Question

A company is analyzing two mutually exclusive projects, S and L, with the following cash flows: 0 1 2 Project S -$1,000 $862.66 $260 $15 $10 Project L -$1,000 $10 $250 $380 $852.17 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

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

Project S

NPV = [ 862.66 / (1 + 8%)^1 ] + [ 260 / (1 + 8%)^2 ] +  [ 15 / (1 + 8%)^3 ] + [ 10 / (1 + 8%)^4 ] - Initial investment

NPV = 798.76 + 222.91 + 11.91 + 7.35 - 1000

NPV = $ 40.93

For IRR, r%

NPV = 0

NPV = 0 =  [ 862.66 / (1 + r%)^1 ] + [ 260 / (1 + r%)^2 ] +  [ 15 / (1 + r%)^3 ] + [ 10 / (1 + r%)^4 ] - Initial investment

1000 =  [ 862.66 / (1 + r%)^1 ] + [ 260 / (1 + r%)^2 ] +  [ 15 / (1 + r%)^3 ] + [ 10 / (1 + r%)^4 ]

Solving for r,

r = 11.51%

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Project L

NPV = [ 10 / (1 + 8%)^1 ] + [ 250 / (1 + 8%)^2 ] +  [ 380 / (1 + 8%)^3 ] + [ 852.17 / (1 + 8%)^4 ] - Initial investment

NPV = 9.26 + 214.33 + 301.66 + 626.37 - 1000

NPV = $ 151.62

For IRR, r%

NPV = 0

NPV = 0 =  [ 10 / (1 + r%)^1 ] + [ 250 / (1 + r%)^2 ] +  [ 380 / (1 + r%)^3 ] + [ 852.17 / (1 + r%)^4 ] - Initial investment

1000 =  [ 10 / (1 + r%)^1 ] + [ 250 / (1 + r%)^2 ] +  [ 380 / (1 + r%)^3 ] + [ 852.17 / (1 + r%)^4 ]

Solving for r,

r = 12.68%

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Now , NPV of Project L > NPV of Project S

Hence, better project is Project L

IRR of better project = 12.68%