Time Value of Money

The value of money received today is different from the value of money received after some time in the future. An important financial principle is that the value of money is time dependent.

This principle is based on the following four reasons:

 Inflation:

Under inflationary conditions the value of money, expressed in terms of its purchasing power over goods and services, declines.

Risk:

Re. 1 now is certain, whereas Re. 1 receivable tomorrow is less certain. This ‘bird- in-the-hand’ principle is extremely important in investment appraisal.

Personal Consumption Preference: 

Many individuals have a strong preference for immediate rather than delayed consumption. The promise of a bowl of rice next week counts for little to the starving man.

Investment Opportunities: 

Money like any other desirable commodity, has a price, given the choice of Rs. 100 now or the same amount in one year’s time, it is always preferable to take the Rs. 100 now because it could be invested over the next year at (say) 18% interest rate to produce Rs. 118 at the end of one year.

If 18% is the best risk-free return available, then you would be indifferent to receiving Rs. 100 now or Rs. 118 in one year’s time. Expressed another way, the present value of Rs. 118 receivable one year hence is Rs. 100.

Present Value:

It is a method of assessing the worth of an investment by inverting the compounding process to give present value of future cash flows. This process is called ‘discounting’

The present value of ‘P’ of the amount ‘A’ due at the end of ‘n’ conversion periods at the rate ‘i’ per conversion period.

The value of ‘P’ is obtained by solving the following equation: 

P = A (1 + i)ⁿ

Illustration 8: 

Ascertain the present value of an amount of Rs. 8,000 deposited now in a commercial bank for a period of 6 years at 12% rate of interest.

Solution:

P = A/(1 + i)ⁿ 8,000 = A/(1 + i)ⁿ

8,000 = A/(1 + 0.12)⁶

8,000 = A/1.97382

A = 8,000 x 1.97382 = Rs. 15,791

Illustration 9:

Find out the present value of Rs. 10,000 to be required after 4 years if the interest rate is 6%.

Solution:

.^.. An amount Rs. 7,921 to be deposited into bank to get Rs. 10,000 at the end of 4 years at interest rate of 6%.

Discounted cash-flow is an evaluation of the future cash-flows generated by a capital project, by discounting them to their present-day value. The discounting technique converts cash inflows and outflows for different years into their respective values at the same point of time, allows for the time value of money.

Compounding Rate and Capitalizing Rate –

The compounding rate is used in project evaluation to determine the present value of past investment / cashflow, whereas the capitalizing rate is applied in the reverse process of discriminating present value of future cash flows. Both considers the time value of money.

Annuity:

An annuity is a cashflow, either income or outgoings, involving the same sum in each period. An annuity is the payment or receipt of equal cashflows per period for a specified amount of time. For example, when a company set aside a fixed sum each year to meet a future obligation, it is using annuity.

The time period between two successive payments is called ‘payment period or ‘rent period. The word ‘annuity’ is broader in sense, which includes payments which can be annual, semiannual, quarterly or any other fixed length of time. Annuity does not necessarily mean payment taken to be one year.

Illustration 10:

Find the future value of ordinary annuity Rs. 4,000 each six months for 15 years at 5% p.a. compounded semiannually.

Solution:

 A = P/I [1+i)ⁿ-1]

Where, P = Rs. 4,000 i = 0.05/2 = 0.025

n = 15 x 2 =30

A = 4,000/0.025 [(1 + 0.025)³⁰ – 1]

A= 4,000/ 0.025 [(1.025)³⁰-1] Let x = (1.025)³⁰

Log x = 30 log 1.025

= 30 x 0.0107 = 0.321

x = antilog 0.321 = 2.094

A = 4,000 /0.025 (2.094 – 1)

= 1,60,000 x 1.094 = Rs. 1,75,040

Present Value of Ordinary Annuity: 

The present value of an ordinary annuity is the sum of the present value of a series of equal periodic payments.

V = P/I [1-(1+i)^-n]

Where, V = Present value of annuity

Illustration 13:

Mr. Y is depositing Rs. 8,000 annually for 4 years, in a post office savings bank account at an interest of 5% p.a. Find the present value of annuity.

