6- 1 July 14 Outline Multiple - PowerPoint Presentation

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July 14 Outline

Multiple

Cash Flows: Future and Present Values

Multiple Equal Cash Flows: Annuities and PerpetuitiesSlide2

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Finance Formulas from YesterdaySlide3

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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

$700Slide4

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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

$ 530

Now just

add them up

because they are all

adjusted to be in “year 3” value

$2,354Slide5

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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.

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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

700Slide7

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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

$2,354Slide8

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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

$ 833Slide9

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Multiple Uneven Cash Flows Using the TI BA II + Calculator

Another way to use the financial calculator for uneven cash flows is to use the

cash flow keys

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

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

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

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

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

Clear the cash flow worksheet by pressing CF and then 2

nd CLR WorkSlide10

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Multiple Cash FlowsPresent Value - 1

Consider receiving the following cash flows:

Year 1 CF = $200

Year 2 CF = $400

Year 3 CF = $600

Year 4 CF = $800

If the discount rate is 12%, what would this cash flow be worth today?Slide11

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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?Slide12

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Annuities and Perpetuities Definitions

Annuity – finite series of equal payments that occur at regular intervals

If the first payment occurs at the end of the period, it is called an

ordinary annuity

If the first payment occurs at the beginning of the period, it is called an

annuity due

Perpetuity – infinite series of equal paymentsSlide13

Annuities and Perpetuities Basic Formulas

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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?Slide15

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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: