1. Time Value of Money
Multiple Cash Flows

2. Multiple Cash Flows
We have learned the future and present value of single cash flow
An investment is a claim to a stream of multiple cash flows
How to value multiple cash flows?
Rule:
Only values at the same point in time can be compared or combined

3. Future Value
If you deposit $100 in one year, $200 in two years and $300 in three years.
How much will you have in three years at 7% interest?
How much in five years if you don’t add additional amounts?

4. Future Value

5. Future Value

6. Present Value You are borrowing from bank now and will pay back
$200 in a year
$400 in 2 years
$600 at the end of the 3rd year
If the bank’s lending rate is 12%, at most how much can you borrow now?

7. Present Value

8. Present Value
Instead of receiving 600 in year 3, you can receive in year 2.

9. Buying a Car
Two years ago, you put $10,000 in a savings account earning an annual interest rate of 8%, compounded semiannually. At that time, you thought that these savings would grow enough for you to buy a new car five years later (i.e. three years from now). However, you just re-estimated the price that you will have to pay for the new car in three years at $18,000.
How much more money do you need to put in your savings account now for it to grow to this new estimate in three years?

10. Buying a Car The compounding rate is 8% 2 =4%
You put $10,000 in account 2 years ago, so the number of compounding periods is 2×2=4. Now, you have in account:
10,000× 1+4% 4 =$11,698.59
You need $18,000 in 3 years to buy a car, so the number of periods for discounting is 2×3=6. The account should have amount:
18, % 6 =$14,225.66
So you need to put the difference in the account now:
14,225.66−11,698.59=$2,527.07

11. Buying a Car
Now suppose that you know that the car company will offer you to pay for the car over some time. In particular, you will have the opportunity to make a down payment of $6,000 at the time you get the car (three years from now) and to make additional payments of $6,500 at the end of each of the following two years. With this new offer, how much money do you need to add to your account now?

12. Buying a Car
The car company’s offer asks you to pay $6,000 in the 3rd year and $6,500 in the 4th and 5th year. The present value of all three payments is
% 2× % 2× % 2×5 =$13,882.54
So you need to put the difference in the account now,
13,882.54−11,698.59=$2,183.54