Net Present Value in the Valuation of Investment Projects - Essay Example

Question-2

i.NPV or Net Present Value is the traditional approach for the valuation of investment projects, which involves the risk- adjustment & discount rate, which means discounting of expected CF from a given project which shows the risk of that CF, that means NPV is the sum of all cash inflows & outflows of a project. From the financial point of view, in order to calculate NPV, we need to use the following calculation-

N CFt

NPV = ∑

t=0 (1+k) t

The NPV method is simply used regularly as by this the estimation of risk-adjusted rate of discount is easier relative to similar certain CF.

Thus, to represent this equation, we will need k = interest rate & n = number of years/time which is not clearly mentioned here. So, in such cases, the future spot prices goods, that are highly volatile, future prices can be replaced. This methodology bypasses the requirement to compute a risk- adjustments discount rate. Here, the adjustment for risk has been equally made as the cash inflows of the related discount rate which is the risk-free rate of interest. In our current concern, as there is universal risk neutrality, thus, the risk free rate is zero. If time is assumed to be 1 year, then NPV of initial investment will be £100.

Another equation can also be used to determine NPV of each types of investment. Like-

For company-A:

VA in = D11 (1 + µ/R) Y0 – I or £100

Here, I = investment

VA = NPV

VAout = D01 (1 + µ/R) Y0

Here, there is no investment.

So, optimal strategy is-

(Ain , Aout) = if I<I2

(Aout, Ain) = I2∞< I I1∞

(Aout,Aout) = if I> I1∞

Similar calculation for B:

VB in = D11 (1 + µ/R) Y0 – I or £100

Here, I = investment

VB = NPV

VBout = D01 (1 + µ/R) Y0

Here, there is no investment.

So, optimal strategy is-

(Bin, Bout) = if I<I2

(Bout, Bin) = I2∞< I I1∞

(Bout,Bout) = if I> I1∞

• NPV for immediate investment by both A & B = 500
• NPV for delayed investment by both A & B = 600
• NPV for non-collusive action-
  • • • 800 for A & 200 for B. or,
      • 800 for B & 200 for A.
• Here is graph that is showing the required condition as a format of game theory-

After picturing the above conditions as a shape of game theory, we can now explain the behavior of the two players. Here, we can see a payoff table where the two duopolists companies are named as A & B. It is showing a strategic game between these two companies. Here, each firm can choose its own strategy in the rows or columns. Such as, company A can choose between the two rows. In this example, each firm can decide whether to make the investment immediately or lately.

Combining those two decisions, the two companies can give four possible outcomes that have been shown in the diagram. Cell 1, existing in the upper left is showing the outcome when both firms simultaneously invest immediately & earn an inflow of 500 equally. Cell 4 is the outcome when both firms delay in investing to the project & gain an inflow of 600 each. Cell 2 & 3 result when one company invests immediately & other delays. The numbers that stay inside of the cell are showing the payoffs of the two firms. That means the amount of possible inflows that has been obtained by individual firm for each of the four outcomes. The number in the lower left shows the payoffs of the company B & right corner of the upper left shows the payoff of the company A (player of the top). As the firms are identical, the payoffs are visualized as mirror images. Applying the maximum benefits to the duopoly example we can identify several key issues. First, in outcome 1, each firm earns a combined profit of 1000 while they are ready to invest immediately. While the delay option adds value because here the PV of future cash flow will be 600 for each project.

ii.This game will significantly represent 2 types of equilibrium. Such as-

• Dominant Equilibrium: In this game, consider the option opened to A. If B conducts the project as useful with a delayed investment, A will get the profit of 800 by investing immediately. Similarly, if B starts this investment opportunity war by investing immediately, A will lose 600 (800-200), if its investment is delayed. So, there is no attention to the other firms’ strategy, rather than each one’s best strategy is to invest immediately. So, immediate investment is the dominant strategy for both firms in this situation, when all players have dominant strategy, the outcome is called dominant equilibrium & here cell 1 is that equilibrium.

• Nash Equilibrium: We can also find out Nash equilibrium in this aspect.

Here, it is the rivalry game while both firms consider whether to invest immediately or make a delay. The firms can stay at the immediate investment equilibrium or they can make a delayed investment in the hope of earning monopoly inflows. Thus, they have the highest joint amount in cell 4, while they can earn a total of 1200 when each follows a delayed investment strategy. At the other extreme, it is the competitive strategy of prompt investment inflow where each rival can obtain only 500. In cell 3, A undercuts A as it is taking most of the benefits & has high inflow than any other situation while B is losing money. In cell 2, A introduces late & B immediate investment means a loss of A. Here, the main theme is- a company should set its strategy on the assumption that the opponents will act in his / her best interest. This is the Nash Equilibrium of the game that has been just described. Here, no players can improve the own payoff that has been given to the other players strategy. That means, here each player’s strategy is a best response against the others. It is also a non co-operative equilibrium as each party chooses the option that is best for itself without any collusion.

