University of Texas at Dallas
	School of Management

Finance 6301		Professor Day
Corporate Finance		Fall 1999

	Lecture 5:  Capital Budgeting

Tax Shields from Depreciation

	The yearly depreciation expense from writing off a firm's plant and equipment is an example of an expense that does not affect cash flow.  Apart from tax consequences, all of the cash outflow associated with the purchase of any depreciable asset occurs when the asset is acquired.  The asset is then expensed over its useful life.  The concept of matching an expense with the future revenues created by that asset is referred to in accounting as the matching principle.  In the analysis of the firm's investment decisions, we focus on the present value of the cash flows from capital investment projects, rather than on the matching of historic costs with future revenues.  Consequently, our discussion will concentrate on determining the exact timing of future cash flows, with no explicit consideration (apart from the tax savings from the tax deduction for depreciation) to the matching of expenses with the cash flows which they generate.

	Since the focus of our analysis is cash flow, the importance of depreciation expense arises from the fact that depreciation expense can be used to reduce future tax liabilities through the reduction of taxable income by an amount equal to depreciation expense.  To illustrate the impact of depreciation expense on cash flow, consider the following simplistic example.  Assume that a firm has revenues of $1000 and a corporate tax rate of 34 percent.  The firm also has $200 of depreciation expense.  Although corporations are currently allowed a deduction for depreciation expense by the Internal Revenue Service, the tax code can be changed by Congress at any time (retroactively in some cases).  Consider the following cases.

	I.  Depreciation Expense Not Deductible as an Expense

		Cash Flow

		Revenue	$1000
		  Taxes @ 34%	   340

		After-Tax Income	 $660

Since there are no non-cash expenditures included above, after-tax revenue is equal to cash flow.

		II.  Depreciation Expense Deductible

			Cash Flow

		Revenue		$1000
		  Depreciation		   200
		Taxable Income		$800
		  Taxes @ 34%		   272
		After-Tax Income	$528
		  Plus Depreciation	   200

		Cash Flow		  $728

	When depreciation expense is tax deductible, cash flow increases by $68.  Since depreciation expense reduces taxable income and the resulting tax liability without creating a “matching” cash outflow, cash flow is increased by the tax savings.  Since a $1 deduction for depreciation expense reduces taxable income by $1, and since the taxes on the additional dollar of revenue would have been $0.34 ( tc ), an additional dollar of depreciation increases cash flow by $0.34.  Since the depreciation expense above was $200, and since each dollar of depreciation expense increases cash flow by $034 (the tax liability on one dollar of revenue), the increase in cash flow attributable to the deduction for depreciation expense is $0.34 x $200 ($68).

	In general, the cash flow or “tax shield” provided by depreciation expense is 

		Tax Shield from Depreciation     =     tc  x  Depreciation Expense

where tc is the corporate tax rate.  Therefore, given the revenues (net of variable costs) and depreciation expense in the above example,

	Cash Flow	=     ( 1 -  tc  ) x Revenue    +    tc x Depreciation

	=     ( 1 - .34) x $1000        +   .34 x $200  

	=      $728.

Annual Equivalent Cost

	We often need to estimate the yearly fixed cost associated with the use of a piece of equipment.  For example, a meaningful estimate of the yearly fixed costs of manufacturing capacity is critical to determining the unit costs at a given level of production.  To estimate the yearly fixed costs of production capacity, we need to determine the present value of the costs that must be recovered over the productive life (to be distinguished from depreciable life) of the machine.  Given the present value of the costs that must be recovered, the annual equivalent cost is the level stream of costs (cash flows) having a present value equal to the present value of the cost of acquisition less the present value of the tax shields from depreciation.

	The present value of the costs that must be recovered over the productive life of an asset can be thought of in terms of

		Purchase Price    -    Present Value of Tax Shields from Depreciation

In addition, we might also need to consider the tax savings from any investment tax credit associated with the purchase of the equipment, as well as the present value of any proceeds from selling the asset at the end of its useful life.  These complications will be ignored for the moment.

