P ROFIT CONCEPTS AND NET PRESENT VALUE

Accounting profit and economic profit  What is profit?  Generally: the difference between revenues and costs  Accounting profit: the sales of the firm less the (accounting) costs (such as wages, rent, fuel, raw materials, interest on loans, and depreciation)  In other words: sales revenues minus all costs except for the cost of equity capital; or accounting revenues in excess of accounting expenses  Economic profit: sales revenues minus all costs including the opportunity cost of all kinds of capital  That is, including also the cost of equity capital, so economic profit is usually lower than accounting profit

Sources of economic profit  For economic decisions the economic profit is the relevant term  The definition of costs is difficult, so profit is determined somewhat arbitrarily, and has thus only a “usual approach”  According to that common definition of economic profit, it has three basic sources:  Entrepreneurial ability: discovering profitable arbitrage opportunities, introducing innovations (in products and production processes), and copying (either the innovations or the arbitrage opportunities), profit is the reward  Monopoly power: profit may result from the possession of monopoly power in the market  Uncertainty: profit can be thought of as a reward for taking risks  Profit is risky – it has an expected value and standard deviation  Expected value stems from entrepreneurial ability and/or monopoly power, and the actual profit – that is, the deviation from the expected – yields as the result of uncertainty

Profit in future, and discounted to present (I.)  The microeconomic definition of economic profit takes all opportunity costs of factors of production into consideration  From the microeconomic point of view, entrepreneurial ability or monopoly power cannot be in the background of an alternative opportunity  Consequently, the microeconomic approach also refers to the gains from either entrepreneurial ability or monopoly power as profit  → We have a definition equivalent to the common  The timing of microeconomic profit is not as clear – rather posterior summation: “This has been the revenue and this has been the opportunity cost, so this is the result: the profit.”  Even in a decision-making situation, it evaluates the (expected) final situation as of the end of the project

Profit in future, and discounted to present (II.)  Finance also strives to grasp the economic profit, but wants to evaluate as of the present  E.g., the basic question is whether to invest or not in a given project at the (current) moment  → Both future cash flows and profits are calculated back to the present, to the time of the decisions  Overall, the microeconomic and financial approaches are practically the same regarding the meaning of profit – the main difference is in the time of reference: future vs. present  Consider the example of a one-year-long business project  F 0 investment is required to launch the project  If the owners of the project borrow this amount, they will have to pay r D interest  The project will have R 1 revenue in one year

Profit in future, and discounted to present (III.)  How much is the profit from the microeconomic point of view?  F 0 and r D F 0 interest give a C 1 cost of the project at the end of the year, which must be subtracted from the R 1 revenue  That is, owners will receive an amount F 1 = R 1 – C 1 at the end of the year:  How can the profit be interpreted according to the financial approach?

Profit in future, and discounted to present (IV.)  For this, π 1 is to be discounted by both time and risk  What gives the riskiness of π 1 ?  Its riskiness stems from the riskiness of R 1, F 0, and r D  The riskiness of R 1 comes from the business activity; R 1 is obviously risky  F 0 is a certain present amount; therefore, it is riskless  The case of r D is not that simple It may be that on the basis of the debt contract it is practically risk-free, e.g., it is covered somehow It may be that r D is risky too; e.g., the lender is similar to a shareholder, or the interest is agreed to depend on the course of business – then, a part of business risk (that is, a part of the risk of R 1 ) falls on r D, hence the risk of π 1 decreases So, the level of risk of π 1 is not straightforward

Profit in future, and discounted to present (V.)  Suppose that the risk of π 1 is known – then, there must be a particular level of interest rate (let’s denote it by r) reflecting the level of risk of π 1 in the financial market  Thus:  π 0 is called net present value, NPV, which is namely the economic profit expressed as of the present  How can multi-period cases be handled?

Profit in future, and discounted to present (VI.)  The microeconomic approach is problematic because of the various reference points of time in multi-period cases  It may be kept for separate analyses of yearly business situations, but it must be rejected as a general method of analysis for a multi-period project as a whole  Thus, the π n “yearly profits” are first analyzed in the microeconomic way, and then these „profit pieces” are discounted in the financial way to the present  Finally, these present values are added up to arrive at the net present value of a multi-period project  The F n (net) cash flows are these „profit pieces”, so:

