Question
Please show all work. Must be completed using financial formulas, NO EXCEL. a. Calculate the NPV, IRR, MIRR, and traditional payback period for each project, assuming a required rate of return of 8%....
Please show all work.
Must be completed using financial formulas, NO EXCEL.
a. Calculate the NPV, IRR, MIRR, and traditional payback period for each project, assuming a required rate of return of 8%.
b. If the projects are independent, which project(s) should be selected? If they are mutually exclusive, which project should be selected?
Answers
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.