Question

Shrieves Casting Company is considering adding a new line to its product mix, and the capital budgeting analysis is being conducted by Sidney Johnson, a recently graduated MBA. The production line would be set up in unused space in Shrieves’ main plant. The machinery’s invoice price would be approximately $200,000, another $10,000 in shipping charges would be required, and it would cost an additional $30,000 to install the equipment. The machinery has an economic life of 4 years, and Shrieves has obtained a special tax ruling that places the equipment in the MACRS 3-year class. The machinery is expected to have a salvage value of $25,000 after 4 years of use.

The new line would generate incremental sales of 1,250 units per year for 4 years at an incremental cost of $100 per unit in the first year, excluding depreciation. Each unit can be sold for $200 in the first year. The sales price and cost are both expected to increase by 3% per year due to inflation. Further, to handle the new line, the firm’s net working capital would have to increase by an amount equal to 12% of sales revenues. The firm’s tax rate is 40%, and its overall weighted average cost of capital, which is the risk-adjusted cost of capital for an average project (r), is 10%.

(a) Disregard the assumptions in part a. What is Shrieves’ depreciable basis? What are the annual depreciation expenses?

(b) The sales price and cost are both expected to increase by 3% per year due to inflation. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include inflation when estimating cash flows?

Answer 1

answer a)

Answer: Note that because of the half-year convention, a 3-year project is depreciated over 4 calendar years:

YEAR RATE ´ BASIS = DEPRECIATION ANNUAL DEPRECIATION EXPENSE

1 0.33 $240 $ 79 $79

2 0.45 $240 $108 $187

3 0.15 $240 $36 $223

4 0.07 $240 $17 $240

$240

answer b)

With an inflation rate of 3%, the annual revenues and costs are:

	Year 1	Year 2	Year 3	Year 4
Units	1250	1250	1250	1250
Unit Price	$200.00	$206.00	$212.18	$218.55
Unit Cost	$100.00	$103.00	$106.09	$109.27
Sales	$250,000	$257,500	$265,225	$273,188
Costs	$125,000	$128,750	$132,613	$136,588

The cost of capital is a nominal cost; i.e., it includes a premium for inflation. In other words, it is larger than the real cost of capital. Similarly, nominal cash flows (those that are inflated) are larger than real cash flows. If you discount the low, real cash flows with the high, nominal rate, then the resulting NPV is too low. Therefore, you should always discount nominal cash flows with a nominal rate, and real cash flows with a real rate. In theory, you could do either way and get the correct answer. However, there is no accurate way to convert a nominal cost of capital to a real cost. Therefore, you should inflate cash flows and then discount at the nominal rate.

With an inflation rate of 3%, the annual revenues and costs are:

Here are the annual operating cash flows (in thousands of dollars):

1   2   3   4

Net Revenues $125 $125 $125 $125

Depreciation 79 108   36   17

Before-Tax Income $ 46 $ 17 $ 89 $108

Taxes (40%) 18    7   36   43

Net Income $ 28 $ 10 $ 53 $ 65

Plus Depreciation 79 108   36   17

Net Operating CF   $107 $118 $ 89 $ 82