Question

A firm with a WACC of 10% is considering the following mutually exclusive projects: $55 $120 $215 $120 $215 $120 Project 1 - $500 $55 $55 Project 2 - $650 $300 $300 Which project would you recommend? Select the correct answer. O O O a. Both Projects 1 and 2, since both projects have NPV's > 0. b. Project 2, since the NPV2 > NPV1. c. Neither Project 1 nor 2, since each project's NPV < 0. O d. Project 1, since the NPV1 > NPV2. O e. Both Projects 1 and 2, since both projects have IRR's > 0.

Answer 1

NPV is given by:

Σ Rt/(1 i)ttvaries from 1 to n NPV where Rt Cash flow netted (Inflow - Outflow) during the period "t" i Discount rate t number of periods

Project 1

NPV = [ 55 / (1 + 10%)^1 ] + [ 55 / (1 + 10%)^2 ] +  [ 55 / (1 + 10%)^3 ] + [ 215 / (1 + 10%)^4 ] + [ 215 / (1 + 10%)^5 ] - Initial investment

NPV = 50 + 45.45 + 41.32 + 146.85 + 133.5 - 500

NPV = $ - 82.88

For IRR, r%

NPV = 0

NPV = 0 = [ 55 / (1 + r%)^1 ] + [ 55 / (1 + r%)^2 ] +  [ 55 / (1 + r%)^3 ] + [ 215 / (1 + r%)^4 ] + [ 215 / (1 + r%)^5 ] - Initial investment

0 = [ 55 / (1 + r%)^1 ] + [ 55 / (1 + r%)^2 ] +  [ 55 / (1 + r%)^3 ] + [ 215 / (1 + r%)^4 ] + [ 215 / (1 + r%)^5 ] - 500

500 = [ 55 / (1 + r%)^1 ] + [ 55 / (1 + r%)^2 ] +  [ 55 / (1 + r%)^3 ] + [ 215 / (1 + r%)^4 ] + [ 215 / (1 + r%)^5 ]

Solving for r,

r = 4.724%

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Project 2

NPV = [ 300 / (1 + 10%)^1 ] + [ 300 / (1 + 10%)^2 ] +  [ 120 / (1 + 10%)^3 ] + [ 120 / (1 + 10%)^4 ] + [ 120 / (1 + 10%)^5 ] - Initial investment

NPV = 272.73 + 274.93 + 90.16 + 81.96 + 74.51 - 650

NPV = $ 117.29

For IRR, r%

NPV = 0

NPV = 0 = [ 300 / (1 + r%)^1 ] + [ 300 / (1 + r%)^2 ] +  [ 120 / (1 + r%)^3 ] + [ 120 / (1 + r%)^4 ] + [ 120 / (1 + r%)^5 ] - Initial investment

0 = [ 300 / (1 + 10%)^1 ] + [ 300 / (1 + 10%)^2 ] +  [ 120 / (1 + 10%)^3 ] + [ 120 / (1 + 10%)^4 ] + [ 120 / (1 + 10%)^5 ] - 650

650 = [ 300 / (1 + 10%)^1 ] + [ 300 / (1 + 10%)^2 ] +  [ 120 / (1 + 10%)^3 ] + [ 120 / (1 + 10%)^4 ] + [ 120 / (1 + 10%)^5 ]

Solving for r,

r = 18.596%

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Hence, Option b (NPV project 2 > Project 1)