Question

A twelve year project has a cost of $250,000, annual cash flows of $40,000 in years 1-5, and annual cash flows of $30,000 in years 6-12. The company's required return is 12%. Given this information calculate the IRR of the project.

Answer 1

NPV is given by:

NPV = L Rt/(1 + i) ,t varies from 1 ton where Rt = Cash flow netted (Inflow - Outflow) during the period "t" i = Discount rate t = number of periods

Now, the discount rate at which NPV = 0 is known as IRR

At IRR

NPV = 0 = Sum of Discounted Future CAshflow - Initial Investment

Initial Investment =  Sum of Discounted Future CAshflow

250000 = [40000 / (1+r%)^¹ ] + [40000 / (1+r%)^² ] + [40000 / (1+r%)^³ ] + [40000 / (1+r%)^⁴ ] + [40000 / (1+r%)^⁵ ] + [30000 / (1+r%)^⁶ ] + [30000 / (1+r%)^⁷ ] + [30000 / (1+r%)^⁸ ] + [30000 / (1+r%)^⁹ ] + [30000 / (1+r%)^¹⁰ ] + [30000 / (1+r%)^¹¹ ] + [30000 / (1+r%)^¹² ]

Solving for r,

r = 9.32% = IRR

SUM X v fx =IRR(C16:C28) A A BC Year Project -$2,50,000| S40,000 S40,000] S40,000 S40,000 S40,000 S30,000 S30,000 S30,000 S30,000 | S30,000 | $30,000 12 $30,000] IRR |=IRR(C16:C28) লললললল

029 @ fx =IRR(C16:028) в Year с Project 0 $2,50,000 1 $40,000 2 $40,000 3 $40,000 4 $40,000 5 $40,000 6 $30,000 7 $30,000 $30,000 9 $30,000 10 $30,000 11 $30,000 12| $30,000 9.32% IRR