Question

Can someone help me with the appropriate equation for the following question?

What is the IRR of the following cashflows?

Now: - $120

After 1 year: + $20

After 2 years: + $90

After 3 years: - $10

After 4 years: + $30

After 5 years: + $30

After 6 years: + $30

After 7 years: + $40

Answer 1

There are several ways of calculating IRR ( I am using Interpolation method with trial and error method)

IRR is the rate at which Net present value of the cash flows is zero

Therefore the formula is:

0 = CF₀ + CF₁ / ( 1 + r)^1 + CF₂ / ( 1 + r)^2 + ........................... CF_n / (1 + r)^n

where CF is cash flow , r = rate , n = time period

Applying the above formula:

0 = - 120 + 20 / ( 1 + r) ^1 +  90 / ( 1 + r) ^2 + (- 10) /( 1 + r) ^3 +  30 / ( 1 + r) ^4 + 30 / ( 1 + r) ^5 + 30 / ( 1 + r) ^6 + 40 / ( 1 + r) ^7

Applying trial and error method:

Taking R = 20%, NPV = $ 1.11375

Taking R = 21% , NPV = (-) $ 1.99091

Applying interpolation method :

Formula = Lower rate + (NPV (lower rate) / (NPV (lower) - NPV (higher))) * (difference of higher and lower rate)

IRR = 0.20 + (1.11375 / (1.11375 - (- 1.99091)) ) * ( 0. 21 - 0.20)

IRR = 0.20359 or 20.36 % approximately