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Intro to Financial Management. The Time Value of Money. Review. Homework How do you calculate and what do these ratios mean ? Current ratio Acid-test Inventory turnover ROS, Return on sales ROA, Return on assets ROE, Return on equity Debt ratio Leverage ratio P/E. Review.
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Intro to Financial Management The Time Value of Money
Review • Homework • How do you calculate and what do these ratios mean? • Current ratio • Acid-test • Inventory turnover • ROS, Return on sales • ROA, Return on assets • ROE, Return on equity • Debt ratio • Leverage ratio • P/E
Review • What is on an income statement? • What is common-sized? • What are gross profit margin, operating profit margin, net profit margin, earnings, and earnings per share? • What do these terms tell you? • What is on a balance sheet? • What is common-sized? • What are book value, working capital, debt and leverage ratios? • What do these terms tell you? • What is on a cash flow statement? • What are the three major areas of cash flow? • Why is this different from profit? • What are the basics of computing corporate taxes?
The Time Value of Money • Would you loan $1000 today and want $1000 in ten years? • Examples • Lottery • Mortgage • Banking • Foregoing money today for money in the future • “Opportunity cost” • Interest is the cost of money
Future Value (FV) • If you invest a lump sum today, what will it be worth in the future? • Compounding interest • No more new money put in • Receive interest each year; it builds up • Future value • Formula • Future value factor
Calculating FV • Calculating future value. Excel and calculator. • Must have both a positive and negative number • May also need to solve for n • E.g. How many years will it take to reach $1M? • May want to know r • E.g. What interest rate do I need to reach $1M in n years? • Examples • How long to get to $1M? • Here you have to solve for n. • On a calculator with PV/FV, enter the data and CPT n • On a calculator without PV/FV, the formula is n = log(FV/PV) / log(1+r) (you can also use ln instead of log)
Present Value (PV) • What is a single payment in the future worth today? • Future money can be expressed in today’s dollars. • Formula • Present value factor • Calculate using calculator and Excel • Example • What is $10,000 ten years from now worth today at 4% interest? • How do we deal with two different flows? • E.g. $5k in 5 years plus $10k in 10 years
Annuities • Series of equal payments • Want to know either • How much you would pay today to receive those payments in the future or • If you are investing those payments, how much will they be worth in the future
Simple Annuity • Receive the same payment every year for n years • What is that worth now? • I.e., what would you pay now to get that annuity? • PV = PMT * (1 – present value factor) / r
Compound Annuity • You invest the same amount each period for n periods • The value grows as you: • Receive interest on your balance • Invest new money each year • FV = PMT * (future value factor – 1) / r
Amortized Loans • Loans where you pay back the principal plus interest in equal payments throughout the period • E.g. a mortgage • Treat like a simple annuity and solve for PMT • PV is the amount of the loan, what you are given • n is the number of periods • For a 30-year mortgage, you have 12*30 periods because they are paid monthly • r is the interest rate • For a mortgage, take the interest rate and divide by 12 (you pay 1/12th each month) • Solve for PMT • The payments include both interest and principal • Example, how big a mortgage can you get if you can afford $1250 a month for 30 years at a rate of 4%?
Comparing Interest Rates • Interest can be calculated in many ways • Compare annual interest of 1% and monthly at 1% • Need a common benchmark • Annual percentage rate (APR) • Also known as effective annual rate (EAR) • FV and PV for non-annual periods (m periods in a year) • General case of a mortgage. • Instead of n, substitute n*m • Instead of r, substitute r/m
Perpetuity • An annuity that continues forever PV = PMT / r • What is the value of a perpetuity that pays $1000 if the interest rate is 8%?
Problem Congratulations, you just won the lottery for $25 million. The lottery will pay you $100,000 a year for 25 years What is the cash value of this lottery, assuming an interest rate of 8%? What would you do if the cash value offered by the state was less or more than the amount you calculated?