classes of external decisions investment decisions distribution decisions
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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.
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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
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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
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1(1 + .10) + [1(1 + .10)].10
= 1(1 + .10)(1 + .10)
-$1 1(1 + .10) = 1(1 + .10)²
= 1.21
1 2
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-$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 fiveyears?
$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
r´s
n´s 1% 2% 3% . . . 8%
1
2
3
4
5
.
.
.
1.47
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FV = PV (fvf - .08 - 5) = $1,000 (1.47 = $1,470
)
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$1 $1.21 |___________________|_________________|
1 2
r = ?{
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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
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$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 PV’s of the inflows; sum the PV’s of the outflows
c. NPV = sum of PV’s 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
PV’s = -4,500 + 3,600 ( ) + 3,360 ( ) + 3,120 ( )
= -4,500 + 3,272 + 2,775 + 2,343
PV’s = -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
PV’s = -4,500 + 3,600 (.909) + 3,360 (.826) + 3,120 (.751)
= -4,500 + 3,272 + 2,775 + 2,343
PV’s = -4,500 + 8,390
NPV = 3,890
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-6,900 4,080 4,320 4,560
Fiat |__________|____________|___________|
1 2 3
PV’s = -6,900 + 4,080 (.909) + 4,320 (.826) + 4,560 (.751)
= -6,900 + 3,709 + 3,568 +3,425
PV’s = -6,900 + 10,702
NPV = 3,802
Decision: Choose ____________