1. Time Value of Money and Quantity of Money

2. Time Value of Money
When financing something the decisions are based on TIME and RISK (interest rates)
Businesses make decisions based on the time value of money
The future value versus the present value
Investors and businesses must decide if the present value of a project is worth the future returns they will receive

3. How interest rates effect time values of money
If interest rates are 0%, then a dollar borrowed today has a value of $1 today and $1 at the end of the year.
There was no cost to borrow and no profit to loan (inflation not included)
At an interest rate of 10% in one year’s time
The present value of the dollar would be approximately $.91
Because it would take $.91 to generate $1 in a year
The future value of the dollar would be $1.10
Because 10% of the value is added on when you are paid back (lender)

4. Why this is important
Anyone taking and giving loans has to make a decision as to whether or not it is worth borrowing/lending
If I borrow money for $100m in equipment that will depreciate to a value of $50m in 10 years, based on the interest rate and estimated levels of profit…will this be worth it?
If businesses evaluate these things based on profit, what thing would influence why banks would want to loan other than the interest rate?
Think price level

5. The Formulas PV is the Present Value FV is the Future Value
R or I is the interest rate
n is the number of years

6. Present Value
Present value is the amount of money today that would be needed to produce a given amount of money in the future.
How much would I need today at X% to get Y amount?
Based on interest rates
So how much money would need to be needed to produce $110 dollars in one year based on 10% interest rate?
Present value of $110 in one year would be $100
PV = 110 / 1.1

7. Future Value
The amount of money that would be produced in the future by a present dollar amount based in interest rates.
How much would X amount yield in the future given Y%
So how much money would $100 produce in 1 year at 10%
FV = 100 x 1.1
So the future value of $100 is $110, based on 10% interest rate

8. Present vs Future
Present values are lower than future values (ceteris paribus)
What is the present value of $110 at 10% over 1 year?
Where do I start to get to a certain point?
If in one year you will have $110, what amount did your start with?
$100
What is the future value of $110 at 10% over 1 year?
What point will I be at in the future if I start at X amount?
If you started with $110 what amount would you have in the future?
$121

9. So what is important with this PV and FV
So what is important with this PV and FV? What do I really need to take away from this garbage?
Know what the difference is between Future/Present Values
Present: How much I need now to reach a given output
You need X amount for a car in 5 years, how much to save
Future: How much my money now will yield in a given time
You have X amount to invest and want to know how much it will yield
Know the formulas (PV and FV)
Know how/why these are used
Business decisions
How interest rates effect investment and values
Incentives to borrow and loan

10. Practice some PV/FV
What is the future value of $1,000 invested at a 12% interest rate for 10 years?
If your friend loans you $10 and ask for you to pay them back at 10% in three years, how much might you owe them?
If you are 10 years from retirement and want to have $300,000 in your savings, with a current interest rate of 11%, how much money do you need to save right now?
You parents agree to give you an amount now to pay for your first house in 15 years. If you know that you want a $250,000 home and the current interest rates are 15%, how much do your parents need to pony up now?
If you want to save to buy a new car after college at $45,000, with interest rates at 8%, how much would you need to save to reach this goal in 5 years?