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

( ) 24,000 ( ) 24,000 ( )24,000 -4,500 =3,600 =3,360 =3,120 Chevy |___________|___________|_____________| 123 ( )24,000 ( ) 24,000 ( ) 24,000 -6,900 =4,080 =4,320 =4,560 Fiat |___________|___________|_____________| 1 2 3

Savings  Savings-  Costs =Net SavingsPer Year Chevy 10, ,500 = 5,580 1,860 Fiat 12, ,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(1 +.10) + [1(1 +.10)].10 = 1(1 +.10)(1 +.10) -$1 1(1 +.10)= 1(1 +.10)² =

-$1 1(1 +.10) 1(1 +.10)² 1(1 +.10)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 five years? $1,000 ?

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%

FV = PV (fvf ) = $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 X=1 X=1/1.21 =$.83

$1 $1.21 |___________________|_________________| $1

$1 $1.21 |___________________|_________________| 1 2 ? $1

Problem: What is $1,000 promised at the end of five years worth today if r = 8%? ________________________________ ? ___________________________________ PV= 1,000 (pvf ) = 1,000 (.681) = $681 $1,000

Annuity |___________|____________|____________| |___________|____________|____________| 12 3

|___________|____________|____________| 12 3

Present Value of an Annuity (r = 10%) |___________|____________|____________| 12 3 PV= $200(.909) + $200(.826) + $200(.751) = = $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 |__________|____________|___________| PV’s = -4, ,600 ( ) + 3,360 ( ) + 3,120 ( ) = -4, , , ,343  PV’s = -4, ,390 NPV = 3,890

Auto Replacement Problem Revisited (r = 10%) -4,500 3,600 3,360 3,120 Chevy |__________|____________|___________| PV’s = -4, ,600 (.909) + 3,360 (.826) + 3,120 (.751) = -4, , , ,343  PV’s = -4, ,390 NPV = 3,890

-6,900 4,080 4,320 4,560 Fiat |__________|____________|___________| PV’s = -6, ,080 (.909) + 4,320 (.826) + 4,560 (.751) = -6, , ,568 +3,425  PV’s = -6, ,702 NPV = 3,802 Decision: Choose ____________