Question

Darrox, Inc. is considering a four-year project that has an initial outlay or cost of $90,000. The future cash inflows from its project are $50,000, $30,000, $30,000, and $30,000 for years 1, 2, 3 and 4, respectively. Darrox uses the internal rate of return method to evaluate projects.

What is the approximate IRR for this project?

a. The IRR is between 12% and 20%
b. The IRR is about 28.89%
c. The IRR is less than 12%
d. The IRR is about 22.80%

Answer 1

d. The IRR is about 22.80%

Step-by-step explanation:

Given: Initial investment= $90000

The future cash inflows from its project are $50,000, $30,000, $30,000, and $30,000 for years 1, 2, 3 and 4, respectively

Internal rate of return(IRR) is a minimum rate at which company can reach break even of investment, so that managment can decide which project they should invest in.

Formula;
`((cash\ flow\ year 1)/((1+IRR)^(1)  ) +(cash\ flow\ year 2)/(1+IRR)^(2)) +(cash\ flow\ year 3)/((1+IRR)^(3)) +(cash\ flow\ year 4)/(1+IRR)^(4)))-Initial\ investment= 0`

Here, we need to solve for the discount rate or IRR that will make net present value (NPV) equal to 0.

We can start with an approximate rate to check if it give NPV equal to zero, as we have option in this question, so we can start with any options. Lets begin with last one that is given about 22.80%

Now, solving it

`((50000)/((1+22.80\%)^(1) ) +(30000)/((1+22.80\%)^(2)) +(30000)/((1+22.80\%)^(3)) +(30000)/((1+22.80\%)^(4)))-90000= 3.64`

Here we have return which is very close to initial investment.

We can also check another rate close to 22.80, lets take 23%

`((50000)/((1+23\%)^(1) ) +(30000)/((1+23\%)^(2)) +(30000)/((1+23\%)^(3)) +(30000)/((1+23\%)^(4)))-90000= -291.70`

Here, we have negative NPV and we can not have IRR which give negative return.

∴ We can have IRR close to 22.80% to make NPV equal to zero.

Answer is the IRR is about 22.80%