Uncertainty, Financing and Limited Liability

Uncertainty The necessity of fixed cost often raises the question of financing. Sometimes financing cannot be repaid. This raises the question of liability. All estimation at the beginning of projects contains uncertainty. How uncertainty affects decision making processes for producers and financiers?

Example A person has an opportunity to undertake two projects Project one: –Initial investment: one thousand dollars –Payoff: 50% chance 1,500 dollar,50% chance 1,000 dollars after one year Project two –Initial investment: one million dollars –Payoff: 50% chance 1,500,000 dollar,50% chance 1,000,000 dollars after one year.

Example (Continued) The person has one thousand dollar capital. The loan interest rate is 10% per year. If the liability is unlimited, which means the debtors could be imprisoned or have to work as slaves, which project you would choose? If the liability is limited, which project you would choose? Please calculate net present values of project one and two from social perspective and owner’s perspective

Calculations We assume the cost of capital is the loan interest rate. Both projects are bank financed. Social perspective NPV of project one (1500*50%+1000*50%)/ = NPV of project two ( *50% *50%)/ =

Owner’s perspective in limited liability environment Project one (1500/ )*50%= Project two ( / )*50%= Are values from the social perspective and the owner’s perspective same?

Discussion In a limited liability environment, project value from social perspective is always lower than project value from owner’s perspective. The difference is ultimately subsidized by the society. The cause of financial crisis Why we still support limited liability system?

Unlimited liability system In a unlimited liability system, the person is most likely choose project one, which can be self financed with his own money. This results in the choice of low NPV project.

Conclusion By supporting limited liability system and taxing profitable projects, whole society could benefit. Limited liability system stimulate economic growth. Potential downside of limited liability system?

Example A person has an opportunity to undertake two projects Project one: –Initial investment: one thousand dollars –Payoff: 50% chance 1,500 dollar,50% chance 1,000 dollars Project two –Initial investment: one million dollars –Payoff: 50% chance 1,500,000 dollar,50% chance 300,000 dollars

Example (Continued) The person has one thousand dollar capital. The loan interest rate is 10%. If the liability is unlimited, which means the debtors could be imprisoned or have to work as slaves, which project you would choose? If the liability is limited, which project you would choose? Please calculate net present values of project one and two from social perspective and owner’s perspective

Calculations We assume the cost of capital is the loan interest rate. Social perspective NPV of project one (1500*50%+1000*50%)/ = NPV of project two ( *50% *50%)/ =

Owner’s perspective in limited liability environment Project one (1500/ )*50%= Project two ( / )*50%= Are values from the social perspective and the owner’s perspective same?

Some observation Value from social perspective is very negative while from owner’s perspective is very positive. Moral hazard How to weigh the tradeoff between more potential for economic growth and moral hazard?

Discussion When the growth potential is high, we are willing to invest more in risky projects and are more willing to bear the downside risk. Consequently, we are more tolerant to moral hazard as long as the policy generate high economic growth overall.

Methods of external financing Debt financing and equity financing Debt has higher level of liability than equity

Research shows that in places with high growth potential, such as USA, equity financing is more popular while in places with less growth potential, such as Europe, debt financing is more popular. In places with high growth potential, laws favor more equity holders than debt holders while in places with less growth potential, it is the opposite. Chapter 11 in US allow equity holders to stop interest payment for a period of time while in continental Europe, laws are more concerned about the residual values for debt holders.

Causality and correlation In many researches, correlations are explained as causalities. For example, relation between limited liability and wellbeing of society Why the global financial crisis originated in US?

What ultimately determines the growth potential? The interactions between technology and resources Technology increase resource base. It also consumes more resources. Most highly developed civilizations eventually turn into desolate places. How the attitude on limited liability and risk taking will evolve in the future?

Level of uncertainty, limited liability and project choices

Example A person has an opportunity to undertake two projects Project one: –Initial investment: one million dollars –Payoff: 50% chance 1,800,000 dollar,50% chance 600,000 dollars after one year Project two –Initial investment: one million dollars –Payoff: 50% chance 1,500,000 dollar,50% chance 1,000,000 dollars after one year.

