Classes%20of%20External%20Decisions

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Classes of External Decisions

• Investment Decisions
• Distribution Decisions

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• Investment decision sacrificing current
  wealth for increased wealth in the
  future.
• Wealth command over good and services.

3
Features of Investment Decisions

• 1. Investment alternatives associated with a
  stream of expected economic consequences
• example
• 2. Expected consequences are uncertain
• example
• 3. Expected consequences differ in timing and
  magnitude
• example

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Assumptions Underlying Our Decision Model

• 1. Expected consequences can be expressed in
• terms of money flows
• 2. Expected cash flows are certain
• 3. No decision constraints

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(.25-.10) 24,000 (.25 - .11) 24,000
(.25-.12)24,000 -4,500
3,600 3,360 3,120 Chevy
___________________________________
1 2 3 (.25 - .08)24,000
(.25-.07) 24,000 (.25-.06) 24,000
-6,900 4,080 4,320
4,560 Fiat _____________________________
______ 1 2
3
6

• Savings
• ?Savings- ?Costs Net Savings Per Year
• Chevy 10,080 - 4,500 5,580
  1,860
• Fiat 12,960 - 6,900 6,060
  2,020
• Decision Choose
  _______________

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Time preference rate f (opportunity rate of
return)

• the rate of return you
  require for giving up the use of money for
  a period of time.

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Opportunity Set

• Passbook savings
• Money market accounts
• Tax exempts
• Junk bonds
• Stocks

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Assume r 10

• 1 1(.10)
• 1(1 .10)
• -1 1.10

1
10
1(1 .10) 1(1 .10).10 1(1
.10)(1 .10) -1 1(1 .10) 1(1
.10)² 1.21
2
1
11
-1 1(1 .10) 1(1 .10)²
1(1 .10)³ 1.33

1
2
3
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Future Value of a Sum

• Let FV future value of a sum
• r time preference rate
• n number of compounding periods
• pv principle sum to be invested at
• present
• FV PV (1 r)n

interest factor
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Problem What will 1,000 invested at
8 accumulate to at the end of five years?
?
1,000
1
2
3
4
5
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FV PV (1 r)n

• 1,000 (1 .08)5

1,000 (1.47)
1,470
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Future Value of 1
rs
ns
1
2
3
. . .
8

• 1
• 2
• 3
• 4
• 5
• .
• .
• .

1.47
16
FV PV (fvf - .08 - 5) 1,000 (1.47
1,470
)
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r ?

1 1.21 ___________________
_________________ 1
2
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Present Value of a Sum
FV PV (1 r)n PV FV/(1 r)n FV 1/(1
r)n int. factor

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• 1 1.21
• X 1
• 1.21X 1
• X 1/1.21
• .83

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• 1 1.21
• ____________________________________
• 1
  2
• .83 1

21

• 1 1.21
• ____________________________________
• 1
  2
• ? 1

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Problem What is 1,000 promised at the end of
five years worth today if r 8?

• ________________________________
• ?
• ___________________________________
• 1 2 3 4 5
• PV 1,000 (pvf - .08 - 5)
• 1,000 (.681)
• 681

1,000
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Annuity

• 100 100 100
• ___________________________________
• 1 2 3
• 100 200 100
• ___________________________________
• 1 2 3

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• 200 200 200
• ___________________________________
• 1 2 3

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Present Value of an Annuity(r 10)

• 200 200 200
• ___________________________________
• 1 2 3
• PV 200(.909) 200(.826) 200(.751)
• 182 165 150
• 497

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Alternatively,

• PV 200 (2.49)
• 498

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Net Present Value Model of Investment Choice

• 1. Felt need Maximize wealth
• 2. Problem Identification
• a. Objective function cash flows associated
  with each alternative
• b. Decision constraints none
• c. Decision rule choose alternative that
  maximizes wealth
• 3. Identify alternatives predicting (estimating)
  cash flows associated with each alternative

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Net Present Value Model of Investment Choice

• 4. Evaluate alternatives
• a. Calculate PV equivalents of each cash inflow
  and cash outflow associated with each alternative
• b. Sum the PVs of the inflows sum the PVs of
  the outflows
• c. NPV sum of PVs of inflows minus sum of
  present value of outflows
• 5. Choose alternative that promises the highest
  NPV!

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Auto Replacement Problem Revisited (r 10)

• -4,500 3,600 3,360
  3,120
• Chevy _________________________________
• 1 2 3
• PVs -4,500 3,600 ( ) 3,360 ( )
  3,120 ( )
• -4,500 3,272 2,775
  2,343
• ?PVs -4,500 8,390
• NPV 3,890

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Auto Replacement Problem Revisited (r 10)

• -4,500 3,600 3,360
  3,120
• Chevy _________________________________
• 1 2 3
• PVs -4,500 3,600 (.909) 3,360 (.826)
  3,120 (.751)
• -4,500 3,272 2,775
  2,343
• ?PVs -4,500 8,390
• NPV 3,890

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• -6,900 4,080 4,320
  4,560
• Fiat _________________________________
• 1 2 3
• PVs -6,900 4,080 (.909) 4,320 (.826)
  4,560 (.751)
• -6,900 3,709 3,568
  3,425
• ?PVs -6,900 10,702
• NPV 3,802
• Decision Choose ____________