Classes of External Decisions

Investment Decisions

Distribution Decisions

Investment decision = sacrificing current wealth for

increased wealth in the future.

Wealth = command over good and services.

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:

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

(.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

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 _______________

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.

Opportunity Set

Passbook savings

Money market accounts

Tax exempts

Junk bonds

Stocks

Assume r = 10%

$1 + $1(.10)

1(1 + .10)

-$1 = 1.10

1

1(1 + .10) + [1(1 + .10)].10

= 1(1 + .10)(1 + .10)

-$1 1(1 + .10) = 1(1 + .10)²

= 1.21

1 2

-$1 1(1 + .10) 1(1 + .10)² 1(1 + .10)³

= 1.33

1 2 3

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

Problem: What will $1,000 invested at 8%accumulate to at the end of fiveyears?

$1,000 ?

1 2 3 4 5

FV = PV (1 + r)n

= $1,000 (1 + .08)5

= $1,000 (1.47)

= $1,470

Future Value of $1

r´s

n´s 1% 2% 3% . . . 8%

1

2

3

4

5

.

.

.

1.47

FV = PV (fvf - .08 - 5) = $1,000 (1.47 = $1,470

)

$1 $1.21 |___________________|_________________|

1 2

r = ?{

Present Value of a Sum

FV = PV (1 + r)n

PV = FV/(1 + r)n

= FV 1/(1 + r)n

int. factor{

1 = 1.21

X 1

1.21X = 1

X = 1/1.21

= $.83

$1 $1.21

|___________________|_________________|

1 2

.83 $1

$1 $1.21

|___________________|_________________|

1 2

? $1

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

Annuity

100 100 100

|___________|____________|____________|

1 2 3

100 200 100

|___________|____________|____________|

1 2 3

200 200 200

|___________|____________|____________|

1 2 3

Present Value of an Annuity(r = 10%)

200 200 200

|___________|____________|____________|

1 2 3

PV = $200(.909) + $200(.826) + $200(.751)

= 182 + 165 + 150

= $497

Alternatively,

PV = 200 (2.49)

= 498

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

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!

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

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

-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 ____________