Profit in future, and discounted to present (VII.)  Because cash flows are typically risky, therefore:  The NPV is the expected economic profit discounted to the present  But where is the risk in the above formula?  It “hides” in the cost of capital r, as the level of this rate depends on risk  Some elaboration: in the above, some kind of debt was considered for which the owners had to pay r D F 0 interest – what if the owners themselves provide this initial amount for the business?  Practically, nothing new: the owners of the business are also lenders (more precisely, owners of all the financial assets of the business)  Thus, the interest is paid to them, but this affects neither the profit nor the NPV – they receive r D F 0 as financial asset owners; it is their opportunity cost of capital, but it is a kind of cost, and not a profit

Net present value and internal rate of return (I.)  Consider now the risky intertemporal decision- making of an individual  The illustration applies, for now, only to a given level of risk  Let this single risk level be equal to the risk level of the previously introduced market portfolio  Thus, E(r M ) determines the relation between certain present and risky future cash flows  Suppose that a particular individual starts from situation A (next slide)

Net present value and internal rate of return (II.)

Net present value and internal rate of return (III.)  He would move along the intertemporal budget line to maximize his utility  Invest or take out a loan at rate E(r M )

Net present value and internal rate of return (IV.)  Extend now the opportunity set of the given individual to include project opportunities of a company owned by the individual  Thus, beside the lending and borrowing opportunities in the market, he may invest in several different corporate projects too  As only one particular level of risk is assumed to exist in the world, the projects also have to be of this very level of risk (which is equal to the risk of the market portfolio for this discussion)

Net present value and internal rate of return (V.)  Moving by the arrows (the starting point is unimportant):

Net present value and internal rate of return (VI.)  Combining projects with capital market opportunities:  Clearly, only Q and T are „good” projects (worth undertaking)

Net present value and internal rate of return (VII.)  Would a different owner of the same company also approve of these projects (Q and T) for investment?  Let’s look at a “totally different” individual: vs. former:

Net present value and internal rate of return (VIII.)  The choice of the „totally different” individual:

Net present value and internal rate of return (IX.)  The choices of the two “totally different” owners are the same  The reason is obvious: a corporate investment project generates the same wealth for the different owners, it “pushes” the intertemporal budget lines to the same degree, which means the same increase in wealth  → A company may be run in consensus among several “very different” owners  For this to hold, owners need only one common trait: utility (or profit) maximization  The boundary between “good” and “bad” projects: the slopes of the arrows ~ the expected returns of the projects  The rule is obvious: the company should invest in every project that has expected return higher than the market return at the same level of risk, i.e., their cost of capital is lower than their expected return:

Net present value and internal rate of return (X.)  Now relax the „single-risk world” assumption  The above-mentioned rules are obviously valid for any level of risk  The general rule can be formulated: a company acting in the interest of its owners (the shareholders) is to invest in every, but only such, project for which expected return > cost of capital  Consider an analogous rule:  F 0 investment yields a net cash flow of E(F 1 ) in one period  If this F 0 investment had the same (expected) return as the capital market offers for its level of risk, it would yield an amount F 0 (1+r) – so this amount is the opportunity cost of the F 0 investment  At the end of the project, it would yield an amount E(F 1 ) – F 0 (1+r) for the owners (an excess over the opportunity cost)  The present value of this surplus is the net present value (NPV), which was introduced earlier:

 Generalizing for multiple periods (cash flow diagram):  The net present value criterion is generalized for multiple periods as: the one-year cost of capital is applied repeatedly according to the rule of compounding interest: Net present value and internal rate of return (XI.)

Net present value and internal rate of return (XII.)  It is more complicated to extend the expected return (or rate of return) criterion  For the single-period case, the rule is simple: the project is “good,” if and only if E(F 1 )/F 0 – 1 > r  For multi-period cases, some kind of “average” (yearly) return should be calculated, although the sequential F n cash flows might have different magnitudes  The starting point: 1) if the “average” return of an investment is just equal to the cost of capital r, then the NPV is obviously zero; 2) if the NPV is zero at a return (discount rate) r, then the project’s “average” return must be equal to that return r  This logic leads to the concept of the internal rate of return (IRR):

Net present value and internal rate of return (XIII.)  Finally, the two fundamental and general decision rules are the followings:  1) NPV rule: An investment should be accepted if its net present value > 0, and be rejected otherwise  NPV is the sum of a project’s cash flows discounted at the cost of capital of the project  According to the theory of NPV, undertaking a project with positive NPV will increase shareholder wealth  2) IRR rule: An investment should be accepted if its internal rate of return (“average” expected return) is greater than its cost of capital, and be rejected otherwise  It is easy to see that these two decision rules lead to the same result: if the IRR of a project is greater than the cost of capital, then the NPV must be positive