6-1

July 14 Outline

• Multiple Cash Flows: Future and Present Values• Multiple Equal Cash Flows:

Annuities and Perpetuities

5-2

Finance Formulas from Yesterday

6-3

Multiple Cash FlowsFuture Value 1

Suppose you have $1,000 now in a savings account that is earning 6%. You want to add $500 one year from now and $700 two years from now.

How much will you have two years from now in your savings account (after you make your $700 deposit)?

Today 1 Year 2 Years

$1,000 $500 $700

6-4

Multiple Cash FlowsFuture Value 1

Simply look at each payment separately and move them through time as we did in the earlier chapter. Today 1 Year 2 Years

$1,000 $ 500 $ 700$1,124$ 530Now just add them up

because they are all adjusted to be in “year 3” value

$2,354

6-5

Multiple Cash FlowsFuture Value 1B

Today 1 Year 2 Years

$1,000 $ 500 $ 700

$1,060$1,654

$2,354$1,560

Could we do this problem another way? Bring each of the cash flows forward one year at a time and add them up each year.

6-6

Multiple Cash FlowsFuture Value 1C

Let’s add one more twist to the problem: What would be the value at year 5 if we made no further deposits into our savings account?Today 1 2 3 4 5

$1,000 500 700

6-7

Multiple Cash FlowsFuture Value 1C

We could do this two different ways:1. Bring the “year two” figure we previously produced to year five Today 1 2 3 4 5

$2,803$1,000 500 700

$2,354

6-8

Multiple Cash FlowsFuture Value 1C

We could do this two different ways:2. Bring each of the three original

dollars to year 5 and add them all up. Today 1 2 3 4 5

$2,803

$1,000 500 700 $1,338$ 631$ 833

6-9

Multiple Uneven Cash Flows Using the TI BA

II + CalculatorAnother way to use the financial calculator for uneven cash flows is to use the cash flow keys

1. Press CF and enter the cash flows beginning with year 0.

2. You have to press the “Enter” key for each cash flow

3. Use the down arrow key to move to the next cash flow

4. The “F” is the number of times a given cash flow occurs in consecutive periods

5. Use the NPV key to compute the present value by entering the interest rate for I, press “Enter”, then the down arrow, and then “CPT” computing the answer

6. Clear the cash flow worksheet by pressing CF and then 2nd CLR Work

6-10

Multiple Cash FlowsPresent Value - 1

Consider receiving the following cash flows:

Year 1 CF = $200Year 2 CF = $400Year 3 CF = $600Year 4 CF = $800

If the discount rate is 12%, what would this cash flow be worth today?

6-11

Quick Quiz I

Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%.

What is the value of the cash flows at year 5?

What is the value of the cash flows today?

What is the value of the cash flows at year 3?

6-12

Annuities and Perpetuities Definitions

Annuity – finite series of equal payments that occur at regular intervalsIf the first payment occurs at the end of the period, it is called an ordinary annuityIf the first payment occurs at the beginning of the period, it is called an annuity due

Perpetuity – infinite series of equal payments

Annuities and Perpetuities Basic

Formulas

6-13

6-14

Annuity: Saving for a Car

After carefully going over your budget, you have determined you can afford to pay $632 per month towards a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much can you borrow?

6-15

Annuity: Saving for a Car

You borrow money TODAY so you need to compute the present value.

48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 ($24,000)

Formula: 54.999,2301.)01.1(1

1632

48

PV