## What is the relationship among an annuity, a perpetuity, and a growing cash stream?

All three are patterns of future cash flows for which simplifying time value formulas have been derived. An annuity is a sequence of equal cash flows for a finite period of time that are equal in three dimensions: amount, direction, and spacing. A perpetuity is a “perpetual annuity,” an annuity that continues forever; it is still made up of equal (amount, direction, and spacing) cash flows. A growing cash stream is a perpetuity in which the cash flows are still equal in direction and spacing but no longer equal in amount; instead each cash flow differs from the previous cash flow by a constant ratio, the rate of growth.

## What is the relationship between a future value and a present value?

A future value equals a present value plus the interest that can be earned by having ownership of the money; it is the amount that the present value will grow to over some stated period of time. Conversely, a present value equals the future value minus the interest that comes from ownership of the money; it is today’s value of a future amount to be received at some specified time in the future.

## Would an increase in interest rates increase the amount of money you saved?

Some economists argue that people increase their savings when interest rates rise since they can earn more money. Suppose you were putting money away with the goal of raising \$50,000 in five years. Would an increase in interest rates increase the amount of money you saved?

No. With a higher interest rate you could save less and still reach your goal of \$50,000 in five years. More of the \$50,000 could now come from your interest, hence less would have to come from your savings. In this case, where the future value is given, an increase in interest rates always lowers the principal required to reach that goal. The economists are discussing another scenario in which the future value is not specified. The evidence is that they are correct in that case, since higher interest rates make the future worth of one’s savings grow to a greater amount.

## A well-known advertisement by American Express urged travelers returning home to keep their travelers checks rather than cash them in.

A well-known advertisement by American Express urged travelers returning home to keep their travelers checks rather than cash them in. The reason given was to have cash in an emergency, but could American Express have had any other reason for encouraging this behavior?

They certainly could. At any time, American Express is holding over \$1 billion from clients who have purchased travelers checks but have not yet used them. American Express invests this money and earns a sizable income on it. As long as their clients keep travelers checks outstanding, it is American Express and not the clients that earn interest on this money.

## Why do airlines often insist that you pay for your ticket on the date you book your flight rather than the date you actually fly?

One reason is time value of money¾the earlier the airlines receive the cash, the more valuable it is to them. A second reason is that airlines follow a practice they call “yield management” in which they try to charge the highest price for every ticket they sell. By insisting that some customers pay at the time of booking, they can charge more for tickets that do not require immediate payment.

## What Can I Learn from Profitability Ratios?

The profitability ratios include: operating profit margin, net profit margin, return on assets and return on equity.

Profit margin measures how much a company earns relative to its sales. A company with a higher profit margin than its competitor is more efficient. There are two profit margin ratios: operating profit margin and net profit margin. Operating profit margin measures the earnings before interest and taxes, and is calculated as follows:

 Gross Profit Margin = Profits Before Interest and Taxes Sales

Net profit margin measures earnings after taxes and is calculated as follows:

 Net Profit Margin = Profits After Taxes Sales

When asked for a ratio you simply put either gross or net profit x100 over the total sales.

While it seems as if these both measure the same numbers, their results can be dramatically different due to the impact of interest and tax expenses. Similarly, the next two ratios appear to be similar but they tell different stories. As an investor, banker or any other interested stakeholder, you are interested in getting a return on your investment. So are a company and its shareholders!

Return on capital employed (ROCE)) tells how well management is performing on all the firm’s resources. However, it does not tell how well they are performing for the shareholders. It is calculated as follows:

 Return on Capital employed Net profit before Taxes and interest Total Capital Employed

These ratios are easy to calculate and the information is readily available in a company’s annual report.

## When Is an Increase in Earnings a Loss?

Sometimes an increase in company earnings can disguise an operating loss. If a company’s operating expenses exceed its operating income; it has an operating loss. If it also has income from investments and tax benefits, this income can offset the loss and show an increase in earnings per share. However, if these other sources of non-operating income are not recurring, the unsuspecting investor may come to the wrong conclusion about the company’s overall financial health.

## How to Use Profitability Ratios to Make Investment Decisions

When considering a company as a prospective investment you should review its financial statements. Pay particular attention to the profitability ratios. If you can, calculate the ratios for the same company over several successive years to see if the company earnings are consistent, growing, or declining.

Compare your candidate’s ratios to other companies in the same industry. This will help you determine where your candidate stands in the industry.

Do not ignore other financial information on the profit and loss statement and balance sheet. Pay particular attention to losses in income items.

## Price to Earnings Ratio (P/E)

The price to earnings ratio, or P/E, is figured by dividing the stock price by the company’s earnings per share (EPS). The P/E is a performance benchmark that can be used as a comparison against other companies or within the stock’s own historical performance. For instance, if a stock has historically run at a P/E of 35 and the current P/E is 12, you will want to explore the reasons for the drastic change. If you believe that the ratio is too low, you may want to buy the stock.

You will generally find a P/E ratio based on either the prior reporting year’s earnings, or the earnings of the prior four quarters added together. This latter number is referred to as LTM or Latest Twelve Months. While this is useful for understanding the history of a company, most analysts prefer to view a forward-looking P/E ratio. This ratio is calculated by dividing the stock price by the analysts’ earnings estimate for the next year or two.

One other note on P/E Ratios – sometimes, when a company is not doing well, it will buy back shares so that the EPS and P/E Ratio will appear better. This can be seen in the example below.

 Example 1 Example 2 Net Income £1,000,000 £1,000,000 Shares Outstanding 10,000,000 8,000,000 Earnings Per Share (EPS) £0.10 £0.125 Stock Price £3.00 £3.00 P/E Ratio 30 24

In the table above, the only change from Example 1 to Example 2 is in the number of shares outstanding. The net income and stock price remain the same. However, by changing the shares outstanding, the EPS has changed quite a bit. This means that the P/E ratio has also changed. At first glance, if a stock’s EPS has increased 25% and its P/E ratio has gone from 30 to 24 it might look like a better buy. However, the truth is that nothing has changed but the number of shares. The stock is not a better buy in Example 2 than it was in Example 1.

## Current Ratio

The current ratio provides an indication of how liquid a company may be in the coming year. To calculate it, take the current assets and divide that number by the current liabilities. You will find all of these figures on the balance sheet.

An answer of 1.0 or better is generally considered good. However this, like other ratios, can depend on a company’s current stage of growth. A start-up company should have a lower ratio than an established company. If it does not, then you will want to ask yourself why and do further research.

A current ratio can also be affected by how much long-term debt a company has in relation to its short-term debt. Some companies prefer to use short-term debt and reissue it more often. Other companies minimise their use of short-term debt. Most companies use a mix depending on what is available to them, what is cheaper at the moment and how their economists project interest rates for the future. Hence, this ratio also needs to be used to build a bigger picture rather than in isolation.

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