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# Payback Methods, Even and Uneven Cash Flows

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Payback methods, even and uneven cash flows You have the opportunity to expand your business by purchasing new equipment for \$159,000. The equipment has a useful life of nine years. You expect to incur cash fixed costs of \$96,000 per year to use this new equipment, and you expect to incur cash variable costs in the amount of 10% of cash revenues. Your cost of capital is 12%.

Required
1. Calculate the payback period and the discounted payback period for this investment, assuming you will generate \$140,000 in cash revenues every year.

2. Assume instead that you expect the following cash revenue stream for this investment:
Year 1 \$ 90,000
Year 2 115,000
Year 3 130,000
Year 4 155,000
Year 5 170,000
Year 6 180,000
Year 7 140,000
Year 8 125,000
Year 9 110,000
Based on this estimated revenue stream, what are the payback and discounted payback periods for this investment?

Solution:

1.Payback problem:
Annual revenue \$140,000
Annual costs
Fixed \$96,000
Variable 14,000 110,000
Net annual cash inflow \$ 30,000

Discounted Payback Period with even cash flows:
Period Year Cash Revenues Fixed Costs Variable Costs Net Cash Inflows Disc Factor (12%) Discounted Cash Savings Cumulative Disc. Cash Savings Un-recovered Investment
0 \$159,000
1 \$140,000 \$96,000 \$14,000 \$30,000 .893 \$26,790 \$ 26,790 \$132,210
2 \$140,000 \$96,000 \$14,000 \$30,000 .797 \$23,910 \$ 50,700 \$108,300
3 \$140,000 \$96,000 \$14,000 \$30,000 .712 \$21,360 \$ 72,060 \$ 86,940
4 \$140,000 \$96,000 \$14,000 \$30,000 .636 \$19,080 \$ 91,140 \$ 67,860
5 \$140,000 \$96,000 \$14,000 \$30,000 .567 \$17,010 \$108,150 \$ 50,850
6 \$140,000 \$96,000 \$14,000 \$30,000 .507 \$15,210 \$123,360 \$ 35,640
7 \$140,000 \$96,000 \$14,000 \$30,000 .452 \$13,560 \$136,920 \$ 22,080
8 \$140,000 \$96,000 \$14,000 \$30,000 .404 \$12,120 \$149,040 \$ 9,960
9 \$140,000 \$96,000 \$14,000 \$30,000 .361 \$10,830 \$159,870

\$9,960/\$10,830 = .92
Discounted Payback Period = 8.92 years

2.
Year Revenue
(1) Cash Fixed Costs
(2) Cash
Variable Costs
(3) Net Cash Inflows
(4) = (1) − (2) − (3) Cumulative
Amounts
1 \$ 90,000 \$ 96,000 \$ 9,000 \$(15,000) \$(15,000)
2 115,000 96,000 11,500 7,500 (7,500)
3 130,000 96,000 13,000 21,000 13,500
4 155,000 96,000 15,500 43,500 57,000
5 170,000 96,000 17,000 57,000 114,000
6 180,000 96,000 18,000 66,000 180,000
7 140,000 96,000 14,000 30,000 210,000
8 125,000 96,000 12,500 16,500 226,500
9 110,000 96,000 11,000 3,000 229,500

The cumulative amount exceeds the initial \$159,000 investment for the first time at the end of year 6. So, payback happens in year 6.

Using linear interpolation, a more precise measure is that payback happens at:
5 years +

Discounted Payback Period with uneven cash flows:

Year Cash Revenues Fixed Costs Variable Costs Net Cash Inflows Disc Factor (12%) Discounted Cash Savings Cumulative Disc. Cash Savings Un-recovered Investment
0 \$159,000
1 \$ 90,000 \$96,000 \$ 9,000 \$(15,000) .893 (\$13,395) (\$13,395) \$172,395
2 \$115,000 \$96,000 \$11,500 \$ 7,500 .797 \$ 5,978 (\$ 7,417) \$166,417
3 \$130,000 \$96,000 \$13,000 \$ 21,000 .712 \$14,952 \$ 7,535 \$151,465
4 \$155,000 \$96,000 \$15,500 \$ 43,500 .636 \$27,666 \$ 35,201 \$123,799
5 \$170,000 \$96,000 \$17,000 \$ 57,000 .567 \$32,319 \$ 67,520 \$ 91,480
6 \$180,000 \$96,000 \$18,000 \$ 66,000 .507 \$33,462 \$100,982 \$ 58,018
7 \$140,000 \$96,000 \$14,000 \$ 30,000 .452 \$13,560 \$114,542 \$ 44,458
8 \$125,000 \$96,000 \$12,500 \$ 16,500 .404 \$ 6,666 \$121,208 \$ 37,792
9 \$110,000 \$96,000 \$11,000 \$ 3,000 .361 \$ 1,083 \$122,291 \$ 36,709

At a 12% rate of return, this project does not generate sufficient cash flows to ever recoup the investment under the discounted payback method.

Please view the attachment to see the questions formatted properly.

#### Solution Summary

The payback methods, evens and uneven cash flows are discussed. Cash revenue streams for an investment are given.

\$2.19

## The CEO has given you 3 different large projects he's evaluating to see which might be most beneficial to the company to invest in...

Can you help me get started with this assignment?

The CEO has given you 3 different large projects he's evaluating to see which might be most beneficial to the company to invest in. These include:

A new labor-saving piece of equipment that cost \$400,000 and will reduce labor and quality costs by \$75,000/year for 6 years.

A new marketing program, costing \$500,000 is expected to increase current sales of \$10,000,000/year by 30% for the next 4 years only. The current contribution margin of 30% will remain in effect even with this sales increase.

Launching a new product will cost \$600,000; the product is expected to sell for \$15/unit at a volume of 20,000 units/year for 3 years, at a 40% contribution margin.

The firm's overall cost of capital is 10%.

Why does a firm need to have a capital budgeting process?
What is/are
-¦the 3 primary methods of capital budgeting?
-¦the pros and cons of each?
-¦the method you feel is the best and why do you think so?

Is it better for the firm to have a higher or lower discount rate (or cost of capital)? Why?
What could happen if you pick a discount rate that is too high?

** DETAILS ARE ATTACHED IN EXCEL **

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