University of Texas at Dallas
	School of Management

Finance 6301		Professor Day
Corporate Finance		Fall 1999

	Lecture 6:  Advanced Topics in Capital Budgeting

	Corporate capital budgeting systems often use acceptance criteria for capital investments that depend on the objective of the project.  While non-quantitative criteria are sometimes accepted as a justification for projects involving considerations such as safety, convenience, or product quality, projects designed to increase profits are usually subjected to strict quantitative guidelines on the payback period and internal rate of return computed from projected after-tax cash flows.  For example, the following example of a typical capital budgeting system is taken from the classic Harvard case titled the  “Super Project”.

		Project Objective	Acceptance Criteria

		Cost Reduction	Payback ≤ 10 and PBT ≥ 0.20

		 Increase of Production Capacity	Payback ≤ 10 and PBT ≥ 0.20
		 for Existing Products

		Manufacture and Distribute	Payback < 10 and PBT ≥ 0.40
		 New Product or New Product Line

	Of particular interest among the investment criteria listed above is the evaluation of projects involving the manufacture and distribution of new products.  The criteria listed above are consistent with the argument that investments in new products should be evaluated by computing the net present value of the projected cash flows using a discount rate which includes an added risk premium  to reflect the additional risk associated with new product introductions.

	Although there is no question that a new product introduction exposes the company to above average risk, discounting the projected cash flows using an extremely high discount rate may not be the best way to adjust for the additional uncertainty associated with the market's acceptance of the new product.  Since new products are typically test-marketed prior to reaching a decision to engage in full scale production and distribution, a sequential analysis of the proposed project using a decision tree approach is often useful in evaluating a proposal for the introduction of a new product.  The following example illustrates the decision tree approach.

Example:

	Assume that your company has an opportunity to produce and distribute an electric mop.  The product will have a test market phase which lasts for one year.  The cost of the test marketing phase is expected to be $125,000.  Based on the company's past experience with new product introductions, there is a 0.50 probability that the test marketing phase will indicate that the product is economically viable.  Conversely, the probability that the product will be a failure in the test market phase is 0.50.

	If the test market phase suggests that the electric mop will be commercially viable, then full scale production and distribution of the product will require (in one year) an investment of $1,000,000 in plant and equipment.  The project would then be expected to generate annual cash flows of $250,000 per year beginning one year following the end of the test market phase.  If the test market phase indicates that the product is not commercially viable, then the company would discontinue all efforts to produce and distribute the electric mop.

	Given that the probability of a successful test market phase is 0.50, the expected cash flows from the project during the first 5 years of an infinite project life are expected to be

		Unconditional Expected Cash Flows

		(1000s)

			0	1	2	3	4	5	

		Cash Flows	<125>	<500>	125	125	125	125

On the time line above, the expected future cash flows in years two and beyond are determined by multiplying the expected cash inflows, conditional on a successful test market phase, by the probability that the test market phase will be successful (0.50 x $250).  Similarly, the expected cash outflow in year one is determined by multiplying the expected cost of plant and equipment by the probability of a successful test market phase (0.50 x $1000).  By contrast, the initial cash outflow of $125 is known in advance, since the cost of test marketing is required in order to evaluate the product market’s reaction to the new product.

	Although the opportunity cost of capital is 10 percent for projects having the same “level of risk” as the firm's current asset mix, the Chief Financial Officer believes that the additional risk associated with a new product introduction makes it advisable to use a discount rate of 25 percent to compute the present value of the projected cash flows from the electric mop project.

	Assuming that the correct approach to determining the Net Present Value of the project requires that the cash flows depicted above be discounted at a rate of 25 percent, the Net Present Value of the project is 

	NPV	=      <$125>      +      [  <$500>      +      ]  ,

		=       <$125>  ,

suggesting that the decision to test market the electric mop is a negative Net Present Value project.

