Learning Objectives

  1. Describe the implications and institutions associated with the short term interest rate, and describe how to compute single and compound interest.
  2. Identify the difference between coupon and discount bonds, and calculate the present discounted value of discount bonds
  3. Determine the origin, the meaning and valuation of  of two debt securities: consols and annuities
  4. Understand the meaning of forward rates and to describe how to calculate them
  5. Define the meaning and how to calculate the market capitalization of a company
  6. Explain the structure of corporations in the U.S. and the implications of owning shares in a company
  7. Identify the differences between common and preferred stocks, and the concepts of dilution and dividends
  8. Describe how and why companies repurchase their shares
  9. Describe the basics of corporate governance
  10. Further understand the pricing of stocks and the price-to-earnings ratio

Lesson #8

Video: 1982 Savings Account

The current economic situation is quite different from 1982. For instance, you could open a "Passbook Savings Account" which had interest rates up to 7.40%. Currently, interest rates are virtually 0%.

Contract Term: the minimum amount of time that may pass before you can withdraw your money without penalty

Video: Federal Funds and Interest Rates

Shortest-Term interest rates have a term of 1 day and currently are virtually 0%. Only banks really deal with terms this short. One could say that these are targeted rates set by the Federal Reserve by announcing the Federal Funds rate target. It could also be an economic crisis that's brought short-term rates down to zero, and anyone would have done the same.

EONIA (European Over Night Index Average) is the European counterpart to Fed Funds. European banks have a similar trend, except they have even gone below 0% into negative interest rates.

Interest rates cannot remain in the negatives for a prolonged period of time because banks have the option of simply holding on to the bash and not lending it out. Why would banks lend at a negative interest rate? It's costly to store cash. A bank must incur costs such as securing the cash and insuring the cash.

Causes of Interest Rates

Interest rates tend to be small positive numbers like 3% or 5% because of technical progress, time preferences and advantages to round aboutness -  Eugen Böhm von Bawerk

Technical progress could be interpreted as such that interest rates are the rate of progress. For example a 3% interest rate shows the economy is moving forward at a rate of 3%. Time preferences is related to our human tendency to want things now. Round aboutness is when a roundabout process is used to attain something. For example, stating a customer wants something, but you don't have the means to produce it. You could sell the customer the future products now, and use the funds now to increase your production.

Question: Do you think that low interest rates are contributing to inequality?

There is definitely a connection. For example, elderly people retire on fixed incomes and live off of their interest. If interest is 0%, they have no income. Monetary policy is a blunt tool. Altering interest rates does not effect everyone the same, and because they don't affect everyone the same, any change has the potential to lead to inequality.

Video: Compound Interest

Formula

$$ \displaystyle \begin{array}{lll}\\ \displaystyle A = P(1+ \frac{r}{n})^{nt} \\\\ \text{Where:}\\ A & = & \text{Final amount}\\ P & = & \text{Principal (initial balance)}\\ r & = & \text{Interest rate}\\ n & = & \text{Number of times interest is applied per time period}\\ t & = & \text{Number of time periods elapsed}\\ \end{array} $$

Examples

  1. What is the final balance with a $100 principal, 3% interest rate, compounded annually after 3 years?
    • $A = 100(1+ \frac{0.03}{1})^{1 \cdot 3} = 109.2727$
  2. $100 principal, 3% interest rate, compounded monthly after 3 years?
    • $A = 100(1+ \frac{0.03}{12})^{12 \cdot 3} = 109.4051401$
  3. $100 principal, 5% interest rate, compounded semi-annually after 3 years?
    • $A = 100(1+ \frac{0.05}{6})^{6 \cdot 3} = 116.111233$

Video: Discount Bonds

Comments: This video is difficult to follow and the information presented doesn't seem to be in line with other sources. It's also not entirely on the topic of Discount bonds. Dr. Shiller goes back and forth between coupon bonds and discount bonds. He also mentions that a discount bond is a  bond that doesn't pay coupons. According to other sources, a discount bond is one that is selling for less than the par value and a zero-coupon bond is a bond that does not pay coupons. These notes are supplemented with additional sources.

Coupon Bonds

Historically bonds pay coupons. Coupons allowed you to claim certain amounts at certain intervals and at the end of the maturity of the bond; you would get your principal back. For example, you could purchase a bond issued at \$100 with \$3 coupons claimable at 6 month intervals with a maturity time span of  3 years. This means that every 6 months, you could claim \$3 for a total of \$18 and when the bond matures, you would get back your initial \$100 investment. The bond's interest rate or coupon rate is 6% (2 semi annual coupons of \$3).

