1. Intro to Financial Management
The Time Value of Money

2. 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

3. Review What is on an income statement? What is on a balance sheet?
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 are book value, working capital, debt and leverage ratios?
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?

4. 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

5. 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

6. 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)

7. 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

8. 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

9. 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

10. 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

11. 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%?

12. 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

13. 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%?

14. Summary Today Periods Payments Future Type Formula ?? n -- $FV
Simple PV
=PV()
$PV
Simple FV
=FV()
Receive $PMT
Simple Annuity -
Invest $PMT
Compound Annuity
$PMT
= NPER()
=RATE()
forever
Perpetuity
PV = PMT / r

15. 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?