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Fast Easy Accounting Marginal Revenue Vs. Marginal Cost Reference Guide Present Value, Internal Rate of Return, Discounted Cash Flows and Opportunity Costs

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Fast Easy Accounting Marginal Revenue Vs. Marginal Cost Reference Guide Present Value, Internal Rate of Return, Discounted Cash Flows and Opportunity Costs Fast Easy Accounting Marginal Revenue Vs. Marginal Cost Reference Guide Present Value, Internal Rate of Return, Discounted Cash Flows and Opportunity Costs PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Thu, 30 May 2013 19:14:20 UTC Contents Articles Present value 1 Internal rate of return 8 Discounted cash flow 13 Opportunity cost 18 Time value of money 21 Rate of return 31 Capital budgeting 41 References Article Sources and Contributors 45 Image Sources, Licenses and Contributors 46 Article Licenses License 47 Present value 1 Present value Present value, also known as present discounted value, is a future amount of money that has been discounted to reflect its current value, as if it existed today. The present value is always less than or equal to the future value because money has interest-earning potential, a characteristic referred to as the time value of money.[] Time value can be described with the simplified phrase, “A dollar today is worth more than a dollar tomorrow”. Here, 'worth more' means that its value is greater. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent.[] Just as rent is paid to a landlord by a tenant, without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed their authority over the money, and is compensated for it in the form of interest. The initial amount of the borrowed funds (the present value) is less than the total amount of money paid to the lender. Present value calculations, and similarly future value calculations, are used to evaluate loans, mortgages, annuities, sinking funds, perpetuities, and more. These calculations are used to make comparisons between cash flows that don’t occur at simultaneous times.[] The idea is much like algebra, where variable units must be consistent in order to compare or carry out addition and subtraction; time dates must be consistent in order to make comparisons between values or carry out simple calculations. When deciding between projects in which to invest, the choice can be made by comparing respective present values discounted at the same interest rate, or rate of return. The project with the least present value, i.e. that costs the least today, should be chosen. Background If offered a choice between 100 today or 100 in one year and there is a positive real interest rate throughout the year ceteris paribus, a rational person will choose 100 today. This is described by economists as time preference. Time preference can be measured by auctioning off a risk free security—like a US Treasury bill. If a 100 note, payable in one year, sells for 80 now, then 80 is the present value of the note that will be worth 100 a year from now. This is because money can be put in a bank account or any other (safe) investment that will return interest in the future. An investor who has some money has two options: to spend it right now or to save it. But the financial compensation for saving it (and not spending it) is that the money value will accrue through the compound interest that he will receive from a borrower (the bank account on which he has the money deposited). Therefore, to evaluate the real value of an amount of money today after a given period of time, economic agents compound the amount of money at a given (interest) rate. Most actuarial calculations use the risk-free interest rate which corresponds to the minimum guaranteed rate provided by a bank's saving account for example. To compare the change in purchasing power, the real interest rate (nominal interest rate minus inflation rate) should be used. The operation of evaluating a present value into the future value is called a capitalization (how much will 100 today be worth in 5 years?). The reverse operation—evaluating the present value of a future amount of money—is called a discounting (how much will 100 received in 5 years—at a lottery for example—be worth today?). It follows that if one has to choose between receiving 100 today and 100 in one year, the rational decision is to choose the 100 today. If the money is to be received in one year and assuming the savings account interest rate is 5%, the person has to be offered at least 105 in one year so that two options are equivalent (either receiving 100 today or receiving 105 in one year). This is because if 100 is deposited in a savings account, the value will be 105 after one year. Present value 2 Interest Rates Interest is the additional amount of money gained between the beginning and the end of a time period. Interest represents the time value of money, and can be thought of as rent that is required of a borrower in order to use money from a lender.[][] For example, when an individual takes out a bank loan, they are charged interest. Alternatively, when an individual deposits money into a bank, their money earns interest. In this case, the bank is the borrower of the funds and is responsible for crediting interest to the account holder. Similarly, when an individual invests in a company (through corporate bonds, or through stock), the company is borrowing funds, and must pay interest to the individual (in the form of coupon payments, dividends, or stock price appreciation).[] The interest rate is the change, expressed as a percentage, in the amount of money during one compounding period. A compounding period is the length of time that must transpire before interest is credited, or added to the total.[] For example, interest that is compounded annually is credited once a year, and the compounding period is one year. Interest that is compounded quarterly is credited 4 times a year, and the compounding period is three months. A compounding period can be any length of time, but some common periods are annually, semiannually, quarterly, monthly, daily, and even continuously. There are several types and terms associated with interest rates. Compound Interest Compound interest is multiplicative. Interest is earned on the interest that has already accrued (credited) in addition to the principal (initial amount).[] The term is the factor often used to make various calculations concerning compound interest[] Simple Interest Simple interest is additive. Simple interest is earned only on the principal amount, and there is no interest earned on interest already accrued.[] The term is the factor used to make various calculations when simple interest is applied. Simple interest is often used when calculating interest earned during a fraction of the year. Simple interest earns a higher return during the first year, and compound interest earns a higher return after the first year. At the end of the first year, simple interest and compound interest earn the same return.[] Effective Annual Rate of Interest Effective annual rate of interest is the percentage increase in an amount of money after a year of accumulating interest. This does not depend on what happens during the year. It can be calculated by Where represents the amount of money at time .[] Present value 3 Nominal Annual Rate of Interest Nominal annual rate of interest is NOT the same as effective annual rate of interest. Instead, nominal annual interest is compounded more than once a year, say, times. For instance, if the nominal annual interest rate is 8% and interest is compounded quarterly (4 times a year, or every three months), then the interest rate for ¼ of the year is (8/4)%=2%. Because it is compounded more often, the effective annual interest rate is actually more than 8%[] The formula to convert between effective annual interest rate and nominal annual interest rate is Where is the effective annual interest rate and is the nominal annual interest rate, and is the number of times interest is compounded in a year[] Rate of Discount The rate of discount, , refers to interest that is payable in advance, before funds have been transferred. There also exists a nominal annual discount rate, , which is analogous to nominal interest rate The formula to convert between effective annual interest rate, and effective annual discount rate is Where is the effective annual interest rate, and is the effective annual discount rate[] Continuous Compounding Continuous compounding is nominal interest that is compounded infinitely throughout the year. It is the instantaneous growth rate in the principal amount, i.e. the interest rate can change as a function of time. A force of interest, which describes the accumulated amount of money as a function of time, characterizes continuous compounding: Where is the force of interest, and is the amount of money as a function of time, , and its derivative. The formula to convert between effective annual interest rate, , and the constant force of interest, , is [] Real Rate of Interest Real rate of interest refers to the interest rate that has been adjusted to account for inflation; it is the percent change in buying power due to inflation.[] The real return refers to the surplus associated with an interest rate compared to an investment rate that matches the inflation rate. Where is the inflation rate.[] Present value 4 Calculation The operation of evaluating a present sum of money some time in the future called a capitalization (how much will 100 today be worth in 5 years?).
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