	To illustrate the concept of annual equivalent cost, consider a leasing concern that purchases a piece of manufacturing equipment at a cost of $10,000.  Assume that the machine has a useful life of seven years but that Internal Revenue Service regulations permit the machine to be depreciated over a five year life using straight line depreciation.  Further, assume that the purchaser is in the 40 percent tax bracket with a required return of 12 percent.  The yearly depreciation will be

		Yearly Depreciation	=     ,

			=      $2000  ,

giving yearly tax savings (positive cash flow) of $800 (.40 x $2000) per year over 5 years.

	Therefore, the present value of the tax shields from depreciation will be

		$2884     =     .40  x  x   [ ]  .
Therefore, the present value of the costs which must be recovered by the lessor is

		$7116	=     $10,000    -    $2,884  .

	Given that the machine in our example has a useful life of seven years and that fixed costs are incurred at the end of the year, we define the annual equivalent cost for the machine as level stream of costs having the same present value as the present value of the costs to be recovered

		AEC  x  [ ]	=     $7116  ,

which implies that

		AEC	=    ,

			=    $1559  .

		Since equipment must be purchased using after-tax dollars and since the tax shields from depreciation are by definition after-tax cash flows, the present value of the costs that must be recovered reflects after-tax dollars.  Consequently, the annual equivalent cost must also be an after-tax cost.  If for some reason it is more convenient to think of the AEC on a before-tax basis, the ARC can be grossed up by a factor of ( 1 - tc ) to determine the equivalent before-tax amount, $2598 ($1559/(1 - .40) ).

Minimum Acceptable Rental Payments

	A problem closely related to the annual equivalent cost is the determining the minimum rental payment that a lessor must charge in leasing a piece of equipment to the final user (i.e., the lessee).  Consider a piece of equipment which the lessor purchases for the sole purpose of leasing to the actual user.  In order for the purchase of the equipment to be a positive net present value project, the lessor must require that the present value of the after-tax rental payments be equal to or greater than the present value of the costs associated with acquiring the asset.  As the actual owner of the equipment, the lessor is allowed to deduct depreciation expense.  The information in the previous example can be used to determine the minimum rental payment required to lease the equipment .

	Since rental payments are usually due in advance, the present value of the after-tax (for a lessor in a 40 percent tax bracket) rental payments over the next seven years would be

	( 1 - .40 ) x Yearly Rent x [ 1  +  ]  .

Note that the term in brackets in the expression above represents the annuity factor for an annuity of 7 payments where the first payment is due immediately.  That is the factor in brackets is equal to an immediate payment of one dollar plus the present value of a regular annuity of six payments.

	Given that the cost of the asset net of the present value of the tax shields from depreciation is $7116, the minimum before-tax rental payment that would be required is

		Rental Payment	=     ,

			=      $2320  .

Note that the after-tax value of yearly rentals of $2320 to the lessor is $1392 ( (1 - .40) x $2320 ).

	The table below illustrates the timing of the cash flows to the lessor from purchasing the machine at a cost of $10,000, receiving the tax shields from depreciation ($800) during each year for 5 years, in addition to receiving the after-tax rental payment for 7 years (with the first rental due immediately).  Computing the net present value of the total cash flow stream confirms that a before-tax rental payment of $2320 (giving an after-tax yearly rental stream of $1392) would make the acquisition of the machine would be a zero net present value prospect.

		Cash Flows for Leased Equipment

			0	1	2	3	4	5	6	

	Cost of Machine	<$10,000>

	Tax Shields from		800	800	800	800	800
	Depreciation (10/5)xtc

	After-Tax Rentals	1392	1392	1392	1392	1392	1392	1392

	Total Cash Flow	<$8608>	$2192	$2192	$2192	$2192	$2192	$1392

Capital Budgeting and Net Present Value

	The term capital budgeting refers to the procedures that are used by firms to allocate scarce capital to investments in productive capacity that are expected to generate cash flows over a given future period.  While each capital investment project is in some sense unique, a common set of principles can be used to apply the net present value rule to a wide range of investment alternatives.  These principles are illustrated by the example that follows.

