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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.

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Solution Summary

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

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