Question

By purchasing training software for $7,000, you can eliminate other training costs of $3,400 each year for the next 10 years. What is the IRR of the software?

Answer 1

Solution:-

Calculation of IRR

Information given,

Initial investment = $7000

Cash flow in the next 10 years = $3400 each year

Internal Rate Of return(IRR) is the interest rate (discount rate) that makes the NPV of the project zero. In other words the present value of its expected cash inflows will be equal to the present value of its expected cash outflows. IRR of this project can be calculated using trial and error method as follows:-

Here the cash inflows in each each is same therefore we can get a approximate value around the IRR by dividing the initial investment by cash inflow in an year and comparing the result with present value of annuity factor of given number of years  in the present value of annuity factor table.

Here,

Initial Investment / Annual Cashflow = $7000 / $3400 = 2.0589

Its between present value of annuity factor of 10 years and 45% (2.1681) and present value of annuity factor of 10 years and 50% (1.9653). therefore lets take 40% and 50% for trial and error.

a. NPV with 45%

NPV with equal cashflow in future periods = (cashflow per period * present value of $1 annuity factor) - Initial investment

= ($3400 * 2.1681) - $7000

= $371.65

b. NPV with 50%

NPV with equal cashflow in future periods = (cashflow per period * present value of $1 annuity factor) - Initial investment

= ($3400 * 1.9653) - $7000

= -$317.9

Since the NPV of 45% is positive and 50% is negative IRR lies between 45% and 50%, to get the exact IRR we have to interpolate using the following formula:-

IRR = 45% +[(50%-45%) * {$371.65 / ($371.65 + -$317.9)}]

= 45% + 2.6%

IRR = 47.6% Approx.