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
An Example of Simple Interest
A 100,000 euro investment earns 5% simple interest for 20 years:
100,000 = the present value
5% = the simple interest rate
20 = the number of periods
Solve for future value
100,000 x .05 = 5,000 euros annual interest
5,000 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 value
5% = the compound annual interest rate
20 = number of periods
Solve 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
300,000
250,000
200,000
Simple
Compound
150,000
100,000
50,000
Y
ea
r
Y 9
ea
r1
2
Y
ea
r1
5
Y
ea
r1
8
r6
Y
ea
r3
Y
ea
Y
ea
r0
0
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 rate
10 = number of periods
Solve for Present Value
500,000(1.08) -10 = 231,596.74 euros