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 - Simple Annuity PV = PMT * (1 – present value factor) / r

- Invest $PMT each periodBalance earns r each period

?? Compound Annuity

FV = PMT * (future value factor – 1) / r

?? Receive $PMT forever - Perpetuity PV = PMT / 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?