TIME VALUE REDUX: DISCOUNTED CASH FLOW VALUATION

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TIME VALUE REDUX DISCOUNTED CASH FLOW VALUATION
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TIME VALUE OF MONEY AGAIN MULTIPLE CASH FLOWS

• Terminology
• Annuities
• Ordinary annuities
• Annuities Due
• Perpetuities
• Special Situations
• Deferred annuities
• Unequal payments
• Intrayear compounding

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TIME VALUE OF MONEY EXAMPLE

• Present Value of an Annuity (PVA)

0
1
2
3
100
100
100
PVA
Equation Approach PVA 100 PVIFA(10,3) PVA
100 1 - 1/(1.10)3/.10 PVA 100 2.4868
248.68
HP 10B Approach gold, clear all 1, gold, P/YR 10,
I/YR 3, N 100, PMT PV ? -248.6851
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PVA EXAMPLE

• Youve just been notified that you hold the
  winning ticket in the Missouri lottery. The
  jackpot is 1 million. You are given the option
  of receiving 450,000 today, or 50,000 annually
  at the end of each of the next 20 years. Assume
  your opportunity rate is 10, and that taxes are
  not an issue. Which option should you take?

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LOTTERY PROBLEM SOLUTION
OPTION 1 450,000 TODAY PV _____________
OPTION 2 50,000 AT THE END OF THE EACH OF THE
NEXT 20 YEARS PVA 50,000 ? PVIFA(10,20)
425,678.1859
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TIME VALUE OF MONEY EXAMPLE

• Present Value of an Annuity Due (PVAD)

0
1
2
3
100
100
100
HP 10B Approach gold, clear all 1, gold,
P/YR gold, begin 10, I/YR 3, N 100, PMT PV ?
-273.5537
PVAD
Equation Approach PVA 100 PVIFA(10,3)(1.10) P
VA 100 1 - 1/(1.10)3/.10(1.10) PVA
100 2.4868 1.10 273.5480
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PVAD EXAMPLE

• Refer again to the Missouri lottery problem. Now
  assume that you are given the option of receiving
  450,000 today, or 50,000 annually at the
  beginning of each of the next 20 years. Assume
  your opportunity rate is 10, and that taxes are
  not an issue. Now which option should you take?

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LOTTERY PROBLEM SOLUTION
OPTION 1 450,000 TODAY PV 450,000
OPTION 2 50,000 AT THE BEGINNING OF THE EACH
OF THE NEXT 20 YEARS PVA 50,000 ?
PVIFA(10,20)(1.10) 468,246.0046
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TIME VALUE OF MONEY EXAMPLE

• Future Value of an Annuity (FVA)

0
1
2
3
100
100
100
FVA
Equation Approach FVA 100 FVIFA(10,3) FVA
100 (1.10)3 - 1/.10 FVA 100 3.31 331
HP 10B Approach gold, clear all 1, gold, P/YR 10,
I/YR 3, N 100, PMT FV ? -331
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FVA EXAMPLE

• Bill and Sam are both 25 years old and plan to
  retire at age 65. Suppose Bill begins investing
  2,000 annually next year and does so through his
  65th birthday. Sam doesnt begin investing until
  his 46th birthday, but invests 10,000 annually
  through age 65. Both earn 10 annually. Which one
  has more money at retirement?

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BILL AND SAM SOLUTION
25
65
46
26
0
40
1
2,000 . . . . . . . . . . . . . . . . . . . . . .
. 2,000
Bill
Sam
10,000 . . . . . . . 10,000
Assume r 10
Who has more money at retirement?
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TVM APPLICATIONRETIREMENT PLANNING
Waldo is 35 and wishes to retire in 30 years. He
would like to make 25 100,000 withdrawals from
his IRA, the first at age 66. Waldo also needs to
accumulate enough money to put his four-year-old
daughter, Laura, through college. He believes
she will require 25,000 at the beginning of each
of her four years in college. Assume Waldo can
earn a 9 after-tax return on his invested
capital, and plans to make 30 equal annual
deposits, the first to occur one year from today.
How large must each deposit be for Waldo to
accomplish his goals?
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SOLVING COMPLEX TIME VALUE PROBLEMS

• MARTINS METHOD
• Step 1 Draw a timeline, detail the cash
  inflows and outflows
• Step 2 Choose a focal point on the timeline
• Step 3 Equate the inflows and outflows at
  the focal point solve for the unknown.

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WALDO PROBLEM SOLUTION
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TVM APPLICATION INTRAYEAR COMPOUNDING
You are looking at a home in Sunset Hills. The
selling price is 330,000 you plan to put
30,000 down. If you borrow the balance on a
30-year 8 1/8 fixed-rate mortgage, how much will
each monthly payment be? (Note the first payment
is due in one month.) How much interest will
you pay over the life of the loan? Suppose
that mortgage rates rise to 9 while you are
negotiating with the seller, and you didnt lock
in your rate. Now how much will each monthly
payment be? How much more interest will you pay
over the life of the loan?
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TVM SUMMARY

• ? Equilibrium and the Equivalence Theorem
• ? Value f(size, timing, and risk) of future
  cash flows
• ? The Time-Value Model and the Financial Markets