MF807 Corporate Finance

MF807 Corporate Finance

Prof. Thomas Chemmanur

Topic Note-1

1. Introduction

This course is aimed at providing you with the foundation for the debt markets, investments, option pricing, corporate finance, and other finance courses. The course will focus on finance theory, and my objective will be to cover much of the well established theory in finance. Unlike some other areas of business, finance has a core of theory which is fairly widely applied in the real world. The jump you will have to make from academics to application will, therefore, be somewhat smaller in the case of what you learn in your finance courses (though I admit that such a jump exists!). A recent article by two economics professors listed some of the contributions made by theoretical research in economics (economists consider finance to be part of economics) which are now widely adopted in practice.[1] Of the ten contributions they listed, five were in finance. These were: (i) The use of Net Present Value for capital budgeting (ii) Portfolio selection rules (iii) The Beta co-efficient and the Capital Asset Pricing Model (iv) Duration Analysis (v) The Black-Scholes option pricing model. (Of these, we will study all but (iv) and (v) in this course.)

Finance is concerned with the theory of financial markets. To begin with, we will be concerned with valuation. We will study how investors value various financial assets (or securities or instruments: we will use these words interchangeably). These financial assets, like stocks, bonds, etc., are sold by firms in financial markets (like the stock market or bond market) to raise capital for investment in their "projects". Thus, financial assets are a way in which investors' wealth is transferred to firms, who invest it in productive assets.

Why do investors buy these financial assets? Because firms will give them cash flows in the future: dividends in the case of stocks, or interest or coupon in the case of bonds. We will study how investors should make their "portfolio decision" with respect to these assets: i.e., what fraction of their wealth to invest in each asset, etc. This decision is somewhat complicated by risk: the fact that investors do not know for sure the amount or timing of the cash flows they will get from each asset.

In the second part of the course, we will look at various decisions from the point of view of the corporation. First, given the way in which investors value various assets, how should corporate financial managers choose projects to invest in? This decision is often referred to as the "investment" or "capital budgeting" decision. Second, how should they make their "financing decision?" i.e., what is the mix or proportion of each type of financial security they should sell to raise the money to invest in their projects? We will also look briefly at the dividend decision: i.e., how much dividend should the firm pay?

2. Forms of organization of a firm:

(1) Sole Proprietorship (2) Partnership (3) Corporation.

(1) A sole proprietorship is a business or firm owned by one individual. It is easily and inexpensively formed; the business pays no corporate income taxes, and business income is taxed at the tax rate of the individual who owns the business. The business is not subject to extensive government regulation. Against these advantages must be weighed the disadvantage that the liability of the owner is unlimited: the proprietor's personal assets may be held accountable for debts incurred for running the firm. Further, it may be difficult to raise large amounts of money under this organizational form.

(2) In a partnership, two or more persons associate to conduct a business. Many of the features of a partnership are similar to that of a proprietorship: unlimited liability and tax treatment, for instance. (However, there can be limited partnerships, quite common in the real estate business.)

(3) The corporation, however, is quite distinct from the other two forms of business organization. It is a legal entity separate from its owners and managers. This gives it some advantages: (a) It has an unlimited life (b) It permits easy transfer of ownership interest, simply by transferring shares of stock (c) it permits limited liability: i.e., shareholders' assets cannot be attached against the corporation's debt. Only the corporation goes bankrupt if it cannot pay its debt. However, corporations are subject to corporate income tax. Thus, assume that the corporation earns $1 in income. If the applicable corporate tax rate is 25%, the amount left to be divided among the shareholders is only $0.75! Corporations are of two types: private limited companies and public limited companies. In the case of the latter, its shares are freely traded in the stock market. These are also subject to additional government regulation (disclosure requirements, etc.)

In this course, we will assume that the corporations we are dealing with are ones whose shares are actively traded. We will also assume in general that all investors have free access to the capital market, and there are no "frictions" (for instance, transactions costs) preventing the free trading of securities.

3. The objective of the financial manager

Suppose you are the CEO of a car manufacturing company, which has the following three share holders, each holding a third of its shares: an old lady, a little boy, and a pension fund manager. At a meeting of shareholders, you ask them: what should the firm manufacture? The old lady wants quick profits. She asks you to manufacture large cars, which is currently in demand. The little boy, who doesn't need much money now, asks you to spend a lot of money on R&D and come up with electric cars, which he says will be the wave of the future. The pension fund manager wants you to build small cars. What decision will you make?

The above question already exposes the problem with saying "maximize profits", since then the question arises: Profits in which period? Also, the question arises: how much risk should the management take in order to maximize profits? We can show that if all shareholders have free access to the capital markets (i.e., frictions are quite small) the answer to the above question is: manufacture that product that maximizes shareholder wealth (i.e., the share price of the firm). Will this solution please everybody? Yes, because even if the project chosen by this measure is a long-term project which is going to yield large profits to the firm only ten years from now, the old lady can borrow money against the shares in the company (or sell her shares) to generate wealth to consume today. We will see as we go along that the objective of maximizing shareholder value also takes into account automatically the different risk characteristics of different projects.

