Chapter 3 Measuring Wealth: Time Value of Money

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Chapter 3 Measuring Wealth Time Value of Money
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Future Value and Present Value

• These can be solved using formulas, tables, a
  financial calculator or a computer spreadsheet
  package
• Formula solution FV PV (1i)n
• Formula solution PV FV/ (1i)n

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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

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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

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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).

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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

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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

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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

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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

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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

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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

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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)