	Consider a firm having an opportunity to produce a product with a life cycle of 5 years.  The projected sales for the project are $100,000 per year at the end of each of the next 5 years.  The before-tax profit margin on each dollar of sales is 10 percent.  The firm has a marginal tax rate of 40 percent and a required rate of return of 15 percent.

	The production of the product in question will require the purchase of machinery at a cost of $10,000.  The machinery can be depreciated over 5 years using straight line depreciation.  In addition, the project will require an investment in inventories and accounts receivables which may reasonably be expected to be recovered at the end of 5 years, when the project terminates.  Although the required investment in inventory and receivables is not known at the present time, the industry standards for inventory turnover and accounts receivable turnover are respectively 6 times per year and 12 times per year.

Required Investment

	The first step in analyzing any capital investment project is to determine the required investment.  As stated above, the project will require an immediate investment of $10,000 for the machinery required to produce the product.  In addition, the project will require an immediate investment in inventory and accounts receivable.

	The required investment in inventory and receivables for this project can be determined using estimates of inventory and receivables turnover for the industry.  The inventory turnover ratio is given by

		Inventory Turnover	=     .

Based on the projected profit margin (10 percent) and the projected yearly sales, we know that the yearly cost of goods sold will be $90,000.  Since the industry standard for inventory turnover is 6 times per year, a reasonable estimate of the average inventory required for the project is

		Average Inventory	=     

			=     

			=         $15,000  .

	Similarly, the required investment in accounts receivable can be determined from the receivables turnover 

		Receivables Turnover	=     .

Given that the receivables turnover for the industry is 12, the average level of accounts receivables will be approximately

		Average Receivables	=     ,

			=            ,

			=              $8,333  .

Since the cost of goods sold is approximately $0.90 per dollar of sales (given a profit margin of 10 percent), the investment required to maintain an average accounts receivables balance of $8,333 is $7,500 (0.90 x $8,333).

Projected Cash Flows

	The analysis above shows that the investment in working capital that is required to support the project is $22,500 ($15,000 + $7,500).  This amount is shown in the worksheet below as an immediate (time 0) cash outflow.  We will assume that all inventories are sold and that all receivables are collected when the project is liquidated.  This assumption implies that there will be an additional cash inflow of $22,500 when the project is terminated at the end of year 5.

	The machinery purchased at a cost of $10,000 can be depreciated over 5 years using straight line depreciation.  Given that the firm's tax rate is 40 percent, the yearly tax shields from depreciation will be

		.40 x 	=     $800  .

	The after-tax cash flow generated by the sales revenue from the project will be

		( 1 - tc ) x Profit Margin x Sales	=     ( 1 - .40 ) x .10 x $100,000   ,

			=       $6,000   .

	Although we could have computed a separate cash flow statement for each year of the project's life, it is often more convenient to determine the after-tax cash flow for each component of the project separately.  For example, in the worksheet on the following page, the tax shields from depreciation and the after-tax profit margin on sales revenues (i.e., net of cost of goods sold) are shown on separate lines.

	The cash flows for the project are summarized in the following worksheet.

		Project Cash Flows

			0	1	2	3	4	5	

	Working Capital	<$22,500>	$22,500

	Machinery	<$10,000>

	Inv Tax Credit	0

	Tax Shields from	800	800	800	800	800
	Depreciation (40/8)xtc

	After-Tax Profit on Sales	6000	6000	6000	6000	6000
	[Sales x .90 x (1 - tc )]
							 
	Cash Flow	<$32,500>	$6800	$6800	$6800	$6800	$6800
						+$22500

	Given a required rate of return of 15 percent, the net present value for the project will be

	NPV	=     <$32,500>    +    $6,800 [ ]    +   ,

		=     $1481  .

