For independent projects is it true that if PI10 then NPV0 a

For independent projects, is it true that if PI>1.0, then NPV>0 and IRR>K? prove

Solution

Assume that XYZ corporation is considering an investment of $50 million in a capital projcet that will return after tax cash flows of $16,000,000 per year for the next 4 years and anoth $20 million in year 5. the required rate of return in is 10%.

NPV = Present value of cash inflows - present value of cash outflows

NPV = 16 / ( 1.1)¹ + 16 / ( 1.1)² + 16 / ( 1.1)³ + 16 / ( 1.1)⁴ + 20 / ( 1.1)⁵ - 50

NPV = 14.545 + 13.223 + 12.021 + 10.928 + 12.418 - 50

NPV = $13.36 million

IRR is the rate of return that makes NPV equal to 0

NPV = 16 / ( 1 + R)¹ + 16 / ( 1 + R)² + 16 / ( 1 + R)³ + 16 / ( 1 + R)⁴ + 20 / ( 1 + R)⁵ - 50

Using trial and error method, let\'s try R as 19.52%

NPV = 16 / ( 1 + 0.1952)¹ + 16 / ( 1 + 0.1952)² + 16 / ( 1 + 0.1952)³ + 16 / ( 1 + 0.1952)⁴ + 20 / ( 1 + 0.1952)⁵ - 50

NPV = 0

Therefore, IRR is 19.52%

PI = present value of cash inflows / initial investment

PI = ( 14.545 + 13.223 + 12.021 + 10.928 + 12.418 ) / 50

PI = 1.26

Since PI of 1.26 is more than 1, IRR of 19.52% is more than K of 10% and NPV of 13.36 is greater than 0

it is true that if PI>1.0, then NPV>0 and IRR>K