If share-price maximization is then the proper objective, how should projects be selected? We can show that if management picks that project which has the highest Net Present value (NPV), it is, in essence, maximizing shareholder value, since (given that investors have enough information about project cash flows and so on) the firm's share price will go up by the extent of the NPV of the project undertaken. In summary, if the company's stock is publicly traded, and all investors have free and cheap access to the capital markets, individual share holders do not have to interfere in the day to day running of the company. They can leave these decisions to a manager, with instructions to maximize shareholder wealth, which, in turn, is equivalent to asking him/her to pick positive NPV projects (and, if he has to choose between projects, pick those with the highest NPV). (This result is often referred to as the Fisher Separation Theorem).

4. Net Present Value

Recall that the Net Present Value is the present value of the benefits from undertaking a project minus the present value of the investment amounts required to undertake the project. If this difference is positive, the project is yielding the firm more benefits than it costs, so that it increases firm value, and should be undertaken; if it is negative, the project will reduce firm value if undertaken, and should not be.

5. Review of Present Value Computation:

All of you must be somewhat familiar with computing present values from previous classes. Computing present value is at the core of all valuation problems in finance, so you should be very comfortable with computing the present values of arbitrary cash flow streams. I will therefore briefly review this material, to make sure that you are comfortable with present value computation.

i. Future value of a single amount

(1)

where F is the future value of an investment P after n periods, at a rate of return r per period. The term (1 + r)n is tabulated, and is often denoted by FVIFn,r.

(2)

ii. Present value of a single amount.

where P is the present value of a single amount F to be received n periods from now, if the opportunity cost of capital is r per period. The term [1/(1 + r)n] is tabulated, and is often denoted by PVIFn,r.

iii. Future Value of an annuity.

An annuity is a stream of cash flows where the cash flow in each period is the same. Consider the following three period annuity;

Note: Throughout this course, we will use this distinction between dates and periods.

Let us first compute the future value (i.e., the value at the end of the last period: i.e., at t=3) of this three period annuity. Using the formula (1) on each individual cash flow, and adding value at t = 3 (remember, we can add values at the same date):

F = A + A(1 + r) + A(1 +r)2.

Notice that the index on the last term is 3 - 1 = 2. Generalizing to the n period case, the future value of an n period annuity is,

F = A + A(1 + r) + A(1 + r)2 + A(1 + r)3 +.....+ A(1 + r)n-1.

= A [ 1 + (1 + r) + (1 +r)2 + (1 + r)3 +....+ (1 + r)n-1 ]

Referring to the mathematical appendix at the end of this note, the series inside the square brackets is a geometric series, with common ratio (1 + r). Making use of the formula for the sum of a geometric series, the term in the square brackets can be shown to be equal to 1. Thus,

(3)

The term in square brackets is tabulated, and is often denoted by FVIFAn,r.

iv. Present value of an annuity.

Using the same three period cash flow stream above as an example,

Present value of the three period annuity (i.e., value at t=0) is,

4(4)

Generalizing to the n period case as before,

5(5)

6(6)

The series in the square brackets is a geometric series with common ratio 1/(1 + r). Using the formula for the sum of a geometric series, this series can be summed as, . This gives,

(7)

The term in square brackets is tabulated, and is denoted by PVIFAn,r.

If the number of periods, n,goes to infinity, (7) can be shown to reduce to

(8)

which is the present value of a perpetual annuity or perpetuity.

v. Compounding and discounting more than once in a given period.

Sometimes the period over which the data is given may not be the period over which compounding is done. Eg. Let R be the interest rate per year, T be the number of years.

a) Future value of an amount P compounded half-yearly after T years at R is given by converting this data to correspond with the compounding period: n = number of effective periods = 2T in this example. r = interest rate per effective period = R/2. Then the future value is given by plugging in these values into (1). Generalizing to the case where compounding is done m times a year,

r = R/m, and n = mT. Using these in (1),

(9)

b) Similarly, the present value of an amount F, T years in the future, if discounting is done m times a year at a rate of return of R per year is,

(10)

vi. Continuous compounding and discounting.

Consider the case when m goes to infinity, i.e., compounding is done continuously. Taking the limit of (9) as ,

(11)

(e is the base of natural logarithms).

The present value of an amount F to be received T years from now, where discounting is done continuously at the rate of return R per year is easily obtained form (11) as,

(12)

Appendix: Sum of a geometric series.

Consider a series of terms of the form 1, k, k2, k3,....kn-1.

Each successive term is k times the previous one; k is therefore called the common ratio. The sum of all the above terms can be shown to be equal to,

S = 1 + k + k2 + k3 +...+ kn-1 = [(kn - 1)/(k-1)].

Whenever we see a series of the above form, we can sum it using the above formula, by setting k equal to the common ratio of that particular series.

Consider now the case where the number of terms in the series,. If k > 1, each successive term is larger than the previous one, and. However, in the special case where k < 1, we can show that the sum is given by, S = 1/(1 - k).

[1]Faulhaber and Baumol, "Economists as Innovators: Practical Products of Theoretical Research", Journal of Economic Literature, (June 1988), Vol XXVI, pp 577-600. Incidentally, Harry Markowitz and William Sharpe, who are credited with (ii) and (iii) respectively, shared the 1990 Nobel memorial Prize in Economics (along with Merton Miller, whose contribution, the Capital Structure and the Dividend irrelevance theorems, we will study also in this course).