Annual Equivalent Cost and Replacement Decisions

	The physical life of a piece of equipment is the maximum length of time that the equipment can be operated given the willingness to incur excessive costs of maintenance and down time.  For example, most automobiles can be operated for 10 years or more with enough maintenance and loss of use due to time in the repair shop.  The economic life of an asset is to be distinguished from the physical life in that the economic life of a piece of equipment is the usage period having the lowest yearly equivalent (rental) cost.

	To understand the distinction between physical life and economic life more clearly, consider the following example.  A particular piece of manufacturing equipment has a physical life of 3 years and an initial cost of $9000.  The firm has a corporate tax rate of 33 1/3 percent and a required rate of return of 10 percent.  The machine will require increasing expenditures on maintenance (with all expenditures occurring at the end-of-the-year) and may be salvaged at any time prior to the end of the third year.  The required maintenance costs (before-tax) and the prospective after-tax salvage values for the machine are given below.  Note that if the machine is used for three years then the cash flow generated by the salvage of the machine is assumed to be zero.  Further, there will be no maintenance costs at the end of any year in which the machine is retired from service.

			Before-Tax	After-Tax
		Year	Maintenance	Salvage

		1	$1800	$5000
		2	$3000	$4000
		3		0

	Three-Year Replacement Cycle

	The present value of the costs associated with using the machine over its entire physical life of three years includes the purchase price of $9000, the yearly tax shields from depreciation over the next three years (.333 x $9000/3 ), and after-tax maintenance costs of $1200 ( 2/3 x $1800 ) at the end of year one and $2000 ( 2/3 x $3000 ) at the end of year two.  The present value of these costs is

	NPV	=     <$9000>     +     [ ]

	+     +     ,

		=     <$9257>  .

	In order to compare the cost of replacing the machine every three years with the (mutually exclusive alternative) cost of replacing the machine more frequently, it is useful to convert the present value of the total cash outflows given above to a constant after-tax yearly (rental) cost having the same present value.  This level stream of rental costs is usually referred as the annual equivalent rental cost.  As will become apparent in the next example, it is convenient to assume that the first “after-tax rental payment” is due immediately (i.e., in advance).  Given this assumption, the annual equivalent rental cost over a three-year replacement cycle is

		Annual Equivalent Rental	=     ,

			=     

			=      <$3384>  .

	Two-Year Replacement Cycle

	The economic life of this machine is less than three years if there is a shorter (more frequent) replacement cycle with a lower after-tax yearly equivalent cost of operation.  The procedure used to determine the annual equivalent rental over a two-year replacement cycle is similar to the procedure above.  However, the present value of the cash flows over a two-year replacement cycle includes the tax shields from depreciation for only the first two years.  Further, since the machine will be sold at the end of the second year, the present value of maintenance costs in the second year must be replaced by the present value of the after-tax proceeds from selling the machine at the end of year two.  The present value of the costs associated with a two-year replacement cycle is  

	NPV	=     <$9000>     +     [ ]

	+     +     ,

		=     <$5050>  .

The annual equivalent rental cost over a two-year replacement cycle is

		Annual Equivalent Rental	=     ,

			=     

			=      <$2645>  ,

which indicates that the yearly cost of using the machine over a two-year replacement cycle is less than the yearly cost of using the machine over a three-year replacement cycle.  In other words, the economic life of the machine cannot be three years since the yearly cost of replacing the machine every two years is less than the yearly cost of replacing the machine every three years.

