Chapter 3 Measuring Wealth: Time Value of Money

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Title: Chapter 3 Measuring Wealth: Time Value of Money

1
Chapter 3-- Measuring Wealth Time Value of
Money

Why must future dollars be put on a common basis
before adding?
Cash is a limited and controlled resource.
Those controlling the resource can charge for its
use.
The longer the period of use the higher the
interest (or rental fee) for the use of the cash.
Therefore, you cannot add a 1 year dollar with a
two year dollar.

2
Future Dollar Equivalent (Future Value) of a
Present Amount

These can be solved using formulas, tables, a
financial calculator or a computer spreadsheet
package
Formula solution FV PV (1i)n
Example -- How much will 1000 grow to at 12 in
15 years?
Enter 1.12, yx, 15, times 1000 5473.56

3
Present Dollar Equivalent (Present Value) of a
Future Amount

These can be solved using formulas, tables, a
financial calculator or a computer spreadsheet
package
Formula solution PV FV/ (1i)n
Example -- how much do you need today to have
1,000,000 in 40 years if your money is earning
12?
Enter 1.12, yx, 40, , 1/x, times 1000000
10,747

4
Finding the Rate Between Two Single Amounts

These can be solved using formulas, tables, a
financial calculator or a computer spreadsheet
package
Formula solution -- i (FV/PV)1/n -1
Example you purchased your house for 76,900 in
1994. Your neighbors house of similar value sold
for 115,000 in 2004 ( 10 years later). What
rate of return are you earning on your house?
Enter 115000 / 76900, yx, .1, , 1, , .0411 or
4.11

5
Finding the Number of Periods Needed Between Two
Amounts

These can be solved using formulas, tables, a
financial calculator or a computer spreadsheet
package
Formula solution -- n LN(FV/PV)/LN(1i)
Example you inherit 120,000 from your great
aunt and invest it to earn 8 interest. How long
will it take for this to grow to 1,000,000?
Enter (1000000 / 120000) ,, ln -- this gives
you 2.1203
Enter (1.08), ln -- this gives you .0770
Divide the two results to get 27.55 years

6
Different Types of Annuities.

Ordinary annuities -- dollars are received or
paid at the end of the period and grow until the
end of the period.
All annuity formulas to be discussed will work
for ordinary annuities with no adjustments.
Annuities due -- dollars are received or paid at
the beginning of the period and grow until the
end of the period.
All annuity formulas to be discussed will need
adjustment (for the extra years worth of
interest).

7
Future Value of an Ordinary Annuity and an
Annuity Due

Example -- How much will you have at the end of
35 years if can earn 12 on your money and place
10,000 per year in you 401k account at the
beginning of the year? (at the end of the year?)
Formula solution ordinary annuity
FV ((1i)r 1) / r payment
Enter (1.12,yx, 35, , 1, ) / .12 times
10000
The answer is 4,316,635
To solve for an annuity due just remove the 1
from the formula above the answer is then
4,834,631

8
Present Value of an Ordinary Annuity and an
Annuity Due

Example -- How much is a trust fund worth today
that promises to pay you 10,000 at the end (or
beginning) of each year for 35 years if can earn
12 on your money?
Formula solution ordinary annuity
FV 1-(1/(1i)r) / r payment
Enter 1.12,yx, 35, , 1/x, ,1, /-, ) / .12
times 10000
this will give you the answer of 81,755
To solve for an annuity due, change the 35 to 34
in the formula above then add an additional 10000
payment to the answer of 81,566 to get 91,566

9
Present Value of an Uneven Stream of Year-end
Cash Flows

Example You can invest in an athletic
endorsement that will increase net cash flows to
your firm by
800,000 at the end of year 1
600,000 at the end of year 2
400,000 at the end of year 3
After that, you do not expect any additional
benefit from her endorsement. What is the
present value of this endorsement if the firm has
a cost of funds of 8 percent?
Formula solution discount each future cash flow
to present by dividing by (1i)n and then add up
these results
Answer -- 1,572,679

10
Rate of Return on an Uneven Stream of Year-end
Cash Flows

Example you can invest in an athletic
endorsement that will increase net cash flows to
your firm by
800,000 at the end of year 1
600,000 at the end of year 2
400,000 at the end of year 3
After that, you do not expect any additional
benefit from her endorsement. If this
endorsement cost the firm 1,000,000 today, what
is the rate of return of this endorsement?
Calculator solution 2nd , CLR WRK, CF 1000000,
/-, enter, 800000, enter, 600000, enter, 400000,
enter, IRR, CPT
The answer 42.06 appears

11
Adjusting for Compounding More Than Once a Year

In the formula, you divide the interest rate by
the number of compoundings and multiple the n by
the number of compoundings to account for
monthly, quarterly or semi-annual compounding
Excel Example -- What will 5,000 dollars
invested today grow to at the end of 10 years if
your account promises a 10 APR compounded
monthly? You Enter -- for the monthly answer --
FV(.10/12,1012,0,-5000,0)
You Enter -- .10/12, , 1, , yx ,120 times 5000
13,535

12
Adjusting for Compounding More Than Once a Year

13
Adjusting for When Cash Flows Are Received Daily

A close approximation for level daily cash flows
is the use of mid-year cash flows.
When using a computer package with both mid year
and year-end cash flows it is easiest to use the
PV function to discount each periods cash flow
back to present individually.
When looking for the internal rate of return of
daily cash flows the problem must be worked as a
goal seek (solving for the interest rate).

14
Valuing Perpetuities