1. Chapter 5
Introduction to Valuation: The Time Value
of Money

2. Key Concepts and Skills
Be able to compute the future value of an investment made today
Be able to compute the present value of cash to be received at some future date
Be able to compute the return on an investment
Be able to compute the number of periods that equates a present value and a future value given an interest rate
Be able to use a financial calculator and/or a spreadsheet to solve time value of money problems

3. Future Value and Compounding Present Value and Discounting
Chapter Outline
Future Value and Compounding
Present Value and Discounting
More on Present and Future Values

4. Time Value of Money
Many financial decisions require comparisons of cash payments at
different dates
Example: 2 investments that require an initial investment of $100
Timing Inv 1 Inv 2
After 1 year $30 $20
After 2 years $30 $20
After 3 years $30 $40
After 4 years $30 $60
If you should choose one of them, which would you choose?

5. Compounding
Future Value: amount to which an investment will grow after earning interest
Compounding: the process of accumulating interest in an investment over time to earn more interest
Compound interest: Interest earned on both the initial principal and the reinvested interest from prior periods

6. Time principal Interest 0 $100 $0 1 $100 $10 2 $110 $11
Future Value
FV of $100 in 2 years if k=10%
Time principal Interest
0 $100 $0
1 $100 $10
2 $110 $11
So $100 today  $121 in 2 years

7. simple and compounded interest?
What is the difference between simple and
compounded interest?
Compound interest assumes accumulated interest is reinvested (therefore, interest earns interest).
Simple interest assumes interest is not reinvested. Interest is earned each period on the original principal only.

8. Present Value and Discounting
Present Value: value today of a future cash flow
PV is simply the reverse of future value
PV works backward through time, while future value goes forward through time
Discounting: finding present value of some future
amount

9. Example 3 different ways to find future value of a single cash flow
Find FV of $100 in 2 10%
FV2= 100*(1+10%) formula
= 100 FVIF2,10% table
PV i n FV financial calculator
in general FVn= PV (1+i)n
PV, FV formulas are based on this equation
4 variables given any 3, you can calculate the 4th

10. solving for n in how many years will $100 grow to $121 @ i= 10%
Formula way:
100*(1+10%)n =121
(1+10%)n =1.21
n ln(1+10%)=ln 1.21
Table way:
100 FVIFn,10% =121
FVIFn,10% =1.21
Refer to FVIF Table. Look down the 10% column to find 1.21.
Financial calculator way:
PV i FV n

11. Solving for i
At what rate of return will $100 grow to $121 in 2 years
Formula way:
100*(1+i)2 =121
(1+i)2 = 1.21
1+i = (1.21)1/2 =1.10
i = 0.10 = 10%
Table way:
100 FVIF2,i =121
FVIF2.i =1.21
Refer to FVIF Table. Look across 2 period row to find 1.21.
Financial calculator way:
PV n FV i