One-Year Replacement Cycle

	To show that the economic life of the machine is two years, we must show that the annual equivalent cost of replacing the machine every year is greater than the annual equivalent cost of replacing the machine every two years.  Assuming that the machine is replaced at the end of the first year, the net present value of the associated cash flows is

	NPV	=     <$9000>     +     +     ,

		=     <$3545>  ,

which is also the annual equivalent rental corresponding to a strategy of replacing the machine every year.  Since this yearly cost ($3545) is greater than the yearly cost of replacing the machine every two years ($2645), the machine has an economic life of two years.

Replacement Decisions

	The conversion of the present value of the cash flows associated with using a piece of equipment over its economic life to an annual equivalent rental payment is particularly useful in evaluating the decision to replace the (old) equipment currently in use with a more recent model.  In most cases, the newer model can be operated at lower per unit costs, with substantially reduced maintenance costs.

	The use of annual equivalent costs in replacement decisions is illustrated by the following example.  Consider a firm having an opportunity cost of capital of 10 percent which is (for simplicity) exempt from paying corporate taxes.  The firm has an opportunity to replace a piece of equipment currently in service with a newer model having a cost of $7000.  The new equipment, which has an economic life of 5 years, will require maintenance (an overhaul) costing $1200 at the end of each of the next 4 years.

	The present value of the costs of using the new machine over the next 5 years is

	NPV	=     <$7000>     +     <$1200> [ ]  ,

		=      <$10,804>  .

Note that if corporate taxes were included in our analysis, the present value of the costs of using the new machine would include the tax shields from depreciation and the maintenance costs would be converted to an after-tax basis.

	The equivalent annual rental cost of using the new machine is

		Annual Equivalent Rental	=     ,

			=      <$2591>  .

Therefore, the total “rental” cost of using the new machine is $2591 per year.

Yearly Cost for Existing Equipment

	To determine whether new equipment should be purchased to replace the equipment currently in service, assume that the schedule for the required maintenance costs and potential salvage values for the old equipment (beginning immediately) over the next two years is as shown below

		Year	Maintenance	Salvage

		0	$1000	$3000
		1	1500	2000
		2		800

The salvage value for the old equipment is crucial in any replacement decision since running the old equipment for one more year as of any future decision point forces the firm to give up the opportunity to sell the old equipment at the salvage value listed above.

	In order to determine whether the old machine should be replaced, we can compare the present value of the costs of running the existing machine one more year with the equivalent yearly rental cost of operating the new machine.  Since the equivalent annual rental cost has been determined under the assumption that the first payment is due immediately, the equivalent rental cost should be compared with the present value of the costs of using the old equipment for one more year.  The present value of the costs of using the old equipment for one more year include $1000 of maintenance required to operate the equipment for an additional year plus the opportunity cost of not salvaging the old equipment immediately ( $3000) minus the present value of the proceeds from salvaging the old equipment next year (when the new equipment is purchased).  (Note that we are implicitly assuming that the old machine can be replaced in one year at today's costs.)

	The present value of the costs of operating the existing machine one more year are currently

		$2182	=     $1000     +     $3000    -    .

Since the cost of using the old machine one more year is only $2182, compared with a yearly cost of using the new machine of $2591, we should use the old equipment for one more year.

	At the end of one year, the decision to use the old equipment for one more year will require that the firm spend $1500 for maintenance and give up the opportunity to salvage the old machine for $2000.  These costs will be offset in part by the present value of the proceeds from salvaging the old equipment at the end of the year for $800.  Therefore, the present value of the costs of operating the existing machine one more year are currently

		$2773	=     $1500     +     $2000    -    .

	Assuming that the annual equivalent cost of using the new machine has remained at $2591, the old machine should be replaced since the cost of using the old machine for a second year is $2773.  If the costs of using the new equipment are not expected to remain constant, we could always factor this into our decision by including the present value of the increase in the costs of using the new machine as one of the components of the cost of using the old machine for one more year as of the initial date (i.e., date zero).  In other words, we could treat the projected increase in the cost of new equipment represents as an opportunity cost of using the old machine.