Solution:

V = P/I [1- (1+i)^-n]

P = Rs. 8,000 i = 0.05 n = 4

V = 8,000/0.05 [1-(1+0205)^-4]

= 1,60,000 [1 – (1.05) ^-4]

Let x = (1.05) ^-4

Log x = – 4 log 1.05

= – 4 X 0.0212 = – 0.0848

= – 1 + 1 – 0.0848 = 1.9152

x = antilog (1.9152) = 0.8226

V = 1,60,000 x (1 – 0.8226)

= 1,60,000 x .1774 = Rs. 28,38

Internal Rate of Return

The internal rate of return method is also a modern technique of capital budgeting that takes into account the time value of money. It is also known as ‘time adjusted rate of return’ discounted cash flow’ ‘discounted rate of return,’ ‘yield method,’ and ‘trial and error yield method’.

In the net present value method the net present value is determined by discounting the future cash flows of a project at a predetermined or specified rate called the cut-off rate. But under the internal rate of return method, the cash flows of a project are discounted at a suitable rate by hit and trial method, which equates the net present value so calculated to the amount of the investment.

Under this method, since the discount rate is determined internally, this method is called as the internal rate of return method. The internal rate of return can be defined as that rate of discount at which the present value of cash-inflows is equal to the present value of cash outflows.

It can be determined with the help of the following mathematical formula:

The internal rate of return can also be determined with the help of present value tables.

The following steps are required to practice the internal rate of return method:

• Determine the future net cash flows during the entire economic life of the The cash inflows are estimated for future profits before depreciation but after taxes
• Determine the rate of discount at which the value of cash inflows is equal to the present value of cash This may be determined as explained after step (4).
• Accept the proposal if the internal rate of return is higher than or equal to the minimum required rate of return, i.e. the cost of capital or cut off rate and reject the proposal if the internal rate o return is lower than the cost of cut-off
• In case of alternative proposals select the proposal with the highest rate of return as long as the rates are higher than the cost of capital or cut-off-rate.

Determination of Internal Rate of Return (IRR):

• When the annual net cash flows are equal over the life of the asset:

Firstly, find out present value factor by dividing initial outlay (cost of the investment) by annual cash flow, i.e.,

Then consult present value annuity tables given at the end of the book as Appendix B with the number of years equal to the life of the asset and find out the rate at which the calculated present value factor is equal to the present value given in the table.

• When the annual cash flows are unequal over the life of the asset:

In case annual cash flows are unequal over the life of the asset, the internal rate of return cannot be determined according to the technique suggested above. In such cases, the internal rate of return is calculated by hit and trial and that is why this method is also known as hit and trial yield method.

We may start with any assumed discount rate and find out the total present value of cash outflows which is equal to the cost of the initial investment where total investment is to be made in the beginning. The rate, at which the total present value of all cash inflows equals the initial outlay, is the internal rate of return. Several discount rates may have to be tried until the appropriate rate is found.

The calculation process may be summed up as follows:

• Prepare the cash flow table using an arbitrary assumed discount rate to discount the net cash flows to the present
• Find out the Net Present Value by deducting from the present value of total cash flows calculated in (i) above the initial cost of the investment.
• If the Net Present Value (NPV) is positive, apply higher rate of
• If the higher discount rate still gives a positive net present value, increase the discount rate further until the NPV becomes
• If the NPV is negative at this higher rate, the internal rate of return must be between these two rates:

 Advantages of Internal Rate of Return Method

The internal rate of return method has the following advantages:

• Like the net present value method, it takes into account the time value of money and can be usefully applied in situations with even as well as un even cash flow at different periods of
• It considers the profitability of the project for its entire economic life and hence enables evaluation of true
• The determination of cost of capital is not a pre-requisite for the use of this method and hence it is better than net present value method where the cost of capital cannot be determined
• It provides for uniform ranking of various proposals due to the percentage rate of
• This method is also compatible with the objective of maximum profitability and is considered to be a more reliable technique of capital

Disadvantages of Internal Rate of Return Method:

In-spite of so many advantages, it suffers from the following drawbacks:

• It is difficult to understand and is the most difficult method of evaluation of investment proposals.
• This method is based upon the assumption that the earnings are reinvested at the internal rate of return for the remaining life of the project, which is not a justified assumption particularly when the average rate of return earned by the firm is not close to the internal rate of return. In this sense, Net Present Value method seems to be better as it assumes that the earnings are reinvested at the rate of firm’s cost of
• The results of NPV method and IRR method may differ when the projects under evaluation differ in their size, life and timings of cash flows.

