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.)

  

	IRR
Smallest	%
Largest	%

  

What discount rate results in the maximum NPV for this project?

Answer 1

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