Transcript Measuring Wealth: Time Value of Money

Chapter 3
Measuring Wealth:
Time Value of Money
Future Value and Present Value
 These
can be solved using formulas, tables, a
financial calculator or a computer spreadsheet
package
solution FV = PV (1+i)n
Formula solution PV = FV/ (1+i)n
Formula
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
– you purchased your house for $76,900 in
1994. Your neighbor’s house of similar value sold for
$115,000 in 2004 ( 10 years later). What rate of return
are you earning on your house?
 Example

Enter 115000 / 76900, yx, .1, –, 1, =, .0411 or 4.11%
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(1+i)
– 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?
 Example
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

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 year’s worth of interest).
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
= [((1+i)r –1) / r ] payment
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/(1+i)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
Present Value of an Uneven Stream
of Year-end Cash Flows
– You can invest in an athletic endorsement
that will increase net cash flows to your firm by:
 Example
$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 (1+i)n and then add up these results


 Answer
-- $1,572,679
Rate of Return on an Uneven Stream
of Year-end Cash Flows
– you can invest in an athletic endorsement
that will increase net cash flows to your firm by:
 Example
$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

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(.10/12,10*12,0,-5000,0)
 You
Enter -- .10/12, =, +1, =, yx ,120 times 5000 = $13,535
Adjusting for Compounding More
Than Once a Year
 To
adjust an APR or nominal rate to an effective rate use the
following formula:
 Effective rate = [(1+ nominal rate / # of comp.)n times # of comp]-1
Valuing Perpetuities

Value perpetual no-grow cash flows
 Formula
 Present

value = cash flow / discount rate
Value perpetual growing cash flows
 Formula
 Present
value =
cash flow /(discount rate - growth rate)