Question

Project P costs $10,400 and is expected to produce cash flows of $3,650 per year for five years.

Project Q costs $30,000 and is expected to produce cash flows of $9,250 per year for five years.

a. Calculate the NPV, IRR, MIRR, and traditional payback period for each project, assuming a required rate of return of 8 percent.

b. If the projects are independent, which project(s) should be selected? If they are mutually exclusive, which project should be selected?

Answer 1

Project P:

NPV:

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

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

NPV = 3,650 * [1 - 1 / (1 + 0.08)⁵] / 0.08 - 10,400

NPV = 3,650 * [1 - 0.68058] / 0.08 - 10,400

NPV = 3,650 * 3.99271 - 10,400

NPV = $4,713.39

IRR:

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

NPV = 3,650 * [1 - 1 / (1 + R)⁵] / R - 10,400

Using trial and error method, i.e., after trying various values for R, lets try try R as 22.23%

NPV = 3,650 * [1 - 1 / (1 + 0.2223)⁵] / 0.2223 - 10,400

NPV = 0

Therefore, IRR is 22.23%

MIRR:

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

Future value = 3650 * [(1 + 0.08)⁵ - 1] / 0.08

Future value = 3650 * 5.8666

Future value = 21,413.09

MIRR = (FV / initial investment)^1/n - 1

MIRR = (21,413.09 / 10,400)^1/5 - 1

MIRR = 0.1554 - 1

MIRR = 0.1554 or 15.54%

Traditional payback:

Payback period = Initial investment / cash flow

Payback period = 10,400 / 3,650

Payback period = 2.85 years

Project Q:

NPV:

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

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

NPV = 9,250 * [1 - 1 / (1 + 0.08)⁵] / 0.08 - 30,000

NPV = 9,250 * [1 - 0.68058] / 0.08 - 30,000

NPV = 9,250 * 3.99271 - 30,000

NPV = $6,932.57

IRR:

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

NPV = 9,250 * [1 - 1 / (1 + R)⁵] / R - 30,000

Using trial and error method, i.e., after trying various values for R, lets try try R as 16.41%

NPV = 9,250 * [1 - 1 / (1 + 0.1641)⁵] / 0.1641 - 30,000

NPV = 0

Therefore, IRR is 16.41%

MIRR:

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

Future value = 9250 * [(1 + 0.08)⁵ - 1] / 0.08

Future value = 9250 * 5.8666

Future value = 54,266.06

MIRR = (FV / initial investment)^1/n - 1

MIRR = (54,266.06 / 30,000)^1/5 - 1

MIRR = 1.1259 - 1

MIRR = 0.1259 or 12.59%

Traditional payback:

Payback period = Initial investment / cash flow

Payback period = 30,000 / 9,250

Payback period = 3.24 years

2)

If projects are independent, both should be selected as the NPVs are positive and IRR & MIRR is greater than cost of capital.

When projects are mutually exclusive, we always choose the project with the higher NPV. Therefore, project Q should be accepted.