Calculation of Return on Bonds (With Formula)

Bonds:

Bonds usually have a maturity period. Yield on them can be calculated either for the current period or to maturity. While it is advisable to find out yield to maturity and it is also the common practice, yet current yield on bonds can also be found out. The current yield on a bond is the annual coupon in rupees divided by the bond’s purchase price.

Example 1:

An investor buys a 20-year bond at Rs. 800 and it carries a Rs. 100 worth of coupons per year and its par value is Rs. 1,000, its current yield is:

Current = annual coupon price/ purchase price

= 100/80 = 1.25 or 12.5%

Example 2:

Note:

The investor may sometimes buy the bond at par value. Then the coupon rate and current rate are identical.

An investor buys a Rs. 100 bond of 10-year maturity with Rs. 80 worth of coupons per year. The par value of the bond is Rs. 1,000. Its current yield is:

Current Yield = 80/100

= .08 or 8%

Yield on bonds is more commonly calculated to the date of maturity. (YTM), i.e., the percentage yield that will be earned on bond from the purchase date to maturity date.

STOCK MARKET RETURN:

What is the Stock Market?

The stock market refers to public markets that exist for issuing, buying, and selling stocks that trade on a stock exchange or over-the-counter. Stocks, also known as equities, represent fractional ownership in a company, and the stock market is a place where investors can buy and sell ownership of such investible assets. An efficiently functioning stock market is considered critical to economic development, as it gives companies the ability to quickly access capital from the public

Purposes of the Stock Market – Capital and Investment Income

The stock market serves two very important purposes. The first is to provide capital to companies that they can use to fund and expand their businesses. If a company issues one million shares of stock that initially sell for $10 a share, then that provides the company with $10 million of capital that it can use to grow its business (minus whatever fees the company pays for an investment bank to manage the stock offering). By offering stock shares instead of borrowing the capital needed for expansion, the company avoids incurring debt and paying interest charges on that debt.

The secondary purpose the stock market serves is to give investors – those who purchase stocks – the opportunity to share in the profits of publicly-traded companies. Investors can profit from stock buying in one of two ways. Some stocks pay regular dividends (a given amount of money per share of stock someone owns). The other way investors can profit from buying stocks is by selling their stock for a profit if the stock price increases from their purchase price. For example, if an investor buys shares of a company’s stock at $10 a share and the price of the stock subsequently rises to $15 a share, the investor can then realize a 50% profit on their investment by selling their shares.

History of Stock Trading

Although stock trading dates back as far as the mid-1500s in Antwerp, modern stock trading is generally recognized as starting with the trading of shares in the East India Company in London.

The Early Days of Investment Trading

Throughout the 1600s, British, French, and Dutch governments provided charters to a number of companies that included East India in the name. All goods brought back from the East were transported by sea, involving risky trips often threatened by severe storms and pirates. To mitigate these risks, ship owners regularly sought out investors to proffer financing collateral for a voyage. In return, investors received a portion of the monetary returns realized if the ship made it back successfully, loaded with goods for sale. These are the earliest examples of limited liability companies (LLCs), and many held together only long enough for one voyage.

The East India Company

The formation of the East India Company in London eventually led to a new investment model, with importing companies offering stocks that essentially represented a fractional ownership interest in the company, and that therefore offered investors investment returns on proceeds from all the voyages a company funded, instead of just on a single trip. The new business model made it possible for companies to ask for larger investments per share, enabling them to easily increase the size of their shipping fleets. Investing in such companies, which were often protected from competition by royally-issued charters, became very popular due to the fact that investors could potentially realize massive profits on their investments.

The First Shares and the First Exchange

Company shares were issued on paper, enabling investors to trade shares back and forth with other investors, but regulated exchanges did not exist until the formation of the London Stock Exchange (LSE) in 1773. Although a significant amount of financial turmoil followed the immediate establishment of the LSE, exchange trading overall managed to survive and grow throughout the 1800s.

The Beginnings of the New York Stock Exchange

Enter the New York Stock Exchange (NYSE), established in 1792. Though not the first on U.S. soil – that honor goes to the Philadelphia Stock Exchange (PSE) – the NYSE rapidly grew to become the dominant stock exchange in the United States, and eventually in the world. The NYSE occupied a physically strategic position, located among some of the country’s largest banks and companies, not to mention being situated in a major shipping port. The exchange established listing requirements for shares, and rather hefty fees initially, enabling it to quickly become a wealthy institution itself.

