chapter 10 Choices Involving Time Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-2 Learning Objectives Explain how consumers and firms move cash from one point in time to another by borrowing and lending. Calculate the present discounted value of a claim on future resources. Understand consumers’ decisions regarding saving and borrowing. Analyze the profitability of investment projects with future cash flows. Explain how saving, borrowing, and investment depend on the interest rate. Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-3 Overview Transactions involving time Saving and borrowing by consumers Investment Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-4 Interest Rates and Compound Interest Principal: amount borrowed when one person lends money to another Interest: amount of money a borrower is obliged to pay a lender, over the principal Interest Rate: amount of interest paid on a loan during a particular period, stated as a percentage of the principal Compounding: payment of interest on loan balances that include interest earned in the past Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-5 Principal and Interest TodayOne YearTwo Years $121$110$100 +$10+$11 10% InterestCompound Interest Principal Annual Interest Rate Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-6 Effects of Compound Interest – Account balance – Dollars – Rate of interest – Time, years Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-7 Present Value and the Price of a Future Dollar Present Discounted Value (PDV): monetary value of a claim on future resources – At a positive interest, $1 received in the future is valued at less than $1 today Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-8 Present Value and the Price of a Future Dollar Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-9 Price of a Bond vs. the Prime Interest Rate Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-10 Why Do Interest Rates Differ Risk: Risk exists whenever the consequences of a decision are uncertain. The higher the risk the higher the interest payment demanded by lenders Default: the failure to pay back borrowed money Detail of agreements Timing of repayment Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-11 Real versus Nominal Interest Nominal interest: compensation received by the lender over and above the principal, without adjusting for inflation Real interest: compensation measured in real dollars, adjusted for inflation Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-12 Real versus Nominal Interest Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-13 Preferences for the Timing of Consumption Higher marginal rate of substitution than Brian Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-14 Saving and Borrowing (a) Saving Savings plus interest 220 Earnings next year 200 Savings this year Food this year (kg) Food next year (kg) A 380 Earnings this year Interest rate = 10 % Slope = B A C 110 Debt plus interest 380 Earnings this year 480 Borrowing this year 220 Earnings next year 0 (b) Borrowing Food next year (kg) Food this year (kg) Slope = Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-15 Affordable Consumption Bundles A consumption bundle is affordable if, through borrowing and lending, the consumer can make all the required payments as they come due. Given the more-is-better principle, the best choice leaves no income unspent. PDV of consumption stream = PDV of income stream The slope of the budget is equal to the (negative) ratio of the goods’ prices. P 0 is the price of the good this year and P 1 /(1+R) the price of the good next year (from today’s perspective). Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-16 Best Choices with Saving and Borrowing Best choice Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-17 Effect of a Change in the Interest Rate on Savings (a) Effect of a change in the interest rate Food this year (kg) Food next year (kg) (b) The substitution and income effects Food this year (kg) Food next year (kg) Effect of increasing interest rate Substitution effect Income effect L2L2 l2l2 l1l1 L1L1 B D A L3L3 L2L2 L1L1 A l2l2 l1l1 B E D Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-18 Saving, Borrowing, and the Interest Rate Interest rate increases: saving becomes more rewarding and borrowing becomes more costly (substitution effect) However, if interest rates rise you may decide to save less because you’ll earn more interest on each dollar saved, reaching your future income target with less put in savings (income effect) Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-19 Effect of a Change in the Interest Rate on Borrowing (a) Effect of a change in the interest rate Food this year (kg) Food next year (kg) (b) The substitution and income effects Food this year (kg) Food next year (kg) Effect of increasing interest rate Substitution effect Income effect L1L1 L2L2 l3l3 l4l4 L4L4 A C F F L1L1 L2L2 l4l4 l3l3 A C G Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-20 Life Cycle Hypothesis Life cycle hypothesis: theory of consumption and saving; describes the choices of consumers with realistic life spans Assumptions: 1.Typical person’s adult life has 2 main stages: - First stage: employed - Second stage: retired, earning nothing 2.People prefer stability in consumption Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-21 Life Cycle Hypothesis Not feasible Best feasible alternative Does not exhaust consumer’s lifetime resources Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-22 Investment Investment: up-front costs incurred with the expectation of generating future profits Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-23 Measuring the Profitability of Investments Net present value (NPV): difference between the PDV of the revenue stream and the PDV of the cost stream – NPV criterion: states that an investment project is profitable when its NPV is positive, and unprofitable when its NPV is negative Net cash flow (NCF): difference between revenue and cost during a single year of a project’s life Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-24 Profitability of Investments Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-25 Profitability of Investments Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-26 NPV and the Opportunity Cost of Funds Time value of money (opportunity cost of funds): opportunity cost associated with the economic benefit an investor could receive by lending money at the prevailing interest rate Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-27 Internal Rate of Return Internal rate of return (IRR): rate of interest at which a project’s NPV is exactly zero Importance: – if IRR > rate of interest, project is profitable – if IRR < rate of interest, project is unprofitable Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-28 Internal Rate of Return Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-29 Investment and the Interest Rate An increase in the interest rate usually makes investment projects less attractive – At a higher interest rate, future dollars are worth less compared to current dollars – At a higher interest rate, putting money in the bank becomes more attractive (and borrowing becomes less attractive) Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-30 Choosing Between Mutually Exclusive Projects Best choice among mutually exclusive alternatives is the one that yields the greatest profit. For investment projects, that means the one with the highest NPV. Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-31 Other Criteria for Choosing between Mutually Exclusive Projects Comparing mutually exclusive projects using criteria other than NPV can lead to poor decision making – Choosing based on higher IRR – Payback period: amount of time required before a project’s total inflows match its total outflows Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-32 Investing in Human Capital Human capital consists of marketable skills acquired through investments in education and training Education is an investment and is not always worthwhile Financial returns of education often summarized by calculating the IRR Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-33 Review Interest rates differ because of variations in default risk, flexibility, and the timing of payments. Saving reflects decisions about the optimal timing of consumption NPV is a measure of profitability—it is the difference between the value of a project’s outputs and the value of its inputs, from today’s perspective. An investment project is profitable when its NPV is positive and unprofitable when its NPV is negative. When interest rates rise, most potential projects become less profitable, and the general level of investment falls. Falling interest rates have the opposite effects. Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

10-34 Looking Forward Next we will study risk and how people make decisions under uncertainty Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.