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%?
Summary
Today
n periods
Future
Type
Formula
??
Discount value by r each period
$FV
Simple PV
PV = Fvfactor * FV
$PV
Receive return r each period
??
Simple FV
FV = PVfactor * PV
??
Receive $PMT each period
-
-
Invest $PMT each period
Balance earns r each period
??
Compound
Annuity
FV = PMT * (future
value factor – 1) / r
??
Receive $PMT forever
-
Perpetuity
PV = PMT / r
Simple Annuity PV = PMT * (1 –
present value
factor) / r
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?