Example (Continued) Assume the lender cannot detect the differences in earning structures of two projects and charge the same loan rate at 10% per year. Please calculate net present values of project one and two from social perspective and owner’s perspective Which project you would choose?

Calculations Social perspective NPV of project one ( *50% *50%)/ = NPV of project two ( *50% *50%)/ =

Calculation Owner’s perspective Project one ( / )*50%= Project two ( / )*50%= NPV from the first project is higher. How level of uncertainty affects project choices in limited liability environment? Why banks suffer such huge losses in the financial crisis?

Parental investments and children’s obligations Parental investments are very high. In some societies, children’s obligations to their old age parents are more than others. How to understand the differences from our discussion about limited liabilities?

In a society with low children obligations, children have more freedom to pursue their own interests, which provides more opportunity for economic growth. Old age security is socialized. At the same time, there is more potential for moral hazard. Specifically, many people may take a free ride. They may opt not to have children but still enjoy socialized senior care.

In a society with high children obligation, children may have less opportunity to pursue their own ideas and interests. Less innovative activities. Less moral hazard. How to value the tradeoffs?

Financing cycles: In life and in firms When you are young, you are mainly financed by equity. If you are five years old, try go to a bank and tell a loan officer: “I am going to be a billionaire in twenty years. I would like to get a million dollar loan today.” Similarly, young firms that have not yet generated steady earnings are mainly financed with equity.

For people with steady and growing income, they may be able to obtain loans easily, especially loans mortgaged with tangible assets such as houses. For firms with steady and growing income, they may be able to obtain loans easily, especially loans secured with tangible assets.

When people mature in age, they may raise children and support others. When firms mature, they distribute dividends.

An Investor’s Perspective An investor has two choices in investment. Risk free asset and risky asset For simplicity, the return on risk free asset is zero. The return on risky asset is 1+d for probability p, 1-d for probability 1-p Investor want to maximize his long term return. How should he allocate resources between risk free and risky assets?

Solution Suppose the investor will allocate portion x into risky asset and portion 1-x into riskless asset. The expected rate of return for him is

To determine the value of x at which the portfolio will have the maximal rate of return, we differentiate the above formula with respect to x.

The above differentiation equals zero when At this value of x, the portfolio obtains the highest expected geometric return.

Some numerical examples Assume d = 25%, which is roughly equivalent to standard deviation of 25% for a stock. We set p = 0.55, 0.575, 0.60, 0.625

Example Suppose p = 0.575, d = 0.25 for the risky asset and the risk free rate is 0. What are the expected geometric returns if the portion of the risky asset is 30%, 60% and 90%? What are the expected arithmetic returns if the portion of the risky asset is 30%, 60% and 90%?

Answers expected geometric return expected arithmetic return

Geometric and arithmetic returns In practice, arithmetic means are used to measure performance. Geometric means provide more relevant measure for investors Example: First year 100% return, second year -50%. What is the average return from two years?

Higher Risk, Higher Return? True up to a certain level. If p = 0.6, up to the level of 80% of risky asset, higher risk, higher return. Over 80% limit, higher risk, lower return. In the past, high equity return. Putting all assets in equity may provide high return. If equity premium is lower in the future, as in the past ten years in most of the stock markets, return and risk pictures could be different.

A comparison with standard theory In standard theory, there is always a risk return tradeoff. In our theory, there is a highest possible return at a certain point. The standard theory is a two parameter theory. Ours is a one parameter theory.

Utility based or return based? A deeper sense of difference is whether economic theory should be utility based on return based Measurement of company performances is return based Human decisions are utility based. It is often claimed that human beings have free will. However, company managers are human beings and have free will as well.

Both companies and individuals are subject to the requirement of positive returns. If a person makes a bad investment decision, his wealth will shrink and his impact on market will decline.

Difference on investment decisions In CAPM, there is a capital market line. Investors can pick any point on capital market line based on his utility function. In a geometric return based theory, the ones choose higher rates of return will gradually holding higher shares of total wealth than the ones choose lower rates of return.

Capital Market Line

Forms of Business Ownership Sole Proprietorships Limited Liability Partnership Corporations Advantages and disadvantages of each types of ownership The order of complexity of different forms of ownership