Question

A company is analyzing two mutually exclusive projects, S and L, with the following cash flows:

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1

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3

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Project S	-$1,000	$870.58	$250	$10	$10
Project L	-$1,000	$5	$240	$380	$793.73

The company's WACC is 8.0%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places.

Answer 1

Project S:

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

NPV of project S = -1000 + 870.58 / ( 1 + 0.08)¹ + 250 / ( 1 + 0.08)² + 10 / ( 1 + 0.08)³ + 10 / ( 1 + 0.08)⁴  

NPV of project S = $35.76

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

-1000 + 870.58 / ( 1 + R)¹ + 250 / ( 1 + R)² + 10 / ( 1 + R)³ + 10 / ( 1 + R)⁴ = 0

Using trial and error method, i.e, after trying varuous values for R, let's try R as 11.1%

-1000 + 870.58 / ( 1 + 0.111)¹ + 250 / ( 1 + 0.111)² + 10 / ( 1 + 0.111)³ + 10 / ( 1 + 0.111)⁴ = 0

0 = 0

Therefore IRR of project S is 11.1%

Note: It is always recommended to use a financial calculator to calculate IRR. Trial and error method can be time consuming.

Project L:

NPV of project L = -1000 + 5 / ( 1 + 0.08)¹ + 240 / ( 1 + 0.08)² + 380 / ( 1 + 0.08)³ + 793.73 / ( 1 + 0.08)⁴  

NPV of project L = $95.46

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

-1000 + 5 / ( 1 + R)¹ + 240 / ( 1 + R)² + 380 / ( 1 + R)³ + 793.73 / ( 1 + R)⁴ = 0

Using trial and error method, i.e, after trying varuous values for R, let's try R as 11%

-1000 + 5 / ( 1 + 0.11)¹ + 240 / ( 1 + 0.11)² + 380 / ( 1 + 0.11)³ + 793.73 / ( 1 + 0.11)⁴ = 0

0 = 0

Therefore IRR of project L is 11%

When project are mutulally exclusive, we always go by the NPV rule. Project L is the better project as it has the higher NPV. IRR of project L is 11%.