HOW TO CALCULATE PRESENT VALUES

Transcription

1 HOW TO CALCULATE PRESENT VALUES Chapter 2 Brealey, Myers, and Allen Principles of Corporate Finance 11 th Global Edition Basics of this chapter Cash Flows (and Free Cash Flows) Definition and why is it relevant? Accounting vs. real economic values The Time value of Money Why does money has a time value Discount rates (discount factor) Simple annual interest rates, effective rate Present values and Future Values Discrete time and continuous time (we do both) Techniques and short cuts (formulas) McGraw-Hill Education Copyright 2015 by Bo Sjö and The McGraw-Hill Companies, Inc. All rights reserved. Fundamental Definition cash flow = money (cash) in money (cash) out during a period. We talk about real economic cash flows, not the accounting definition. Cash money = wealth (opportunities in life) => consumption => utlity => value Free cash flow: the cash flow in each period which can be used to pay dividends on equity or interest on debt. Important concept Fundamental The goal of the firm Max value of the firm by maximizing the present value of all future free cash flows adjusted for the time value of money including risk. Each decision to pay out or recieve money, including investment decisions, should be filtered through a Net Present Value (NPV) analysis. Value Based Management (VBM): let this principle be transparent and open through the whole firm and to all stakeholders. It means satisfy all stakeholders without favouring one over the other, taking all facts into account. The Time Value of Money Consumption today does not have the same value as consumption tomorrow. You can choose, and maximise utility from consumption over your whole life if you want. People decide on how much to consume today and in the future (saving=investment). Thereby they create an interest rate, the alternative cost of consuming today compared with tomorrow. To be more exact the interest rate reflect the value people put on decreasing their marginal utility today in order to increase their marginal utility tomorrow. TOPICS COVERED Future Values and Present Values Start with one period, and one certain cash flow Next more than one period Followed by many periods and risky cash flows String of cash flows, often infinite cash flows Therefore, look for shortcuts: No growth: Perpetuities and Annuities Growth: Growing Perpetuities and Growing Annuities 2-6 1

2 VALUATION Economic values vs. Accouting values Economic decisions are taken on economic values not book values 1. Value of debt/bonds/money market instruments/fixed income instruments 2. Value of stocks/equity/shares (Intrinsic value) 3. The value of a firm 4. Value of investment projects 5. The value of everything? 2-7 PRICE IS WHAT YOU PAY. VALUE IS WHAT YOU GET. Cecil Graham: What is a cynic? Lord Darlington: A man who knows the price of everything, and the value of nothing. Cecil Graham: And a sentimentalist, my dear Darlington, is a man who sees an absurd value in everything and doesn t know the market price of any single thing. Oscar Wilde 2-8 VALUATION IS THE KEY TO EVERYTHING The key to prosperity and eliminate poverty Also environmental matters, and Climate change, what to do, when to do it and how much. Finance is a gun. Politics is to know when to pull the trigger Ronald Reagan Work out the cash flows and find the correct discount rate => optimal decision PV AND FV? So how to do it? We start with the mechanics. For this course: Memorize some formulas, do not use financial calculators, tables or Excel VALUATION Always 1) Identify the cash flows, 2) Simplify? Type of flows? 3) Identify the discount rate 4) Use the correct formula to calculate Later we will learn to calculate the correct discount rate in each situation Now, let us travel through time FUTURE VALUES AND PRESENT VALUES Calculating Future Values Future Value Amount to which investment will grow after earning interest Present Value Value today of future cash flow

3 Present and Future Value FUTURE VALUES (COMPOUNDING) Present Value Value today of a future cash flow. Future Value Amount to which an investment will grow after earning interest Future Value (FV) of $100 is = FV, you have $100 today and invest (save), at the end of next period (t=1) you have 2-14 FUTURE VALUES Future Values with Compounding FV (t=2) What is the future value of $100 if interest is compounded annually at a rate of 7% for two years? Interest Rates 2-15 CONVENTION Present Value (Discounting) of a future cash flow C at time 1. Interest rates and yields, are always qouted on an annual basis, to make them comparable. The three-month interest rate is quoted as 6%, meaning that you pay (or recieve) 0.06/4 = 0.015, or 1.5% per quarter. There are no exceptions from this rule

4 Present Value Discount Factor = DF = PV of $1 PRESENT VALUE TWO PERIODS Given any variables in the equation, you can solve for the remaining variable. Also, you can reverse the prior example. PV of one Cash flow coming two periods from now: Discount Factors can be used to compute the present value of any cash flow, if you know the correct r of course Present Values with Compounding Interest Rates VALUING AN OFFICE BUILDING Step 1: Forecast cash flows Cost of building = C 0 = 370,000 Sale price in Year 1 = C 1 = 420,000 Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 5%, then Cost of capital = r = 5% 2-22 VALUING AN OFFICE BUILDING Do you get the money back, in terms of real economic values, compared with alternative? Step 3: Discount future cash flows Step 4: Go ahead if PV of payoff exceeds investment