Modern Stock Trading – The Changing Face of Global Exchanges

Domestically, the NYSE saw meager competition for more than two centuries, and its growth was primarily fueled by an ever-growing American economy. The LSE continued to dominate the European market for stock trading, but the NYSE became home to a continually expanding number of large companies. Other major countries, such as France and Germany, eventually developed their own stock exchanges, though these were often viewed primarily as stepping stones for companies on their way to listing with the LSE or NYSE.

The late 20^th century saw the expansion of stock trading into many other exchanges, including the NASDAQ, which became a favorite home of burgeoning technology companies and gained increased importance during the technology sector boom of the 1980s and 1990s. The NASDAQ emerged as the first exchange operating between a web of computers that electronically executed trades. Electronic trading made the entire process of trading more time-efficient and cost-efficient. In addition to the rise of the NASDAQ, the NYSE faced increasing competition from stock exchanges in Australia and Hong Kong, the financial center of Asia.

The NYSE eventually merged with Euronext, which was formed in 2000 through the merger of the Brussels, Amsterdam, and Paris exchanges. The NYSE/Euronext merger in 2007 established the first trans-Atlantic exchange.

How Stocks are Traded – Exchanges and OTC

Most stocks are traded on exchanges such as the New York Stock Exchange (NYSE) or the NASDAQ. Stock exchanges essentially provide the marketplace to facilitate the buying and selling of stocks among investors. Stock exchanges are regulated by government agencies, such as the Securities and Exchange Commission (SEC) in the United States, that oversee the market in order to protect investors from financial fraud and to keep the exchange market functioning smoothly.

Although the vast majority of stocks are traded on exchanges, some stocks are traded over-the-counter (OTC), where buyers and sellers of stocks commonly trade through a dealer, or “market maker”, who specifically deals with the stock. OTC stocks are stocks that do not meet the minimum price or other requirements for being listed on exchanges.

OTC stocks are not subject to the same public reporting regulations as stocks listed on exchanges, so it is not as easy for investors to obtain reliable information on the companies issuing such stocks. Stocks in the OTC market are typically much more thinly traded than exchange-traded stocks, which means that investors often must deal with large spreads between bid and ask prices for an OTC stock. In contrast, exchange-traded stocks are much more liquid, with relatively small bid-ask spreads.

Stock Market Players – Investment Banks, Stockbrokers, and Investors

There are a number of regular participants in stock market trading.

Investment banks handle the initial public offering (IPO) of stock that occurs when a company first decides to become a publicly-traded company by offering stock shares.

Here’s an example of how an IPO works. A company that wishes to go public and offer shares approaches an investment bank to act as the “underwriter” of the company’s initial stock offering. The investment bank, after researching the company’s total value and taking into consideration what percentage of ownership the company wishes to relinquish in the form of stock shares, handles the initial issuing of shares in the market in return for a fee, while guaranteeing the company a determined minimum price per share. It is therefore in the best interests of the investment bank to see that all the shares offered are sold and at the highest possible price.

Shares offered in IPOs are most commonly purchased by large institutional investors such as pension funds or mutual fund companies.

The IPO market is known as the primary, or initial, market. Once a stock has been issued in the primary market, all trading in the stock thereafter occurs through the stock exchanges in what is known as the secondary market. The term “secondary market” is a bit misleading, since this is the market where the overwhelming majority of stock trading occurs day to day.

Stockbrokers, who may or may not also be acting as financial advisors, buy and sell stocks for their clients, who may be either institutional investors or individual retail investors.

Equity research analysts may be employed by stock brokerage firms, mutual fund companies, hedge funds, or investment banks. These are individuals who research publicly-traded companies and attempt to forecast whether a company’s stock is likely to rise or fall in price.

Fund managers or portfolio managers, which includes hedge fund managers, mutual fund managers, and exchange-traded fund (ETF) managers, are important stock market participants because they buy and sell large quantities of stocks. If a popular mutual fund decides to invest heavily in a particular stock, that demand for the stock alone is often significant enough to drive the stock’s price noticeably higher.

Stock Market Indexes

The overall performance of the stock market is usually tracked and reflected in the performance of various stock market indexes. Stock indexes are composed of a selection of stocks that is designed to reflect how stocks are performing overall. Stock market indexes themselves are traded in the form of options and futures contracts, which are also traded on regulated exchanges.