Sequential Resolution of Uncertainty

	In the example above, we computed the expected cash flows from the electric mop project using what are referred to as the marginal probabilities.  That is, we computed the expected cash flows from the project using the initial (i.e., the pre-test market) probability that the electric mop will be a successful product.  Given that we also discounted these “post-test market expected cash flows” at an abnormally high discount rate to reflect the additional risk of the new product introduction, we have essentially assessed the project with a “double adjustment” for risk.  A more accurate approach to computing the net present value of the project would be to value the project sequentially.  In other words, we work backwards (as in dynamic programming), taking account of the fact that the value of the project at date one will depend on the outcome of the test market phase.  These conditional values at date one can then be used to compute the expected value of the project at date one, which in turn will be used to compute the net present value of the decision to test market the electric mop as of the initial period (decision point).

	Once the test market phase for the project has been completed, the firm has the option to either proceed with the project or else discontinue the project depending on whether the outcome indicates that the product will be successful or not.  If the product is likely to be well received, then it would be reasonable to value the project using the firm's normal required rate of return for projects in this industry.  Of course, if the test market phase indicates that the product will be a failure, then the project could be immediately discontinued without any further cash outflows (or inflows).

	Assuming that the test market phase is a success, the expected cash flows from the project are given by

		Conditional Expected Cash Flows

		(1000s)

			0	1	2	3	4	5	

		Cash Flows		<1000>	250	250	250	250

If we discount these expected cash flows at 0.10, the firm's normal opportunity cost of capital,  the Net Present Value of the expected cash flows (conditional on a successful test market phase) as of date one is

	NPV	=      <$1000>      +      ,

			=        $1500  .

If the test market phase indicates that the electric mop will not be a commercial success, then the project will be discontinued so that the NPV of the future cash flows from further development would be zero.

	Based on the analysis above, the value of the mop project will be $1500 at date one if the test market phase is a success.  If the test market phase is a failure the value of the project will be zero.  Therefore, as of the initial date, the expected value of the project is

				$750	=     0.50 x $1500     +     0.50 x 0  ,

where $1500 and $0 are the possible values of the two equally likely outcomes (probability 0.50) that may occur at date one.

	Now we are ready to determine the net present value of the decision to test market the new product as of date one, the initial decision point.  At date zero, the decision to test market the electric mop may indeed be sufficiently risky to require that the expected cash flows from the project be discounted at a rate which reflects the additional uncertainty surrounding the introduction of a new product.  However, since the expected payoff at date one reflects the fact that the project should be valued at the firm's normal opportunity cost of capital once the uncertainty of the test market phase has been resolved, discounting the expected payoff at date one at a higher than normal discount rate no longer imposes a double penalty for risk.

	Given the expected payoff and the fact that the CFO wishes to discount the expected “payoffs” from new product introductions at a rate of 25 percent, the net present value of test marketing the electric mop is

			NPV	=     <$125>     +     

				=       $475  ,

indicating that the firm should proceed with the project.

Economic Value Added

	Economic Value Added is a simple procedure that is frequently used to adjust the divisional profits of large firms for the cost of using corporate capital.  Although conventional measures of accounting earnings are adjusted for the interest expense on corporate debt, EVA includes charges for both debt and equity capital.  EVA analysis is viewed by many as a recent innovation in measuring corporate profitability.  However, the notion that profits should include a charge for the utilization of scarce resources such as corporate capital dates back (at least) to the writings of Sir John Hicks (see Value and Capital ) early in this century. 

	Although EVA appears to be a new method for the evaluation of divisional performance, it is easy to show that EVA analysis is virtually indistinguishable from the Net Present Value rule.  The Economic Value Added for a division or a firm at date t (EVA) can be determined by adjusting the cash flow at date t (C) by (1) adding back any increase or decrease in corporate capital ( I- I) between date t-1 and date t and (2) subtracting a charge for the (opportunity) cost of the capital tied up in the project or division (r x I).  Most EVA systems estimate the corporate capital being used by the division ( I) using the book value of invested capital adjusted for the economic depreciation of the project's capital assets.  In other words,

		EVA	=      C+    ( I-  I)    -    r I.

