Question

A)Project L requires an initial outlay at t = 0 of $40,000, its expected cash inflows are $15,000 per year for 9 years, and its WACC is 14%. What is the project's MIRR? Do not round intermediate calculations. Round your answer to two decimal places.

B) Project L requires an initial outlay at t = 0 of $88,310, its expected cash inflows are $14,000 per year for 10 years, and its WACC is 14%. What is the project's IRR? Round your answer to two decimal places.

C)What if Project L requires an initial outlay at t = 0 of $2,000, and its cash flows are the same in Years 1 through 10. Its IRR is 15%, and its WACC is 9%. What is the project's MIRR? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

A)

Future value = Annuity * [(1 + r)^n - 1] / r

Future value = 15,000 * [(1 + 0.14)^9 - 1] / 0.14

Future value = 15,000 * [3.251949 - 1] / 0.14

Future value = 15,000 * 16.085347

Future value = 241,280.1987

MIRR = (Future value / initial investment)^1/n - 1

MIRR = (241,280.1987 / 40,000)^1/9 - 1

MIRR = (6.032005)^1/9 - 1

MIRR = 1.2210 - 1

MIRR = 0.2210 or 22.10%

2)

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

88,310 = 14,000 * [1 - 1 / (1 + r)^10] / r

Using trial and error method, i.e., after trying various values for R, lets try R as 9.39%

88,310 = 14,000 * [1 - 1 / (1 + 0.0939)^10] / 0.0939

88,310 = 14,000 * [1 - 0.40759] / 0.0939

88,310 = 14,000 * 6.308943

88,310 = 88,310

Therefore, IRR is 9.39%

c)

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

2,000 = Annuity * [1 - 1 / (1 + 0.15)^10] / 0.15

2,000 = Annuity * [1 - 0.247185] / 0.15

2,000 = Annuity * 5.018769

Annuity = 398.504125

Future value = Annuity * [(1 + r)^n - 1] / r

Future value = 398.504125 * [(1 + 0.09)^10 - 1] / 0.09

Future value = 398.504125 * [2.367364 - 1] / 0.09

Future value = 398.504125 * 15.19293

Future value = 6,054.44516

MIRR = (Future value / initial investment)^1/n - 1

MIRR = (6,054.44516 / 2,000)^1/10 - 1

MIRR = (3.027223)^1/10 - 1

MIRR = 1.1171 - 1

MIRR = 0.1171 or 11.71%