Lecture 4Problems: Return Problem Set 1

25 January 2006Reading Baye, Ch. 1 pp 14-27

(Today)

Lecture 4Problems: Return Problem Set 1,

Problem Set 2 – due Monday.

REVIEW______:

I. Chapter 1. The Fundamentals of Managerial Economics

B. Components of Effective Decision Making

5. Recognize the Time Value of Money.

a. Discounting the Future.

b. Calculating Net Present Value of a Project

Comment: Recall problem 1. A student asked if in deciding whether to undertake a project, it made a difference if the net present value if a project was less than the cost the project. I ERRED IN MY RESPONSE. The correct answer is: ANY PROJECT WITH A POSITIVE NPV SHOULD BE UNDERTAKEN.

To see this, suppose you are given the chance to invest $100,000 in a project that will yield $60,000 for each of the next two years. If i=.10, then the PV of the returns is

60,000/1.1 + 60,000/1.12

=54,540 + 49,587

=104,132.

The Net Present value is 104,132-100,000 = 4,132. (That is, you end up with 4,132 MORE than 100,000 in present value terms.)

Suppose, alternatively, that you took the 100,000 and put it in the bank for two years. If i = .10, you would have 110,000 after one year, and $121, 000 after two years. The present value of that money is (by definition) $121,000/(1.1)2 = 100,000

c. The present value of a firm/ Discounting over an infinite horizon.

With the first payment coming in one year,

PV= /i

If the first payment is tomorrow,

PV= /i + =[(1+i) ]/i

Example: Suppose you can purchase a share of a firm that will pay a dividend of $10 each year, starting one year from today. If the discount rate is .05, what is the present value of this stock?

10/.05 = $200.

How would your answer change if the first payment came tomorrow?

10/.05 + 10 = $210.

5. Appreciate Marginal Analysis. Marginal decisions are an easy way to optimize totals that require less information in the decision-making process.

a. Discrete Decisions

- Allocating time for a test

Preview______

5. Marginal Analysis Continued

- Comparing TR to TC

b. Continuous Decisions

LECTURE______

5. Using Marginal Analysis. A final principle in intelligent decision-making pertains to the unit of analysis used. One can often cut through a very difficult optimization process by confining attention to incremental changes.

a. Discrete Decisions. Example. Suppose you were faced with the problem of trying to allocate study time between two courses for a test on the same day. If you had a total of 6 hours to study, you might have the following possibilities.

Econ Math

One way to approach this problem would be to consider all combinations of all totals that were available:

Scores

Total

Econ

Econ

An equivalent solution, however, is obtained by considering just the marginal changes

A marginal change is the change in the total associated with studying an extra hour.

Econ Math

Note: This process has the advantage that it requires less information.

More generally, we might consider a situation in which there were both costs and benefit (for example the case of profit maximization, where

=TR-TC

TB

TC

NB

MB

MC

MNB

Definition: The Marginal Principle: To maximize net benefits, the manager should increase the managerial control variable to the point where marginal benefit equals marginal costs.

Graphically, this can be illustrated both by graphs of totals and of marginal changes:

Total changes

Observe the role of marginals and totals.

(Notice that the totals and marginal lines should not line up exactly. There are two points of total maximization. This is due to the discreteness of decisions here. )