Among the key stock market indexes are the Dow Jones Industrial Average (DJIA), the Standard & Poor’s 500 Index (S&P 500), the Financial Times Stock Exchange 100 Index (FTSE 100), the Nikkei 225 Index, the NASDAQ Composite Index, and the Hang Seng Index.

Bull and Bear Markets, and Short Selling

Two of the basic concepts of stock market trading are “bull” and “bear” markets. The term bull market is used to refer to a stock market in which the price of stocks is generally rising. This is the type of market most investors prosper in, as the majority of stock investors are buyers, rather than short-sellers, of stocks. A bear market exists when stock prices are overall declining in price.

Investors can still profit even in bear markets through short selling. Short selling is the practice of borrowing stock that the investor does not hold from a brokerage firm that does own shares of the stock. The investor then sells the borrowed stock shares in the secondary market and receives the money from the sale of that stock. If the stock price declines as the investor hopes, then the investor can realize a profit by purchasing a sufficient number of shares to return to the broker the number of shares they borrowed at a total price less than what they received for selling shares of the stock earlier at a higher price.

For example, if an investor believes that the stock of company “A” is likely to decline from its current price of $20 a share, the investor can put down what is known as a margin deposit in order to borrow 100 shares of the stock from his broker. He then sells those shares for $20 each, the current price, which gives him $2,000. If the stock then falls to $10 a share, the investor can then buy 100 shares to return to his broker for only $1,000, leaving him with a $1,000 profit.

Analyzing Stocks – Market Cap, EPS, and Financial Ratios

Stock market analysts and investors may look at a variety of factors to indicate a stock’s probable future direction, up or down in price. Here’s a rundown on some of the most commonly viewed variables for stock analysis.

A stock’s market capitalization, or market cap, is the total value of all the outstanding shares of the stock. A higher market capitalization usually indicates a company that is more well-established and financially sound.

Publicly traded companies are required by exchange regulatory bodies to regularly provide earnings reports. These reports, issued quarterly and annually, are carefully watched by market analysts as a good indicator of how well a company’s business is doing. Among the key factors analyzed from earnings reports are the company’s earnings per share (EPS), which reflects the company’s profits as divided among all of its outstanding shares of stock.

Analysts and investors also frequently examine a number of financial ratios that are intended to indicate the financial stability, profitability, and growth potential of a publicly-traded company. The following are a few of the key financial ratios that investors and analysts consider:

Price to Earnings (P/E) Ratio: The ratio of a company’s stock price in relation to its EPS. A higher P/E ratio indicates that investors are willing to pay higher prices per share for the company’s stock because they expect the company to grow and the stock price to rise.

Debt to Equity Ratio: This is a fundamental metric of a company’s financial stability, as it shows what percentage of a company’s operations are being funded by debt compared to what percentage are being funded by equity investors. A lower debt to equity ratio, indicating primary funding from investors, is preferable.

Return on Equity (ROE) Ratio: The return on equity (ROE) ratio is considered a good indicator of a company’s growth potential, as it shows the company’s net income relative to the total equity investment in the company.

Profit Margin: There are several profit margin ratios that investors may consider, including operating profit margin and net profit margin. The advantage of looking at profit margin instead of just an absolute dollar profit figure is that it shows what a company’s percentage profitability is. For example, a company may show a profit of $2 million, but if that only translates to a 3% profit margin, then any significant decline in revenues may threaten the company’s profitability.

Other commonly used financial ratios include return on assets (ROA), dividend yield, price to book (P/B) ratio, current ratio, and the inventory turnover ratio.

Two Basic Approaches to Stock Market Investing – Value Investing and Growth Investing

There are countless methods of stock picking that analysts and investors employ, but virtually all of them are one form or another of the two basic stock buying strategies of value investing or growth investing.

Value investors typically invest in well-established companies that have shown steady profitability over a long period of time and may offer regular dividend income. Value investing is more focused on avoiding risk than growth investing is, although value investors do seek to buy stocks when they consider the stock price to be an undervalued bargain.

Growth investors seek out companies with exceptionally high growth potential, hoping to realize maximum appreciation in share price. They are usually less concerned with dividend income and are more willing to risk investing in relatively young companies. Technology stocks, because of their high growth potential, are often favored by growth investors.