We have to consider timing when making financial decisions Consider that you have a choice to receive $1000 today or $1000 five years from now

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1 ENGM 401 & 6 X1 Fundamentals of Engineering Finance Winter Lecture 18: The Time Value of Money Many people take no care of their money till they come nearly to the end of it, and others do just the same with their time. - Goethe M.G. Lipsett University of Alberta Time Time Value Value of of Money Money We have to consider timing when making financial decisions Consider that you have a choice to receive $00 today or $00 five years from now Which would you choose? Why? money now is worth more than money later One of the most important economics concepts is the time value of money We use the concept of the time value of money to decide whether to spend money on ways to make create value i.e., to invest or not to invest MG Lipsett, 2 1

2 Possible Possible Case Case Studies Studies for Time Value of Money Should we build a new plant now or two years from now? Will it be economical to build and operate? How much should an oil sands operating company be saving to reclaim an oil sands tailings pond thirty years from now? How much will an LRT expansion cost? How fast should I pay off my student loan? Should I buy a new car or a used one? Other examples? MG Lipsett, 3 Why Why Does Does Money Money Have Have A a Time Time Value? Value? Cash is: Liquid it doesn t need to be converted to anything before it is used Available it can be used at once Relatively safe inflation and government stability are the risk factors Storable We sell money at a price that offsets liquidity, availability, safety and durability Money is subject to supply and demand forces like any other commodity MG Lipsett, 4 2

3 Time-Value Time Value of of Money Money (3) Things change value over time Very few things increase in value Typically rarities that are collectible, increasingly scarce Fine art, jewelry, antiques, vintage wines, Wayne Gretzky rookie cards Most things eventually lose value (even intangibles) Wear out, break, get lost, age, die Become obsolete or irrelevant because of innovation Artificial obsolescence (victims of fashion) Production of additional (equivalent units) reduces scarcity (competition) Familiarity breeds contempt, or at least builds expectations (luxuries become basics) Since money represents value, even cash is not worth as much in the future as it is today MG Lipsett, 5 Monetary Monetary Entropy Entropy Recall the analogy of money as energy 1 st Law : In an closed equilibrium system, money can be transformed but not created or destroyed Assets = Liabilities + Equity 2 nd Law : The value of a good can not maintained forever in a stable or expanding economy (dissipation of value, like entropy) Money is subject to supply and demand forces Money changes value with time Financial calculations thus have to account for time-value What method have we already learned? Depreciation of course! MG Lipsett, 6 3

4 Why Why Does Does Money Money Have Have A a Time Time Value? Value? (2) (2) MG Lipsett, 7 Interest is the cost of money. If you rent an apartment, you expect to pay for it. In the same way, you pay for money if you borrow or rent it The cost is related to: The amount of money How long you keep it Another Way to Think of Time Value of Money: If I let you use my money, I expect to be paid for it (Because if I didn t give it to you, I could have been doing something else with it) Interest is expressed as a percentage per period of time. Value Value in in the the Eyes Eyes of of the the Lender Lender/Investor or Investor The lender or investor has a time value for money that is specific to each investment and reflects: Inflation General supply / demand for money Risk Liquidity The time value must exceed the inflation rate if value is to be created The objective of investing is to increase wealth MG Lipsett, 8 4

5 Value Value in in the the Eyes Eyes of of the the Borrower Borrower Some borrowing is for personal and non-monetary values e.g., home mortgages because we d prefer a house to an apartment, car loans because we like to have our own means of travel, etc. Some borrowing (commercial borrowing) is always based on the belief that you can create value at a higher rate than the cost of borrowing the money i.e., you create value that can be retained The primary objective of commercial borrowing (or selling equity) is to increase wealth MG Lipsett, 9 The The Concept Concept of of Interest Interest The main principle of the concept of interest is that the cash put in to the investment must yield a return (value) in every time period (e.g., a month or a year) A dollar today will be worth more in the future, because if you lend or invest it you expect to create value over time A future dollar is worth less today because you could invest a lesser amount today and have the future dollar Value Time Period Return on investment: Extra value created Today Future MG Lipsett, 5

6 The The Concept Concept of of Interest Interest (2) (2) Some terms in investment analysis are used somewhat interchangeably Interest Rate Discount Rate Return Rate The concept of interest is used more broadly than just payment for debt We discount future dollars because they are worth less than a current or present dollar. The words discount rate are frequently used because we end up comparing the net present value of a stream of future dollars: i.e., we bring back all future dollars to a common value, today. Return on investment is what we expect to get, so return rate is the same thing as interest The value due on money can accrue, for example we may get no interest for five years then all at once after the five years. The fundamental concept is that for as long as a dollar is out it should have a value, either paid or accrued. MG Lipsett, 11 The The Historical Historical Value Value of of Interest Interest Rates Rates Bank of Canada Int. Rate MG Lipsett, Source: Statistics Canada 6

7 Federal Federal Debt: Debt: One One Source Source of of Demand Demand for for Money Money 50,000 Net Change in Canadian Federal Debt (M$) 40,000 30,000,000, ,000 -, Source: Statistics Canada MG Lipsett, 13 The The Concept Concept of of Inflation Inflation Inflation is the concept where as time moves forward, the purchasing power of a unit of currency (money) decreases A dollar tomorrow will buy less than it does today In Canada, inflation is often measured by the Consumer Price Index (CPI) CPI is the retail price of a representative shopping basket of approximately 600 goods and services that the typical household will purchase (food, housing, transportation, furniture, clothing, recreation) Inflation is often higher in times of high interest rates One reason: long-term investment is less likely with high interest rates, increasing the pressure and prices on short term purchasing MG Lipsett, 14 7

8 The The Concept Concept of of Inflation Inflation (2) (2) Annual Change in CPI For wacky finance fun, try the inflation calculator at: Source: Statistics Canada MG Lipsett, 15 Causes Causes of of Inflation Inflation Loss of confidence in a country s currency Loss of investment in economy Investors move their money to another currency Governments printing too much money Prices rising to match inflation If government is not prudent, positive feedback (vicious circle) can even lead to hyperinflation MG Lipsett, 16 8

9 Hyperinflation Hyperinflation in in Weimar Weimar Germany Germany Weimar Inflation Rates: Cost of a Loaf of Bread in Berlin, Marks 1E+12 1E+11 1E+ 1E+09 1E+08 1E+07 1E A German woman feeding a stove with currency notes, which burn longer than the amount of firewood they can buy Jun Jun- Jun Jun Jun MG Lipsett, 17 Real Real versus vs. Market Market Interest Interest Rates Rates The value of money increases over time, but at the same time, its purchasing power becomes less Two competing forces The real interest rate realized by a lender is approximately the difference between the interest rate paid by the borrower (nominal or market interest rate) and inflation: i real = i nominal i inflation where i = the interest rate per period (approximately) MG Lipsett, 18 9

10 Real Real Interest: Interest Nominal Interest Minus Inflation Nominal Interest Rate Inflation Rate MG Lipsett, 19 Bank of Canada Int. Rate. Annual Change in CPI Real Real Interest: Interest (2) Nominal Interest minus Inflation "Real" Interest Rate: Nominal minus Delta CPI Source: Statistics Canada MG Lipsett,

11 Summary Real Interest Things of value do not their value forever Even money is not worth as much in the future as it is today Interest is the rent on borrowing If I m not going to have the use of my money for a while, I want to be compensated for it Interest is affected by many factors Inflation tracks the loss of purchasing power of a currency with time MG Lipsett, 21 11