Cpcu 540 Ch.6

The time value of money concept indicates that the value of an amount received today is greater than receiving that same amount in the future.

When calculating future value some type of interest rate has to be calculated b/c the money received today could be invested and grow beyond what it may be worth in the future.

Simple interest: applies interest rate each period to the same amount of principle.

Compound interest: applies interest rate each period to the original amount of principle as well as interest earned.

N: number of periods

I/YR: interest rate per year

PV: present value

FV: future value

[SHIFT] key used to access secondary functions on calculator.

E.g. if given $1000 today, what will it be worth in the future at 6% interest rate in 5 yrs?

When calculating the following variables are given: N, I/YR, and PV

Must solve for FV

Formula: FV = PV * (1+i)^n (don't need formula if you know calc. key strokes)

Table: PV * FV factor

[SHIFT], C ALL (clears the calc.)

$x, +/-, PV (enters -$x as the present value)

**enter PV as a negative number

x, I/PY (enters x% as interest rate)

x, N (enters x as number of years)

FV (displays the solution to the question)

If interest is calculated quarterly, that means every 3mo. interest will be added, calc. needs to be changed to quarterly interest. This is done following these keystrokes:

4, [SHIFT], P/YR

For N you will need to multiply the # of years by 4 for quarterly payments per year. B/c N is for number of periods the payment will be made.

Gives the real rate of return on investment. E.g. at 5% interest, if interest rate is compounded annually, then the interest for that year will be 5%. If that same interest rate is compounded quarterly then that interest rate will be a little higher.

E.g. if given $1000 @ 10% interest rate that compounds monthly, $1000 will grow to $1104.70 by the end of the year, rendering an EFF% of 10.47%

Higher frequency creates higher effective rate. Nominal and effective interest rates will be identical when compounding occurs annually. Increase in effective annual rate becomes smaller as compounding frequency increases.

Effect on future values, the higher the compounding frequency: The higher the FV of a single sum or annuity. The lower the size of a required payment needed to meet a targeted future amount. The lower the number of years to reach FV.

[SHIFT], DISP, 4 (displays 4 decimal places)

6, [SHIFT], NOM % (enters 6% as the nominal interest rate)

x, [SHIFT], P/YR (sets the calc. to x payments per year)

[SHIFT], EFF % (determines the effective interest rate)

When calculating the following variables are given: N, I/YR, and FV.

Must solve for PV.

Formula: PV = FV / (1 + i)^n

Table: FV * PV factor

$x, FV (enters $x as the FV)

x, I/YR (enters x% as interest rate)

x, N (enters x as number of periods)

PV (displays solution)

*Present value will be negative

When calculating the following variables are given: N, PV, and FV.

Must solve for I/YR

$x, +/-, PV (enters $x as present value)

$y, FV (enters y as future value)

x, N (enters x as number of years)

I/YR (displays solution)

Represent constant cash flow account either saved or received. Multiple payments involved that accrue interest, as opposed to just one payment, like with single sum.

Ordinary annuity means payments received at the end of each period. Annuity due means payments are received at the beginning of each period

PMT - periodic payment (assumes constant payment amount, actual annuity stream. E.g. a deposit).

[SHIFT] BEG/END - beginning or ending payment (END for ordinary annuity, BEG for annuity due)

The PV, FV, I/YR and N keystrokes will also be used

[SHIFT] BEG/END (depends on what kind of annuity)

$x, +/-, PMT, (enters -$x as the annual payment amount)

x, I/YR (enters x as interest rate)

x, N (enters x as number of years)

PV (displays solution)

When calculating the following variables are given: I/YR, N, PV and FV. Must solve for PMT (annual payment)

Actual dollar amount of the annuity itself.

Payment received at the beginning of each period. Amounts payable under life insurance policy settlement option or lease agreement.

Must set calc. to BEGIN mode.

To convert PV of an ordinary annuity to annuity due multiply PV of ordinary annuity by (1 + i) i = interest rate

To convert the PV of an annuity due to an ordinary annuity divide PV of annuity due by (1 + i)

A stream of payments that continues indefinitely (perpetually). Includes dividends on preferred stock and income from real estate.

The PV of perpetuity can be determined by dividing the income stream by a capitalization rate (interest rate.) *Just take annual income and divide it by the given interest rate.

If value per share of stock is being determined, inflation rate won't count against the discount rate.

PV = payment / capitalization rate (interest rate)

E.g. you invest in a project and it gives $200 of income the first year then $230 the next year.

The PV of unequal cash flows can be determined by adding the PVs of the individual cash flows. Financial calcs. use "CFj" button to enter multiple unequal cash flows.

Different keystrokes are required if the cash flow pattern is unequal.

"CFj" - enters periodic cash flow payments. Assumes payments are made at beginning of year. Irrelevant whether calc. set to BEGIN or END mode.

NVP - determines PV of cash flows. [SHIFT] NPV

If payments are rec'd at the end of each year, enter 0 for the 1st year's payment.

The PV of a series of unequal cash flows. Positive NPV indicates the investment's rate of return exceeds the discount rate. If negative it was a bad investment.

Will be provided with the following variables: N, I/YR, cash flow stream (most difficult variable to enter on calc.)

Must solve for NPV

0, CFj (enters $0 for cash flow at time zero)

$x, CFj (enters $x for the end of year 1)

$x, CFj (enters $x for the end of year 2)

$x, CFj (enters $x for the end of year 3)

x, I/YR (enters x% as interest rate)

[SHIFT], NPV (displays solution)