**Unformatted text preview: **even Cash Flows –
Multiple
Using the Calculator
Using Another way to use the financial calculator for uneven cash flows is
Another
to use the cash flow keys
to 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
The
consecutive periods
consecutive Use the NPV key to compute the present value by entering the
Use
interest rate for I, pressing the down arrow and then compute
interest Clear the cash flow keys by pressing CF and then CLR Work 12 Decisions, Decisions Your broker calls you and tells you that he has this great investment
Your
opportunity. If you invest $100 today, you will receive $40 in one
year and $75 in two years. If you require a 15% return on
investments of this risk, should you take the investment?
investments Use the CF keys to compute the value of the investment
• CF; CF0 = 0; C01 = 40; F01 = 1; C02 = 75; F02 = 1
• NPV; I = 15; CPT NPV = 91.49 No – the broker is charging more than you would be willing
No
to pay.
to 13 Saving For Retirement You are offered the opportunity to put some
You
money away for retirement. You will receive
five annual payments of $25,000 each
beginning in 40 years. How much would you be
willing to invest today if you desire an interest
rate of 12%?
rate Use cash flow keys:
• CF; CF0 = 0; C01 = 0; F01 = 39; C02 = 25,000; F02 = 5;
NPV; I = 12; CPT NPV = 1,084.71
NPV; 14 Saving For Retirement Timeline
012 … 39 40 41 42 000 … 0 25K 25K 25K 43 44 25K 25K Notice that the year 0 cash flow = 0 (CF0 = 0)
The cash flows years 1 – 39 are 0 (C01 = 0; F01 = 39)
The cash flows years 40 – 44 are 25,000 (C02 = 25,000;
F02 = 5)
15 Quick Quiz – Part I Suppose you are looking at the following possible cash
Suppose
flows: Year 1 CF = $100; Years 2 and 3 CFs = $200;
Years 4 and 5 CFs = $300. The required discount rate is
7%
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? 16 Annuities and Perpetuities
Annuities
Defined
Defined Annuity – finite series of equal payments that
Annuity
occur at regular intervals
occur If the first payment occurs at the end of the period, it
If
is called an ordinary annuity
is
If the first payment occurs at the beginning of the
If
period, it is called an annuity due
period, Perpetuity – infinite series of equal payments 17 Annuities and Perpetuities –
Annuities
Basic Formulas
Basic Perpetuity: PV = C / r Annuities:
1 1− (1 + ) t r
PV = C r 1 + )t − (
r
1
FV = C r 18 Annuities and the Calculator You can use the PMT key on the calculator for
You
the equal payment
the
The sign convention still holds
Ordinary annuity versus annuity due You can switch your calculator between the two
You
types by using the 2nd BGN 2nd Set on the TI BA-II
types
Plus
If you see “BGN” or “Begin” in the display of your
If
calculator, you have it set for...

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