You are required to submit a bid to supply 200,000,000 widgets per year to the S

Question

You are required to submit a bid to supply 200,000,000 widgets per year to the State of Illinois for the next five years. Your company has an idle tract of real estate that cost $1,500,000 ten years ago; if your company sold the land today, it would generate $3,000,000 after the taxes were paid. The land can be sold for $3,500,000 after taxes in five years. You will need to install $4,900,000 in new plant and equipment to actually produce the widgets; this plant and equipment will be depreciated straight-line to zero over the projects five year life. The equipment can be sold for $610,000 at the end of the project. You will need $500,000 in initial working capital for the project, and an additional investment of $60,000 in every year thereafter. Your production costs are .6 cents per widget and you will have fixed costs of $800,000 per year. If your tax rate is 34% and your required return is 14%, what bid price per widget should you submit?

Explanation / Answer

Let x be the sale value of 200,000,000 widgets.

Variable costs =200,000,000*.006=1,200,000 ----(A)

Fixed costs =$800,000 -----------(B)

Depreciation on plant & equipment =$4,900,000/5 =$980,000. ----(C)

Total costs =$2,980,000.

after tax income on sale of widgets =(x-$2980000)(1-0.34)

Cash inflows after considering depreciation =0.66x -$1,966,800 +depreciation $980,000 =0.66x-$986,800.--------(D)

Present value of working capital outflow is as follows:

But the working capital is ploughed back at the end of five years. Present value of working capital ploughed back=$800,000 * 0.519369 =$415,494.93

Net effect on working capital =$415,494.93 - $705,984.86 = - $290,489.93------------(E)

Cash inflow as a result of sale of equipment =$610,000

As equipment is depreciated to zero, total sale value is considered as gain, therefore after tax cash inflow on sale of equipment is $610,000*66% =$402,600.

Present value of the after tax inflow on sale of equipment=$402,600 * 0.519369=209,097.82-----------------(F).

Present value of the cost of the project:

Opportunity cost of land =$3,000,000 +cost of plant and equipment $4,900,000 =$7,900,000-------------(G)

Present value of cash proceeds received on sale of land =3,500,000 * 0.519369=$1,817,791.5------(H)

NPV of the project is 0 when x is:

Present value of cash inflows - Present value of cash outflows = 0

D+E+H - (F+G) =0

0.66x-$986,800+209097.82 +$1,817,791.5- ( $290489.93+7,900,000) =0

0.66x =7150400.61

x =10833940

Here x is the sale proceeds of 200,000,000 widgets.

Therefore bid price per widget should be =10833940/200,000,000

=0.05417

Year Incremental working capital Total working capital Present value factor Present value 0 $500,000.00 $500,000.00 1 $500,000.00 1 $60,000.00 $560,000.00 0.877193 $52,631.58 2 $60,000.00 $620,000.00 0.769468 $46,168.05 3 $60,000.00 $680,000.00 0.674972 $40,498.29 4 $60,000.00 $740,000.00 0.59208 $35,524.82 5 $60,000.00 $800,000.00 0.519369 $31,162.12 Total $705,984.86

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