Zero-Coupon Bonds

A zero-coupon bond is a debt security that does not pay interest but instead trades at a discount and a profit is gained when the bond is redeemed for its par value. Some bonds are issued as zero-coupon bonds while others started off as coupon bonds, but an institution has repackaged them as a zero-coupon bond. - Investopedia

Discounted & Premium Bonds

A discount bond is a bond that is either issued for less than its par, or face, value or is currently trading for less than its par value. - Investopedia

A premium bond is a bondthat is trading above its face value. A common reason for this is because the bond's interest rate is higher than the current market's interest rates. - Investopedia

Yield to Maturity (YTM)

Yield to Maturity is the total return anticipated on a bond if the bond is held until it matures. YTM is considered a long-term bond yield but is expressed as an annual return. - Investopedia

Note: YTM assumes that all coupon paments are reinvested at the same rate as the bond's current yield.

Formula: YTM of a Discounted Zero-Coupon Bond

$$\displaystyle \begin{array}{lll}\\ \displaystyle YTM = \sqrt[n]{\frac{\text{Face Value}}{\text{Current Price}}} -1 & \\\\ \text{Where:}\\ n & = & \text{Number of years to maturity}\\ \text{Face Value} & = & \text{Bond's maturity value or par value}\\ \text{Current Price} & = & \text{The bond's price today}\\ \end{array}$$

Present Discounted Value (PDV)

Present value is the current value of a future sum of money or stream of cash flows given a specified rate of return. Money received in the future does not have the same value as money received now, either because of the potential for earning interest or because of inflation.

As long as interest rates remain positive and there is inflation, the present value will be worth less than the future value.

Formula

$$\displaystyle \begin{array}{lll}\\ \displaystyle \text{Present Value} = \frac{FV}{(1+r)^n} \\\\ \text{Where:}\\ FV & = & \text{Future Value}\\ r & = & \text{Rate of return}\\ n & = & \text{Number of periods}\\ \end{array}$$

Video: Consol and Annuity

Consol

A debt security which has no scheduled return of principal so it has no maturity date. It perpetually pays interest through coupons. Even though there might not be a default risk with Consols, there is still a market risk. The price of a Consol can change throughout time.

$$\displaystyle \begin{array}{lll}\\ \displaystyle PDV = \frac{c}{r} \\\\ \text{Where:}\\ c & = & \text{Coupon payment}\\ r & = & \text{Rate of return}\\ \end{array}$$

Growing Consol

A growing consul is similar to a consul except that the coupon rate grows at a a constant rate.

$$\displaystyle \begin{array}{lll}\\ \displaystyle PDV = \frac{c}{(r-g)} \\\\ \text{Where:}\\ c & = & \text{Coupon payment}\\ r & = & \text{Rate of return}\\ g & = & \text{Growth rate} \end{array}$$

Annuity

A debt instrument similar to a consul, except that it is not perpetual. There is still no principal to be claimed when the annuity ends.

Video: Forward Rates and Expectation Theory

Forward Rates

Forward rates are interest rates that can be taken in advance using the term structure.

Expectation Theory

  • Forward rates equal expected spot rates
  • Slope of term structure indicates expected future change in interest rates

Video: Inflation

Inflation is the rate at which the price of goods and services are increasing over time. Real interest rate is the interest rate after adjusting for inflation.

Index Bonds

Index bonds are bonds that pay coupons defined in real terms.

Video: Leverage

Leveraging is when a company or an individual borrows money to buy assets. Leveraging increases risk.

The Debt-Deflation Theory of Great Depressions

In a deflationary period wealth gets redistributed from debtors to creditors.

Lesson #9

Video: Market Capitalization by Country

The United States has by far the largest stock market capitalization when compared to other countries. In 2014, it was \$26.33 trillion. In second place is the UK with $\3.183 trillion.

In the US households (including nonprofit) assets have a market cap of \$98.3 trillion with \$13.2 trillion of liabilities resulting in a net worth of \$84.1 trillion. Breaking this down:

  • \$13.9 trillion is in corporate equities
  • \$7.8 trillion in mutual funds
  • \$20.6 trillion in pension funds
  • \$23.7 trillion in real estate

Video: The Corporation

An organization that acts as if it is a person (corpus in Latin means body). Ancient Rome even had corporations and were called publicani.

