You are evaluating a project that costs $61,000 today. The project has an inflow
ID: 2821979 • Letter: Y
Question
You are evaluating a project that costs $61,000 today. The project has an inflow of $132,000 in one year and an outflow of $51,000 in two years.
What are the IRRs for the project? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
What discount rate results in the maximum NPV for this project?
You are evaluating a project that costs $61,000 today. The project has an inflow of $132,000 in one year and an outflow of $51,000 in two years.
Explanation / Answer
At a discount rate of IRR, NPV is 0.
132,000/(1+r) = 61,000 + 51,000/(1+R)2
Let R = 1 +r
132,000/R = 61,000 + 51,000/R2
132,000/R - 51,000/R2 = 61,000
132,000 R – 51,000 = 61,000 R2
61,000 R2 – 132,000 R + 51,000 = 0
61R2 – 132 R + 51= 0
Two roots of this quadratic equation can be compute as:
R = 132 + (132 2 – 4 x 61 x 51) /2 x 61
= 132 + (17424 – 12444) /122
= 132 + 4980 /122
= 132 + 70.56911506/122
= 202.5691151/122 = 1.660402582
Another root,
R = 132 - 70.56911506/122
= 61.43088494/122 = 0.503531844
1 + r = 1.660402582
r = 66 %
1+ r = 0.503531844
r = 0.503531844 – 1 = - 0.496468156
r = – 50 %
IRR
Smallest
-50%
Largest
66%
What discount rate results in the maximum NPV for this project?
Year
Cash flow
PV Factor @ -50%
PV
0
$ (61,000)
1.0000
$ (61,000.00)
1
$ 132,000
0.6667
$ 88,000.00
2
$ (51,000)
0.4444
$ (22,666.67)
NPV1
$ 4,333.33
Year
Cash flow
PV Factor @ 66%
PV
0
$ (61,000)
1.0000
$ (61,000.00)
1
$ 132,000
0.6024
$ 79,518.07
2
$ (51,000)
0.3629
$ (18,507.77)
NPV2
$ 10.31
At -50% Discount rate the NPV is maximum
IRR
Smallest
-50%
Largest
66%
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