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