# Time value of money + rate of return.

Estimating value of an income-generating asset or group of assets such as a business requires considering concepts such as the time value of money, risk and required rate of return. Here is a brief summary.Time Value of Money. Most people would rather receive a dollar today than in the future, and would pay less for a dollar to be received in the future than today. This is the concept of time value of money. A dollar received today can be invested to earn a profit. The simple fact that a dollar received today can be deposited into a bank account to earn income supports the concept.

Risk. The level of uncertainty about whether expected returns will be realized is referred to as risk. Because virtually no investment is 100 percent certain to provide expected return, investors discount anticipated future cash flows by a rate greater than the standard for risk-free investment --U. S. Treasury obligations (the risk-free rate]. When presented with an investment opportunity, one of the key tasks in assigning value is to estimate risk.

Risk-Free Rate. If receipt of a future stream of cash flows were completely certain, the discount rate used to convert them into present dollars would be the risk-free rate. For the past 100+ years, the financial world has looked to U.S. government obligations as the benchmark for risk-free investments, and we presume it still does. As such, we can look at the rate of return or yield paid or earned on U. S. obligations as a pure representation of the time value of money for investors. In theory, to entice investors to contribute money to an investment that is risk-free, a rate of return at least equal to the rate paid on U. S. obligations would be required. A one-year U.S. Treasury bill today earns around 0.2 percent, a very low rate historically.

Discount Rate. The rate at which future dollars are converted or discounted to present dollars is called the discount rate, also commonly referred to as the hurdle rate, cost of capital, opportunity cost of capital or required rate of return. The discount rate is made up of two components, the risk-free rate (to compensate for the time value of money] and the risk rate (to compensate for the uncertainty of the expected future cash flows]. This can be represented by the equation [R.sub.f] + R = D, where [R.sub.f] is the risk-free rate, R the risk rate and D the discount rate.

Discounting. The mechanism used to adjust the value of a dollar received in the future into value today is called discounting. If one were to determine that he or she would pay just 80 cents for a dollar that was certain to be received in one year, the implied discount rate is 25 percent. If the time value of money for this particular investor is consistent over time, then for every year a dollar's receipt will be delayed, a discount of 25 percent will be applied.

The present value of a delayed payoff may be found by multiplying the payoff by a discount factor. If C1 denotes the expected payoff at time period 1 (one year from today], then:

Present Value (PV] = Discount Factor x [C.sub.1]

The discount factor is expressed as the reciprocal of 1 + rate of return:

Discount Factor = 1 / (1+r)

The rate of return r is the reward the investor demands for accepting delayed payment. If we use the numbers from the hypothetical example above, we find that $100,000 to be received in one year, discounted at 25 percent, is indeed $80,000.

PV = [1 / (1+.25)] * $100,000

= [1 / 1.25] * $100,000

= 0.80 * $100,000

= $80,000

To illustrate how this concept is applied, let's assume we buy XYZ business and expect to receive $100,000 at the end of each year for five years. To calculate the present value, list the payment to be received in each year, then discount the dollars to the present value as follows:

The value of XYZ Company is $268,928 or the sum of the present values of each expected future cash payment. To avoid having to calculate each discount factor, refer to any present value table that can be found online (for free) or in the back of any finance textbook.

Return on Investment. The return on investment is generally referred to as the cash or profit gained from equity dollars invested. This is also referred to as Return on Equity (ROE). The return can be expressed as a dollar amount, or converted to a percentage by dividing the return by the equity deployed. Typically, returns are calculated on an annual basis and referred to as annual rate of return.

Dollars Received / Dollars Originally Invested = Rate of Return

The return also can be calculated on total capitalization (debt and equity) as follows:

Dollars Received / (Equity Capital + Debt Capital Invested) = Return on Total Capitalization

Example: If $50 was received in year one as a return on $200 invested, the rate of return would be 25 percent.

Required Rate of Return. When considering the discount rate or required return, it is helpful to study the historical returns of various investments. The table below lists the average annual total returns earned on a variety of investments. Each of the investments is publicly traded (due to lack of information available on private investments).

Each investment listed in the table above is publicly traded, thus marketable, i.e., it can be liquidated and turned into cash in about three days or less. The lowest historical rates of return were U.S. Treasury bills at 3.7 percent annually. The highest was micro-cap stocks at 18.2 percent. Of course, these were the investments with the lowest and highest risks, respectively. If we try to relate the returns on this table to small, privately held businesses, we can assume the required returns for such would be higher than the riskiest investment on the table--micro-cap stocks. The primary reasons are as follows:

1. The private company will be less marketable (very illiquid) than the average publicly traded micro-capsize company and therefore riskier.

2. The average private company will be smaller than the average publicly traded micro-cap-size company and therefore has poorer access to equity and debt capital, lower levels of diversification, diminished opportunities to attract and retain talent, etc.

Business owners should have a working knowledge of the basic concepts of time value of money, return on investment and required rate of return.

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Year Year 1 Year 2 Year 3 Income to be received $100,000 $100,000 $100,000 Discount rate (@ 25% per year) .800 .640 .512 Present value of year's cash flow $80,000 $64,000 $51,200 Present value of business Year Year 4 Year 5 Income to be received $100,000 $100,000 Discount rate (@ 25% per year) .409 .328 Present value of year's cash flow $40,960 $32,768 Present value of business $268,928 Average Annual Returns (3) Inflation 3.1% (1) U.S. Treasury Bills (30 days) 3.7% (1) U.S. Treasury Bonds (5 years) 5.5% (1) U.S. Treasury Bonds (20 Years) 5.8% (1) L.T. Corporate Bonds (20 years) 6.2% (1) Large-Cap Stocks 11.8% (1) Micro-Cap Stocks 18.2% (2) (1) Source: SBBI Valuation Edition 2010 Yearbook. Returns are the average annual total (income and capital appreciation) arithmetic mean for 1926 to 2009 in the United States. (2) Micro-Cap Stocks is defined as the portfolio of stocks comprising the 9th and 10th deciles of the New York Stock Exchange. According to the Center for Research in Security Prices, University of Chicago, the average capitalization of micro-cap companies from 1926 to 2009 was $68 million. (3) Returns are return to total capitalization (debt and equity).

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Title Annotation: | INVESTMENT |
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Publication: | The Business Owner |

Geographic Code: | 1USA |

Date: | Sep 1, 2011 |

Words: | 1308 |

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