Question

Internal rate of Return.

Lepton Industries has three potential​ projects, all with an initial cost of ​$1,900,000.

Given the discount rate and the future cash flows of each​ project, what are the IRRs of the three projects for Lepton​ Industries?

Cash Flow	Project Q		Project R		Project S
Year 1	​ $500,000		​$600,000		​$1,000,000
Year 2	​$500,000		​$600,000		​$800,000
Year 3	​$500,000		​$600,000		​$600,000
Year 4	​$500,000		​$600,000		​$400,000
Year 5	​$500,000		​$600,000		​$200,000
Discount rate	9​%		11​%		15​%

Q? R? S?

Answer 1

Project Q:

IRR is the rate of return that makes initial investment equal to present value of cash inflows

Initial investment = Annuity * [1 - 1 /(1 + r)ⁿ]/r

1,900,000 = 500,000 * [1 - 1 /(1 + r)⁵]/r

Using trial and error method i.e., after trying various values for R, lets try R as 9.91%

1,900,000 = 500,000 * [1 - 1 /(1 + 0.0991)⁵]/0.0991

1,900,000 = 500,000 * 3.799519

1,900,000 = 1,900,000

therefore, IRR of project Q is 9.91%

Project R:

IRR is the rate of return that makes initial investment equal to present value of cash inflows

Initial investment = Annuity * [1 - 1 /(1 + r)ⁿ]/r

1,900,000 = 600,000 * [1 - 1 /(1 + r)⁵]/r

Using trial and error method i.e., after trying various values for R, lets try R as 17.45%

1,900,000 = 600,000 * [1 - 1 /(1 + 0.1745)⁵]/0.1745

1,900,000 = 600,000 * 3.166532

1,900,000 = 1,900,000

therefore, IRR of project R is 17.45%

Project S:

IRR is the rate of return that makes initial investment equal to present value of cash inflows

1,900,000 = 1000000 / (1 + R)¹ + 800000 / (1 + R)² + 600000 / (1 + R)³ + 400000 / (1 + R)⁴ + 200000 / (1 + R)⁵

Using trial and error method i.e., after trying various values for R, lets try R as 23.32%

1,900,000 = 1000000 / (1 + 0.2332)¹ + 800000 / (1 + 0.2332)² + 600000 / (1 + 0.2332)³ + 400000 / (1 + 0.2332)⁴ + 200000 / (1 + 0.2332)⁵

1,900,000 = 1,900,000

therefore, IRR of project S is 23.32%