5 RISK AND PRESENT VALUE RISK AND PRESENT VALUE Higher risk projects require a higher rate of return Higher required rates of return cause lower PVs It is worth less today compared with less risky investments, we will come back to this Risk and Net Present Value NET PRESENT VALUE RULE Accept investments that have positive net present value Use the original example. Should we accept the project given a 10% expected return? 2-28 RATE OF RETURN RULE Accept investments that offer rates of return in excess of their opportunity cost of capital! MULTIPLE CASH FLOWS For multiple periods we have the Discounted Cash Flow (DCF) formula In the project listed below, the foregone investment opportunity is 12%. Should we do the project?

6 NET PRESENT VALUES SHORT CUTS - $370,000 $20,000 $ 420,000 Present Value Year Year 0 -$370,000 20,000/1.12 = $17, ,000/ = $334,800 Total = - $17,300 Sometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods. These tools allow us to cut through the calculations quickly SHORT CUTS Perpetuity - Financial concept in which a cash flow is theoretically received forever. PERPETUITY The firm is typically seen a Going concern meaning that we assume that it will run forever. Therefore the firm s, assets debt, etc are all perpetuities. Mathematically it is easier to work with infinite cash flows than finite flows SHORT CUTS Perpetuity - Financial concept in which a cash flow is theoretically received forever. Simple rule. PRESENT VALUES What is the present value of $1 billion every year, for all eternity, if you estimate the perpetual discount rate to be 10%??

7 PRESENT VALUES - continued What if the investment does not start making money for 3 years? Two-step PV. Net cash flows are zero for year 1 and 2. Short Cuts - Annuity Annuity - An asset that pays a fixed sum each year for a specified number of years. (Bonds, loans, debt) Asset Perpetuity (first payment in year 1) Year of Payment 1 2..t t + 1 Present Value Perpetuity (first payment in year t + 1) Annuity from year 1 to year t 2-37 PRESENT VALUES Tiburon Autos offers you easy payments of $5,000 per year, at the end of each year for 5 years. If interest rates are 7%, per year, what is the cost of the car? Present Value at year 0 5,000 5,000 5,000 5,000 5, Year SHORT CUTS Annuity - An asset that pays a fixed sum (C) each year for a specified number of years. (Please memorize this formula) And, growing annuities Annuity Short Cut Annuity Short Cut You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? - continued You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? 7

8 ANNUITY SHORT CUT The state lottery advertises a jackpot prize of $295.7 million, paid in 25 installments over 25 years of $ million per year, at the end of each year. If interest rates are 5.9% what is the true value of the lottery prize? FV ANNUITY SHORT CUT Future Value of an Annuity The future value of an asset that pays a fixed sum each year for a specified number of years ANNUITY SHORT CUT CONSTANT GROWTH PERPETUITY What is the future value of $20,000 paid at the end of each of the following 5 years, assuming your investment returns 8% per year? g = the annual growth rate of the cash flow CONSTANT GROWTH PERPETUITY CONSTANT GROWTH PERPETUITY NOTE: This formula can be used to value a perpetuity at any point in time. What is the present value of $1 billion paid at the end of every year in perpetuity, assuming a rate of return of 10% and a constant growth rate of 4%?

9 Perpetuities A three-year stream of cash flows that grows at the rate g is equal to the difference between two growing perpetuities. INTEREST QUOTATIONS All interest rates are always stated on an annual basis. There is no expection from this rule. Easier to compare rates!, if we agree to pay 2% actual interest on loan for three months, the interest is stated as 0.02x4= 0.08 or 8%. The one month treasury bill rate is stated as 1.25% (per annum), the rate per month is /12 = or % EFFECTIVE INTEREST RATES Effective Annual Interest Rate - Interest rate that is annualized using compound interest. EFFECTIVE INTEREST RATES example Given a monthly rate of 1%, what is the Effective Annual Rate (EAR)? What is the Annual Percentage Rate (APR)? Annual Percentage Rate - Interest rate that is annualized using simple interest EFFECTIVE INTEREST RATES example Given a monthly rate of 1%, what is the Effective Annual Rate (EAR)? What is the Annual Percentage Rate (APR)? 2-4 HOW INTEREST IS PAID AND OUTLAID Given a monthly rate of 1%, what is the (EAR)? What is the (APR)?

10 TYPICAL EXAMPLE Interest rates are stated as simple annual rates (APR) on credit cards for your monthly debt on the card. Amazon.co.uk offers a Mastercard with APR 16.9%. How much do you pay per month, if you use the credit? How much do you pay in interest if you use the credit for a whole year? (EAR)