unit 1 - understanding the time value of money as managers, we need to be fully aware that money has...
TRANSCRIPT
Unit 1 - Understanding the Time Value of Money
• As managers, we need to be fully aware that money has a time value
• Future euros are not equivalent to present euros, since euros in hand may be used for immediate consumption or invested
• Inflation is the erosion of a currency’s purchasing power• Interest rates, which represent the return on investment,
compensate for foregoing present consumption, loss of purchasing power due to inflation, and other risks associated with uncertain investment outcomes
Understanding Future Values
• The purpose of investing is to grow money, resulting in an increase in future purchasing power
• Money in the present is referred to as present value; future money is referred to as future value
• Interest rates are the mechanism used to equate future values with present values
• Simple interest is an arithmetic process, whereby each period interest is calculated as a function of the principal invested, and added to the total.
• Compound interest is a geometric process, whereby each period interest is calculated as a function of both the principal and any interest already earned on that principal.
An Example of Simple Interest
A 100,000 euro investment earns 5% simple interest for 20 years:
100,000 = the present value5% = the simple interest rate20 = the number of periods
Solve for future value
100,000 x .05 = 5,000 euros annual interest5,000 x 20 years = 100,000 euros total interest earned
Future value = 100,000 + 100,000 = 200,000 euros
An Example of Compound Interest
A 100,000 euro investment earns 5% compound annual interest for 20 years:
100,000 = the present value5% = the compound annual interest rate
20 = number of periodsSolve for future value
100,000(1.05) = 105,000; 105,000(1.05) = 110,250; 110,250(1.05) =
115,762.50;115,762.50(1.05) = 121,550.625; 121,550.625(1.05) = 127,628.15, …
or
Future Value = 100,000(1.05)20 = 265,329.77 euros
Simple versus Compound Interest
Compound interest grows geometrically; simple interest grows arithmetically
0
50,000
100,000
150,000
200,000
250,000
300,000
SimpleCompound
Notes on Compounding to Future Values
• The difference in the two preceding examples, 265,330 – 200,000 = 65,330 euros, is due to earning interest on previously earned interest
• This is the definition of compounding; each period builds on the previous period, resulting in a geometric growth rate
• Most business investments and financial instruments use compound, not simple, interest
• The more frequent the compounding period, the greater the interest earned on previous interest and, therefore, the greater the rate of growth in the money
Examples of More Frequent Compounding Periods
A 100,000 euro investment earns 5% compounded
annually for five years:Future Value = 100,000(1.05)5 = 127,628.15 euros
If semiannual compounding,
Future Value = 100,000(1.025)10 = 128,008.45 euros
If monthly compounding,Future Value = 100,000(1.0042)60 = 128,335.87 euros
Annuities
• An annuity is a series of payments of equal amounts that occur at equivalent intervals
• Examples of an annuity would include a house payment on a mortgage loan, or a lease payment on a piece of rented equipment
• An annuity structured so that each payment is made at the end of the period is known as an Ordinary Annuity
• An annuity structured so that each payment is made at the beginning of the period is known as an Annuity Due
• The difference in an ordinary annuity and an annuity due is that an annuity due involves an extra compounding period, since the first payment begins accruing interest immediately
Discounting – Understanding Present Values
• An important concept for managers in utilizing the time value of money to make sound economic decisions is discounting
• Discounting is the process of taking future money and converting it into present money
• Discounting is the exact opposite of compounding; periodic interest is deducted each period from the future date back to the present
• Discounting is important because managers make decisions in the present, therefore money variables should be expressed in present values to make economically logical decisions
An Example of Discounting
An investment promises to pay off 500,000 euros in 10 years. If the appropriate interest rate is 8%, what is the present value of the investment?
500,000 = the future value
8% = the interest rate10 = number of periodsSolve for Present Value
500,000(1.08) -10 = 231,596.74 euros