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Zara Mahmood Roberts FE101 Time Value of Money An Introduction COST BENEFIT ANALYSIS First step identify the costs and benefits of a decision Role of the Financial Manager Financial manager makes decisions on behalf of the firm s investors How to make decisions that increase the value of the firm to its investors Good decisions benefit exceeds cost Marketing increase in revenues from advertising campaign Economics increase in demand from lowering price of product Organizational Behavior effect of changes in management structure on productivity Strategy competitor s response to a price increase Operations production costs after the modernization of manufacturing plant Quantifying Costs and Benefits Decision in which value of benefit exceeds the cost increases value of firm Quantify values in equivalent terms cash today Net benefit benefit cost Positive net benefit means the decision is valuable Role of Competitive Market Prices Independent on own views benefit is the same Jeweler has no use for gold but should still buy it and then can use money to rebuy silver and still make profit o Personal preference opinion of fair price is irrelevant Competitive Market A market in which the good can be bought AND sold at the same price Price of good during trade determines value of the good MARKET PRICES AND THE VALUATION PRINCIPLE Expressing costs and benefits in cash today terms makes it easy to compare The Valuation Principle Decision that makes value of benefits exceed value of costs Based on competitive market price of commodity or asset Decision will increase the market value of the firm Why There Can Be Only One Competitive Price for a Good Cannot have two different competitive market prices for the same good We would arrive at two different values cost benefit analysis would change Zara Mahmood Roberts FE101 o Market prices keep competitive prices the same Law of One Price In competitive markets securities with the same cash flows must have the same price Gold was trading at two different prices o People would buy at low price and sell at high instant profit o Buy and sell orders would eventually push prices together Arbitrage The practice of buying and selling equivalent goods to take advantage of a price difference Arbitrage Opportunity Any situation is which it is possible to make a profit without taking any risk or making any investment Opportunity benefits are more valuable than its costs o Opportunity appears in financial market investors race to take advantage of it and will eventually eliminate the opportunity THE TIME VALUE OF MONEY AND INTEREST RATES Most financial decisions have costs and benefits that occur at different points in time Typical investment projects incur costs up front and provide benefits in the future The Time Value of Money Have to account for time in longer term cost benefit analysis Cannot treat money today as equivalent to money in future Can use interest rate to determine values o Interest rate price of exchanging money today for money in a year Time Value of Money The difference in value between money received today and money received in the future also the observation that two cash flows at two different points in time have different values Zara Mahmood Roberts FE101 The Interest Rate Converting Cash Across Time Depositing money into savings account convert money today into money in the future with no risk Borrowing money exchange money in future for money today o Rate exchanged determined by current interest rate Interest rate allows us to convert money from one point in time to another the rate at which money can be borrowed or lent over a given Interest Rate r period Interest Rate Factor 1 r rate of exchange between dollars today and dollars in future Equates supply of savings to the demand for borrowing Interest rate depends on supply and demand o Apply valuation principle and use it to evaluate decisions when cost and benefits are separated in time Value of 100 000 Investment in One Year Interest rate 10 1 Cost 100 000 today x 1 10 dollars in 1 year 1 dollar today 110 000 in one year Borrows 100 000 now would owe bank 110 000 in a year would only make 105 000 profit net value is negative reject investment idea Value of 100 000 Investment Today Interest rate factor to convert to dollars today Benefit 105 000 in one year 1 10 in 1 year 1 today 95 454 55 today o Amount bank would lend us if we promised to pay 105 000 in a year o Amount in bank if we wanted to make 105 000 in a year Present Versus Future Value Calculation demonstrates that our decision is the same whether we express the value of investment in terms of dollars in one year or dollars today Should reject investment o 4545 45 x 1 10 in 1 year 1 today 5000 in one year Zara Mahmood Roberts FE101 Present Value PV The value of a cost or benefit computed in terms of cash today Future Value FV The value of a cash flow that is moved forward in time Discount Factors and Rates Money in future is worth less today price reflects discount 0 91cents now 1 00 future Discount Factor The value today of a dollar received in the future Discount Rate The appropriate rate to discount a cash flow to determine its value at an earlier time Timelines Timeline Linear representation of the timing of potential cash flows First step in organizing and solving a financial problem Constructing a Timeline Identifying Dates on a Timeline Interpret each point on the timeline as specific date Date 0 is today Date 1 is end of first year and beginning of second o Cash signifies cash flow coming in at the time Distinguishing Cash Inflows from Outflows Financial decisions include cash inflows and outflows To differentiate we assign a different sign o Inflows are positive cash flows o Outflows are negative cash flows Representing Various Time Periods Timelines can represent cash flows that take place at any point in time Does not have to be by year Approach every problem with a timeline o Can miss events in a transaction VALUING CASH FLOWS AT DIFFERENT POINTS IN TIME Zara Mahmood Roberts FE101 Rule 1 Comparing and Combining Values Only possible to compare or combine values at the same point in time Eg dollar today and dollar in future are not equivalent First need to convert the cash flows into the same units time Rule 2 Compounding Using exchange rate to change unit of time Compounding Computing the return on an investment over a long horizon by multiplying the return factors associated with each intervening period Must

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