# July 14 Outline Multiple Cash Flows: Future and

July 14 Outline Multiple Cash Flows: Future and Present Values Multiple Equal Cash Flows: Annuities and Perpetuities 6-1 Finance Formulas from Yesterday 5-2 Multiple Cash Flows Future 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 1two years

from now. Year 2 Years Today \$1,000 6-3 \$500 \$700 How much will you have two years from now in your savings account (after you make your \$700 deposit)? Multiple Cash Flows Future Value 1

Simply look at each payment separately and move them through time as we did in the earlier chapter. 1 Year 2 Years Today \$1,000 6-4 \$ 500 Now just add them up because they are all adjusted to be in year 3 \$ 700 \$1,124 \$ 530

\$2,354 Multiple Cash Flows Future Value 1B Could we do this problem another way? Bring each of the cash flows forward one year at a time and add them up 1 Year 2 Years Todayyear. each \$1,000 6-5 \$ 500 \$1,060 \$1,560

\$ 700 \$1,654 \$2,354 Multiple Cash Flows Future Value 1C Lets 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? 1 2 3 4 5 Today \$1,000 500 700

6-6 Multiple Cash Flows Future Value 1C We could do this two different ways: 1. Bring the year two figure we previously produced to year five 1 2 3 4 5 Today \$1,000 500 700 \$2,354 6-7

\$2,803 Multiple Cash Flows Future 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. 1 2 3 4 5 Today \$1,000 500 700 6-8

\$1,338 \$ 631 \$ 833 \$2,803 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 1. 2. 3. 4. 5. 6-9 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 Multiple Cash Flows Present Value - 1 6-10 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? Quick Quiz I Suppose you are looking at the following 6-11 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?

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 6-12 Perpetuity infinite series of equal payments Annuities and Perpetuities Basic Formulas C C

C PV = + + . . . + = C (1 + r ) (1 + r )2 (1 + r )n n (1 + r ) t= 1 value factor for a level annuity ( P V F A r , n ). As n goes to infinity, PVFA 1/r.

6-13 ( 1 - ( 1 + r ) ) , where ( 1 - ( 1 + r ) ) -n -t = C r -n r is the present Annuity: Saving for a Car

6-14 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 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) 1

1 (1.01) 48 23,999.54 Formula: PV 632 .01 6-15

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