Question

An investment costs $500 today but will generate $120 in one year, $380 in two years and $ 80 in three years. What is the IRR?

Answer 1

The IRR is computed as shown below:

Lets compute the NPV at 8%

= - $ 500 + $ 120 / 1.08¹ + $ 380 / 1.08² + $ 80 / 1.08³

= $ 0.4064 Approximately

Lets compute the NPV at 8.5%

= - $ 500 + $ 120 / 1.085¹ + $ 380 / 1.085² + $ 80 / 1.085³

= - $ 3.9753 Approximately

Now we know that IRR is the rate at which the project's NPV is zero, which means that it falls between 8 and 8.5%. In order to compute the same, we shall use the below mentioned formula:

= Lower Rate + [ Lower rate NPV / ( Lower rate NPV - Higher rate NPV ) ] x ( Higher Rate - Lower Rate )

Lower rate = 8% or 0.08

Lower Rate NPV = $ 0.4064

Higher Rate = 8.5% or 0.085

Higher Rate NPV = - $ 3.9753

By feeding these values in the above mentioned formula we shall get IRR as

= 8% + [ $ 0.4064 / ( $ 0.4064 - ( $ 3.9753 ) ] x ( 8.5 - 8 )

= 8% + [ $ 0.4064 / $ 4.3817 ] x 0.5 (Negative and negative signs becomes positive)

= 8.05% Approximately

We can also solve this in financial calculator as follows:

Enter CF₀ = - 500

CF₁ = 120

CF₂ = 380

CF₃ = 80

Then press IRR CPT, which shall give IRR as 8.05% Approximately

Feel free to ask in case of any query relating to this question