rate of return, reject the
investment.
Since the net present value of the applicator is positive using the 14 percent rate of return, the
project is acceptable. However, in order to compare the project to other projects being con-
sidered, the internal rate of return is needed. The trial-and-error approach is used to calculate
the net present value for the self-propelled fertilizer applicator for BF&G. A discount factor
