Question

In: Finance

You are evaluating a project that costs $67,000 today. The project has an inflow of $144,000...

You are evaluating a project that costs $67,000 today. The project has an inflow of $144,000 in one year and an outflow of $57,000 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?

Solutions

Expert Solution

A)

IRR
SMALLEST -47.64%
LARGEST 62.60%

B)The discount rate resulting in maximum NPV is 20.83%

The smallest and the largest IRR has been calculated as follows alongwith the calculation of the discount rate resulting in maximum NPV

The IRR of the project is calculated as follows -

0= - $67000+$144000/(1+IRR) -$57000/(1+IRR)2

As the cash flow changes signs twice we know that there will be either two IRRs or zero IRR as per Descartes Rule of signs, so we will rewrite the equation as :

0= -$57000X2+$144000X-$67000

where (1+IRR) =X

This is a quadratic equation, we can solve this equation and find value of X by using the following formula -

X= -b+ /2a

Solving this equation we get

X= 1.91 AND 0.615

now putting the values further we get

1.91 =(1/1+IRR)

IRR= - 47.64%

AND

0.615= (1/1+IRR)

IRR= 62.60%

To find the maximum NPV, we find the derivative and set it to zero. That is as follows

0=-$144000(1+IRR)-2 +$114000(1+IRR)-3

-$144000(1+IRR)3 = 114000(1+IRR)2

-144000(1+IRR) =114000

IRR= -.2083 OR -20.83%


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