In this figure, cell-4 represents a Nash Equilibrium as neither A nor B can improve its payoffs from the (immediate, immediate) equilibrium as the other does not change the strategy.

Prisoner’s Dilemma-

From the price game, we know that competition among firms simply led to the competitive outcome with fewer prices. The invisible hand theory by Adam Smith produces in perfectly competitive markets for the efficient allocation of resources. But this incident does not arise in all situations. In that regard, prisoner’s dilemma is one of the most famous terms in all games that can be applied in our project investment appraisal.

Say, company A & B are in the role of 2 prisoners. Both are simultaneously deciding whether to invest immediately or to delay in an innovative project. Here, the initial investment is 100 regardless the optional condition. Their investment opportunity implies that if both invest immediately, the PV of future CF will be 500, delay investment will have a value addition of 600 for each, but breaking this condition will result in the acquisition of 800 for one & 200 for other.

So, now the questions arise- what should A do? Should it delay & hope to get a big amount? 800 is preferable to 600 that can be earned by avoiding mutuality? Say, A does not invest immediately & B does immediately. A will get only 200. It is clearly better for A to invest immediately to get 500 of inflow that is better than getting 200.

B is in the equal dilemma. If it knew that A was thinking or what A thought B was thinking as a cyclic order.

The optimum result is that when both firms are acting selfishly by investing immediately, they both conclude with long prison terms. Only when the two act collusively will they stop the short prison terms in this case.

• The new game theory for the changed circumstances can be visualized by the following graph-

This payoff table is showing the reformed strategic games between A & B where the companies have taken a collusive decision by signing a contract based on the agreement adopting ‘wait-&-see’ procedure. Here, if a firm breaks the agreement & invests early, it will be finned by other firm as there is a transfer of balance of 400 to the delayed firm. But if both firms break the agreement, there will be no fine or no transfer of account. In this example, each firm has the opportunity to have a stable investment, punishment or finned transfer or another collusive agreement to break down of the agreement at the same time.

Combining all of the possible decisions, the company’s probable outcomes can be shown in the figure. Here, cell A, staying at the upper left of the table, represents the position where each firm is maintaining its argument of delay investment & getting cash inflows of 600 each. Cell 4 also represents the equal outcomes while the breaking of argument by both firms will result in no punishment & remain the same inflows. In case of Dominant Equilibrium, cell 1 & 4 are both representatives of a definite amount. Considering the option disclosed to company A, we can find out that if B operates its business with a hurry-up strategy, that means if B invests early by breaking the mutual agreement, it will lose 400 from its existing inflow of 600 & as a result the deducted gain for B will be 200. The same statement can be applied for A’s changed strategy also. So, cell A is the dominant equilibrium point while it is also predetermined. Here, the consideration of dominant equilibrium is quite clumsy as the entire game is the result of primary mutual agreement. Next, we can consider the Nash Equilibrium point of the companies. In such types of equilibrium point, each company can select its own strategy regardless society & other competitors. So, here, cell 4 is representing Nash Equilibrium as neither A nor B can improves its payoffs from the (finned, finned) equilibrium as long as other does not change the strategies.

While a firm will go to the value addition technique by the exercise of delaying a project, it may find out the option if to collude or not to collude & a prisoner’s dilemma. Such as, non co-operative equilibrium can be inefficient for a company which is a major problem in product market competition. As in cell 4, it brings an equal profit than the collusive outcomes. Here is no best joint solution which may discourage the firms. If each company would move towards a selfish interest it will lose 400 from the original amount & the rival’s total inflow will be 1000 = (600 + 400).

The prisoner’s dilemma will also operate the firm’s confusion in taking right decision. As here is no rewarding point, both the firms may not go for a punishment chance.

Thus, by legal contract, no firm will be able to create additional values because of penalties & ultimate loss rather than competitors. So, a competition will take a straight shape of social welfare.

Bibligraphy:

Brigham, E. F., & Houseton, J. F. (2004), Fundamentals of Financial Management, 10th Edition, Thomson south-western, Singapore, ISBN: 0-324-17829-8

Pandey, I. M. (2007), Financial Management, 9th Edition, Vikas publishing house PVT LTD, New Delhi, ISBN: 81-259-1658-X

Samuelson, P. A., Nordhaus, W. D. (2006), Economics, 18th Edition, Tata Mcgraw-Hill Publishing Company Limited, New Delhi, ISBN: 0-07-059855-X

Mcconnel, C. R., Brue, S. L. (2005), Economics-Principles, problems & policies, 16th Edition, Mcgraw-Hill International Edition, Singapore, ISBN: 007-124914-1

Imai, J. & Watanabe, T. (2004), A Two-stage Investment Game in Real Option Analysis, 2nd ed., Tokyo Metropolitan University,

Boyer, M., & Gravel, E., Lasserre, P., (2004), Real Options and Strategic Competition: A survey, Univ. du Quebec a Montreal

Smit, H.T.J., & L.A., Ankum (1993), A Real Options and Game-Theoretic Approach to Corporate Investment Strategy under Competition