4: Evaluating Choices - Time, Risk, and Value
- Page ID
- 420
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This chapter introduces the critical relationships of time and risk to value. It demonstrates the math but focuses on the role that those relationships play in financial thinking, especially in comparing and evaluating choices in making financial decisions.
- 4.1: Introduction
- This page discusses financial decision-making as a future-oriented process involving speculation on uncertain outcomes. It highlights that past decisions are sunk costs and cannot be changed. Evaluating alternatives requires assessing potential results, values, risks, and opportunity costs over time. The reference to Robert Frost's poem symbolizes the uncertainty and careful consideration necessary in financial planning.
- 4.2: The Time Value of Money
- This page discusses the interplay between liquidity and time in financial decision-making, emphasizing liquidity's role in providing choices. It introduces the time value of money, explaining that future cash flows are less valuable than present ones due to risks and opportunity costs. The text highlights the importance of understanding present and future values for effective financial planning, noting that time diminishes future values due to these associated factors.
- 4.3: Calculating the Relationship of Time and Value
- This page explains the relationship between present value (PV) and future value (FV), emphasizing time, risk, and opportunity costs. It details the formula PV × (1 + r)t = FV, highlighting the significance of liquidity and its greater value over time. The text also covers how to calculate PV and FV, stressing the need for effective liquidity management to enhance cash flows and ensure financial stability, which is essential for informed financial decisions.
- 4.4: Valuing a Series of Cash Flows
- This page explains the time value of money and its significance in financial decisions, focusing on cash flows, annuities, and perpetuities. It defines present value, annuities, and factors like cash flow, payment frequency, and discount rates that influence their value. The text explores the interplay between time, risk, opportunity cost, and liquidity, noting that higher discount rates decrease present value while more cash flow increases it.
- 4.5: Using Financial Statements to Evaluate Financial Choices
- This page discusses pro forma financial statements, which are projected financial outcomes aiding in planning. They assess how decisions impact income, expenses, and cash flow, highlighting uncertainties. Alice's various debt management options illustrate this: getting a second job offers stability, while gambling in Vegas presents high-risk financial fluctuations. Overall, understanding these scenarios helps in evaluating risks and making informed financial choices.
- 4.6: Evaluating Risk
- This page discusses the importance of probabilities in financial decision-making, focusing on independent events and expected value calculation. It emphasizes the complexity of risk and the need for understanding independence, using gambling as an example to measure outcomes and probabilities.