Cash Flow Statement, Including Working Capital. Update the after-tax cash flows for the automated machining center project of Example 10.1 by including a working-capital requirement of $23,333 in year 0 and full recovery of the working capital at the end of year 5.

Question

Cash Flow Statement, Including Working Capital

Update the after-tax cash flows for the automated machining center project of Example 10.1 by including a working-capital requirement of $23,333 in year 0 and full recovery of the working capital at the end of year 5.

Accepted Answer

Given: Flows as in Example 10.1, with the addition of a $23,333 working-capital requirement.
Find: Net after-tax cash flows with working capital and present worth.

Using the procedure outlined in Example 10.2, we group the net after-tax cash flows for this machining-center project, as shown in Table 10.5. As the table indicates, investments in working capital are cash outflows when they are expected to occur, and recoveries are treated as cash inflows at the times they are expected to materialize. In this example, we assume that the investment in working capital made at period 0 will be recovered at the end of the project’s life. [latex]\left( See Figure 10.5.\right) ^{5}[/latex] Moreover, we also assume a full recovery of the initial working capital. However, in many situations, the investment in working capital may not be fully recovered (e.g., inventories may deteriorate in value or become obsolete over time).

5	4	3	2	1	0	Period
0	-$23,333	-$23,333	-$23,333	-$23,333	-$23,333	Investment
$23,333	$23,333	$23,333	$23,333	$23,333	0	Recovery
$23,333	0	0	0	0	-$23,333	Net flow

[latex] ^{5} In fact[/latex], we could assume that the investment in working capital would be recovered at the end of the first operating cycle (say, year 1). However, the same amount of investment in working capital has to be made again at the beginning of year 2 for the second operating cycle, and the process repeats until the project terminates. Therefore, the net cash flow transaction looks as though the initial working capital will be recovered at the end of the project’s life.

The equivalent net present worth of the after-tax cash flows, including the effects of working capital, is calculated as

PW(15%) = -$148,333 + $43,145(P/F, 15%, 1) + ...
+ $104,952(P/F, 15%, 5)
= $31,420

This present-worth value is $11,732 less than that in the situation with no workingcapital requirement (Example 10.1), demonstrating that working-capital requirements play a critical role in assessing a project’s worth.

Comments: The $11,732 reduction in present worth is just the present worth of an annual series of 15% interest payments on the working capital, which is borrowed by the project at time 0 and repaid at the end of year 5:

[latex]\underbrace{23,333\left(15\%\right) }_{annual interest lost} \left(P/A, 15\%,5\right) = 11,732[/latex]

The investment tied up in working capital results in lost earnings.

Question 10.3: Cash Flow Statement, Including Working Capital. Update the a...

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