Rearranging this expression shows that 

		EVA	=      C+   I-    (1 + r) I.

	To verify that EVA analysis is simply the NPV rule in disguise, note that since there is no charge for the opportunity cost of capital at date 0, when a project is initiated, since the capital invested in the project was not utilized during the previous period.  Consequently, the EVA is 

		EVA	=      C+   I

where Crepresents the cash flow required to initiate the project and Irepresents the initial book value of the assets.  Since  I=  - Cby definition, the initial EVA for a capital investment project is equal to zero.

	Assuming that the project is to be liquidated at date T, the EVA at the project's terminal date is   

		EVA	=      C-    (1 + r) I.

	If we compute the Net Present Value of the EVA stream from date 0 through the termination of the project at date T, we have 

PV(EVA)     =     EVA+    +    +    +  .....  +     

Substituting for the EVA at each date t in terms of the cash flow at date t, the change in the book value of the project, and the charges assessed for the use of corporate capital gives 

	PV(EVA)	=    C+   I+     +    

	+    +  .....  +     

	=      C+    +    +  +  .....  +     .

In other words, the discounted present value of the EVA stream for a capital investment project is identical to the net present value of the cash flows for the project.

	To illustrate the computation of Economic Value Added, consider the following example from Grinblatt and Titman's Financial Markets and Corporate Strategy.  NASA is considering three (mutually exclusive) commercial projects for the next space launch.  Each project has industrial spin-offs (e.g., Tang and Teflon were spin-offs from the space projects of the early 60's) that will generate cash flows for NASA over the next two years.  Being a public agency, NASA has an unusually low opportunity cost of capital of 2 percent.  The cash flows from these projects are as shown below.

				Cash Flows
				0	1	2	NPV at 2%

		Project A	<17.0>	12	9	3.420

		Project B	<16.8>	10	11	3.558

		Project C	<16.9>	11	10	3.500

	Since the negative cash flow at date 0 (C) is equal to investment (I), the EVA for each project at date 0 is equal to zero (i.e., C+ Iequals 0).  Assume that none of the projects requires either an increase or a decrease in capital investment at date 1 (i.e., Iequals I).  Further, assume that the book value of each project will equal zero after the respective cash inflows at date 2 have been received.

	To verify that the discounted EVA stream is equal to the Net Present Value of the project flows, we must compute the EVA's for each project at dates 1 and 2.  At date 1, the EVA for project A is

	EVA	=      C+    (I-  I)    -    r I.

		=      12        +         0         -     0.02 x 17.0

		=     11.66

In other words, the EVA for project A at date 1 reflects cash flow of 12.0 less a 2 percent charge for the capital (17.0) tied up in the project.  Similarly, the date 1 EVA's for projects B and C are

	EVA	=     10.00     -     0.02 x 16.8

		=     11.664

and

	EVA	=     11.00     -     0.02 x 16.9

		=     10.662

	To determine the respective EVA's at date 2, note that since the book value of each project will equal zero at date 2, the final EVA for a capital investment project is 

		EVA	=       C+  ( I-  I)   -    r I.

			=       C+   ( 0  -  I)   -    r I.

			=      C-    (1 + r) I.

	Therefore, the terminal EVA's for the respective projects are

	EVA	=      9.00      -     1.02 x 17.0

		=    <8.34>

	EVA	=       11.00     -     1.02 x 16.8

		=      <6.14>

	and

	EVA	=      10.00     -     1.02 x 16.9

		=     <7.24>

	Discounting the EVA stream for project A at a discount rate of 2 percent shows that the present value of the EVA stream for project A is

	PV(A)	=     EVA+    +     

	=         0        +    +     

	=       3.415 .

which is exactly equal to the net present value of the cash flows from project A.  Similarly, the present values of the EVA streams for projects B and C are respectively 3.558 and 3.500, which are equal to the corresponding net present value's of the cash flows for projects B and C.