In the US a corporation is governed by a board of directors which are voted by shareholders. The board will hire a CEO, who is an employee and reports to the board, to run the day to day operations of the organization.

In Germany, a corporation has 2 boards. There is the Aufsichtsrat, a supervisory board, and the Vorstand, a management board.

For-Profit vs Non-Profit

For-profit corporations are owned by the shareholders and have equal claim (after debts and corporate taxes paid) to the profits of the organization. This is why for-profit corporate shares have value.

Non-Profit corporations are not owned by anyone. They have self-perpetuating directors and not subject to corporate profits tax. These organizations exist for some cause. A non-profit organization does indeed make profits, the important factor is that these profits stay within the company and do not get distributed to shareholders.

Video: Shares and Dividends

Shares

Ownership of a company is determined by the number of shares you own divided by the total number shares for that corporation. Share splits are essentially meaningless, but they seem to happen because of psychological factors. If a share of a company continues to grow, investors won't be able to purchase entire shares. There are some companies that do not split shares, such as Berkshire Hathaway.

A share's value increases if the company does something to increase the value of the company without increasing the number of shares.

Dividends

Dividends are payments paid by a company to its shareholders from its profits. Not all companies pay dividends. Usually mature companies pay dividends as they don't need the money for expansion or new initiatives. Newer companies tend not to pay dividends as they are using the funds to grow the business.

If a company pays dividends, the value of the share should go down by the amount of the dividend per share. Historically, dividends were the main purpose of holding shares.

Video: Common vs. Preferred

Preferred stocks require the company to pay out a fixed dividend to the stockholders before it can pay dividends to common stockholders. The company doesn't have to pay dividends on a set schedule as they would with a bond. An example of preferred stock would be the US government buying preferred stocks in a company to bail them out.

Video: Corporate Charter

The basic corporate charter says that all common shareholders are treated equally. This is where the word equity comes from, the equality of shareholders.

Berle and Means argued that for larger corporations this shareholder democracy doesn't work. Consider if you have a diversified portfolio, holding shares for many companies. It's impractical to take the time to investigate and vote effectively for every company you're invested in.

A corporation can issue different classes of shares. For example, voting vs not voting shares.

Video: Corporations Raise Money

There are 3 ways a corporation can raise money:

  1. Retaining earnings
  2. Borrow money (either through a loan or by issuing debt as a corporate bond)
  3. Sell shares

Stuart Myers Pecking Order Theory

Firms like to raise money through retained earnings first, borrowing second and issuing new equity only as a last resort.

He also mentioned that if a company doesn't issue new shares, then the price of the company's shares have no effect on the company's activities.

Fama & French

They criticized Meyers saying that the time period he picked for his studies was atypical. The stock market crashed in 1973, so there wasn't a lot of confidence in investors to purchase shares. On the other hand, from 1993 to 2002, 86% of firms issued some equity.

Also, the market price for a company's share is important to a company's activity because a company with higher share value can raise more money if they need to when they issue new shares.

Video: Dilution

Share dilution occurs when a company issues new shares to raise capital for some corporate activity. Say a company has 1 million shares, and you own 10% of the company. If the company issues 1 million new shares, you now own 5% of the company. This might sound like a bad deal, but if the new shares sell, then the company is worth twice as much. The company also now has money that they can do something with, with the intention that they will raise the worth of their company even more.

Video: Share Repurchase

Share repurchasing is the opposite of dilution. A company goes out into the market and repurchases shares that it issued. When this happens, the value of the company should go down by the amount that was spent repurchasing shares. The share value should remain the same, but you own a bigger portion of the company.

Video: PDV of Expected Dividends

There are 2 important ratios:

  1. Price Earnings (P/E) Ratio: price per share divided by earnings per share
  2. Price Dividend Ratio: dividends per share divided by price per share

If all earnings were paid out as dividends, then these 2 values would be the same.

A P/E ratio of 15 would mean that if you're getting all earnings back as dividends, then it will take you 15 years to get back your initial investment.

What determines the P/E ratio? The efficient markets idea is that the price of a share is the PDV of its expected future dividends. This allows you to calculate P/E with the Gordon Model. ($P/E = \frac{1}{(r-g)}$)

Video: Why do Firms Pay Dividends?

Hersch Shefrin and Meir Statman proposed the Self-Control Theory of Dividends. Many people invest in stocks and want to live off of dividends and never dip into the principal. This framed dividends as income.

Another theory is that dividends are used by corporations to show that they are really worth something. This is called signaling. Firms are trying to show that they are doing well.