I have answered all of the following except for the payback period, I do not understand how to do it. Can you please explain how to do the payback period?
Texas Roks, Inc. is considering a new quarry machine. The costs and revenues associated with the machine have been provided to you for analysis:
Cost of the new project
$4,000,000
Installation costs
$100,000
Estimated unit sales in year 1
50,000
Estimated unit sales in year 2
75,000
Estimated unit sales in year 3
40,000
Estimated sales price in year 1
$150
Estimated sales price in year 2
$175
Estimated sales price in year 3
$160
Variable cost per unit
$120
Annual fixed cost
$50,000
Additional working capital needed
$435,000
Depreciation method
3 years straight-line method, no salvage value
Texas Rok's tax rate
40%
Texas Rok's cost of capital
13%
Required:
Calculate operating cash flow and the change in net working capital.
Determine the NPV and IRR of the project.
Should the company accept or reject the project based on the NPV? Why?
Should the company accept or reject the project based on the IRR? Why?
What is your final accept or reject decision? Why?
What is the payback period for this project?
Would this influence your decision to accept or reject?
To calculate the payback period, you need to determine how long it takes for the initial investment to be recovered through the project's cash inflows.
Here's how to calculate the payback period for this project:
1. Calculate the annual net cash inflow for each of the three years:
- Year 1: (Unit sales x Sales price) - (Unit sales x Variable cost per unit) - Fixed costs - Depreciation
- Year 2: (Unit sales x Sales price) - (Unit sales x Variable cost per unit) - Fixed costs - Depreciation
- Year 3: (Unit sales x Sales price) - (Unit sales x Variable cost per unit) - Fixed costs - Depreciation
Using the given information:
- In Year 1:
Net cash inflow = (50,000 x $150) - (50,000 x $120) - $50,000 - ($4,100,000 / 3)
- In Year 2:
Net cash inflow = (75,000 x $175) - (75,000 x $120) - $50,000 - ($4,100,000 / 3)
- In Year 3:
Net cash inflow = (40,000 x $160) - (40,000 x $120) - $50,000 - ($4,100,000 / 3)
2. Calculate the cumulative cash flow for each year by summing the net cash inflows.
- Cumulative cash flow Year 1 = net cash inflow Year 1
- Cumulative cash flow Year 2 = cumulative cash flow Year 1 + net cash inflow Year 2
- Cumulative cash flow Year 3 = cumulative cash flow Year 2 + net cash inflow Year 3
3. Determine the year in which the cumulative cash flow becomes positive. This will be your payback period.
Now, let's calculate the payback period using the given information:
- Cumulative cash flow Year 1 = net cash inflow Year 1
- Cumulative cash flow Year 2 = cumulative cash flow Year 1 + net cash inflow Year 2
- Cumulative cash flow Year 3 = cumulative cash flow Year 2 + net cash inflow Year 3
If the cumulative cash flow becomes positive by the end of Year 2 or Year 3, then that will be the payback period. If not, interpolate between Year 2 and Year 3 to find the payback period.
Once you calculate the payback period, you can determine if it influences your decision to accept or reject the project. The payback period represents the time it takes to recover the initial investment, so a shorter payback period may be more favorable as it indicates a faster return on investment. However, the payback period alone might not be the sole factor in deciding whether to accept or reject a project. It should be considered alongside other financial indicators like NPV and IRR to make a well-informed decision.