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Module 2

Modeling Decisions

ELEMENTS OF DECISION PROBLEMS

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Learning Objectives

• Elements of decision situations

• Money and decision problems

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Elements of Decision Problems

1. Values and objectives

2. Decisions to make

3. Uncertain events

4. Consequences

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Values and Objectives

• Values: things that matter

• Objective: what you want to achieve

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Values and Objectives

• Values create decision situations

• Values compel the need for objectives

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Values and Objectives

• Each decision situation involves a specific context

• Context influences the viable objectives

• A decision model must include all of the relevant objectives

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Decisions to be Made

• At least two alternatives required.

• “Doing nothing” may be a viable alternative

• In many cases, several sequential decisions are necessary

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Uncertain Events

• Important decisions must often be made without knowing the future

• Potential results from resolving uncertain events are outcomes

• Relevant outcomes have impacts on objectives

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Consequences

• The end results of decision making are consequences

• For multiple objectives, a consequence applies to each objective

• Consequences require planning horizons

• Values of consequences must be determined

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Elements of Decision Problems

1. Values and objectives

2. Decisions to make

3. Uncertain events

4. Consequences

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Decision Elements Relationships

• Fig- 2.4 from Page 29

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Money and Decision Problems

• Money is medium of exchange

• Making money can be an objective

• Money is frequently a surrogate

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Money and Trade-Offs

• Making money may not be maximized

• Making money may be traded off

• Time is an important trade off

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Time Value of Money

• Current value of future money called present value

• Present value uses principle of compound interest

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Time Value of Money

• Invest $100 at 10% compounded annually– Year 1: $100 x 1.1 = $110.00– Year 2: $110 x 1.1 = $121.00– Year 3: $121 x 1.1 = $133.10

• Present Value (PV) of $133.10 three years hence is $100 at 10% compounded annually

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Time Value of Money

• Let:– r = interest rate– n = number of time periods– x = future cash flow

• Then PV (x, n, r) = x/(1+r)n or x(1+r)-n

• For example,

PV (133.10, 3, 0.10) = 133.10 / (1+0.10)3 = $100

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Time Value of Money

• Extension of concept to sequence of cash flows

• Cash flow values may be the same or different

• Determine individual PVs and then sum

• PV = n

i = 0xi / ( 1 + r )i

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Time Value of Money

• Net Present Value (NPV) is difference between PV of negative and positive cash flows

• NPV value:– < 0 = undesirable– = 0 = breakeven– > 0 = desirable

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Time Value of MoneyExample

• Suppose you invested $1,000 in a mutual stock fund for three years. From fund dividends and capital gains, you received $100 the first year, nothing the second year, and $200 the third year. At the end of the third year, you also liquidated your holdings, receiving $1,000 in proceeds. If you could have invested the $1,000 in a different fund earning 10% compounded annually, was your mutual stock fund investment a wise choice?

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Time Value of MoneySolution

• NPV = -1000 1.10

+ $100 1.11

+ ( 200 + 1000)1.13

- = - 1000.00 + 90.91 + 901.58 = $7.51

• NPV < 0 = not a wise choice

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Summary

• Basic elements of decision problems– Values and objectives– Decisions to be made– Uncertain events– Consequences

• Money and decision problems