Unit 6: Economic Value. Detailed Cash Flow Analysis

2. Growing Perpetuity

In a growing perpetuity the amounts grow at a constant rate. A pattern of growth: a growth rate in the cash flows. Each cash flow is the same percent larger than the previous cash flow.

Level Perpetuity

(Per period cash flow ÷ Interest Rate) = (C ÷ r) EX: Preferred Stock... Pay 2$ in preferred dividends. The discount rate is 4%. 2/.4 = $50

***Lesson 1 Questions***

**Work through them!

Impact of Changing Variables on Present Values: Taking a future value and determining its present value (Discounting)

1. Delay in Investment: just changing the N value. Higher present value because the future value is discounted for fewer periods. 2. Change in Interest Rates: As interest rates rise, the present value decreases greatly. Interest rates impact present and future values in opposite ways.

Two Ways of Applying Interest Rates to cash flows:

1. Simple Interest 2. Compound Interest

4 Variables of Interest (Buying a House Example)

1. The present amount that she will deposit. 2. The future amount that she expects to get. 3. The Interest rate, which gives the rate of change in the value of her deposit. 4. The maturity, or time period, which determines the number of periods that interest rates are applied. #3 and 4 determine the relationship between present and future variables.

Declining interest rates

A decline in interest rate will also decline future values

Perpetuity

A perpetuity is a series of regular payments for regular periods that go on indefinitely. As the name implies, a perpetuity is a regular stream of cash flow that is indefinite--it theoretically goes on forever. Two Types: 1. Level Perpetuity 2. Growing

Annuity

A series of regular payments at regular intervals for a defined period of time. EX; Rent, salary, car payments, etc. 1. Level 2. Growing

Annuity Due Formula

As the payments are at the beginning of the month, each cash flow is closer to day, thus it has a higher present value. PV of Annuity Due > PV of Ordinary Annuity (On Calc: be sure to change the PMT button to 'beginning')

1. Level Perpetuity

In a level perpetuity the regular payments are the same amount. No change in the cash flows; each is the same.

Effective Annual Interest Rate

Because the compounding period is less than one year, there are three interest rates that we have to keep track of: 1. The Stated Annual Interest Rate is the interest rate stated on an annual basis. This is the rate normally used in contracts, including loans such as credit cards, auto loans and mortgages. 2. The Periodic Interest Rate is the interest per period, such as the interest applied each month to the principal or the the semiannual rate for bond interest payments and the quarterly rate paid via dividends. 3. The Effective Annual Interest Rate (EAR) is the annual interest rate that reflects the impact compounding over the entire annual period.

Payment Plan Example

Covert each future payment in the payment plan into it's present value: then add them all up. If deciding against a payment plan or a 1 time payment, which present value is better? This depends on perspective? Are you paying the money or receiving it? These differences in perspectives makes sense when we know that a dollar received today is more valuable than a dollar received in the future. .

Economic Choices in Present and Future Value Calculations (Accounts Payable Decision)

Economic choices are not affected by the time value method chosen: Whether you use the PV or FV calculation, you should get the same advice (Not the same numbers necessarily, but the same conclusion)

What happens to a future value if you increase the rate, r? What happens to a present value?

Future values are positively related to interest rates, as the higher the interest rate, the higher the amount of interest earned in each period. Present values are inversely related to interest rates, as calculating present values involves dividing (1 + r)T. These questions show the mirror image of calculating future values and present values. While this seems like a simple, even boring statement, it's surprising how many students end up mismanaging these calculations.

Remember:

Future values increase with longer time periods and higher interest rates. Present values decrease with longer time periods and higher interest rates.

As you increase the length of time involved, what happens to future values? What happens to present values?

Future values: Future values are positively related to the length of time of the investment, as each additional period additional interest is earned. This can be seen in the Future Value Factor = (1 + r)T, which is multiplied by the present value to get the future value. Present values: Present values are inversely related to the length of time of the investment. The Present Value Factor = 1/[(1 + r)T)] is the inverse of the Future Value Factor. This shows that discounting is the inverse of compounding.

Level Annuity

Has the same cash flow for each period of time. Level annuities are further classified as to when the payments are made in each period. 1. Ordinary Annuity: occur at the end of each period, such as the salary a worker gets paid at the end of each month. 2. Annuity Due: occur at the beginning of each period. Your landlord expects the rent at the beginning of each month.

Increasing the Deposit and Time Periods

Increasing the Deposit (initial investment) does increase the future value. Increasing the Time Period allows the future value to grow as a faster rate: Exponentially.

Simple Interest

Interest earned on the original principal. Each period the interest rate is applied, but the principal remains the same. To Solve: EX: First City Bank pays 6 percent simple interest on its savings account balances The simple interest per year is: $8,100 × .06 = $486 So, after 10 years, you will have: $486 × 10 = $4,860 in interest. The total balance will be $8,100 + 4,860 = $12,960

Annual Percentage Rate (APR)

Interest rate charged per period multiplied by the number of periods. Federal regulations require this rate to be disclosed to consumers but, as it does not recognize time-value compounding, it is not as useful as the EAR

***Lesson 2: Multiple Cash Flows***

Rather than taking the present value of one cash flow, you just take the present values for all of the cash flows and then sum them up.

Compound Interest

Occurs when the Interest earned is applied to the principal each period. With compound interest, the principal grows over time and, if the principal grows so does the amount of interest paid each period. Time value calculations in Finance rely on Compound Interest: the base amount for your calculations (the principal) changes with each period as interest is added to principal to make a larger amount for computing interest. The FV and PV formula use Compound Interest.

Ordinary Annuity

On a calc: Enter the payment amount in the PMT button. The n will be the number of payment received. (For ordinary annuity leave the "end" buttom selected)

Growing Annuity

Payments that grow at a steady rate. The cash flows are not the same, but they grow at a constant rate. An example would be a lease payment that is adjusted for a given rate of inflation. Has a finite life.

Preferred Stock vs Common Stock

Preferred - Usually pays a set dividend. Common - riskier than preferred stock, has a higher discount rate. Cash flows of the common stock are more uncertain, and thus investors require a higher rate of return.

A Cautionary Note

This is the present value of a Perpetuity: PV = C/r This is the present value of a single period cash flow (Unit 5) PV= FV/ (1+r)

Compounding Period

The length of time that passes before interest is recognized and added to the principle. We normally state contracts in terms of annual rates and periods; however, many payments are made in periods of less than a year.

n value

The number of periods (typically years or months)

Effective Annual Interest Rate

The rate of interest that reflects the effect of compounding more than once a year. (reflects the effect of intra-year compounding using the periodic rate over an annual period) For the effective annual interest rate, you apply the periodic interest rate for the number of compounding periods within a year. So, what you have are two annual rates, one for the nominal rate stated on an annual basis, the other reflecting the effects of compounding. These two annual rates are connected through the periodic rate. You just apply the quarterly interest rate for the number of compounding periods within a year.

Lesson 1 Summary

Two major techniques you can use to restate cash flows. 1.Compounding allows a decision maker to restate a cash flow to the future. 2. Discounting allows a decision maker to restate a cash flow to the present. Time periods: 1. The longer the time period, the larger the future value because the longer you save the more periods you'll earn compound interest. 2. The shorter the time period the smaller the future value, as you will accumulate fewer compounded interest payments. Interest rates: 1. The higher the interest rate, the larger the future value because the rate you earn in each period will compound into larger future wealth. 2. The lower the interest rate, the smaller the annual (compounded) future value. Present values are influenced in exactly the opposite way by changes in time periods and interest rates as future values.

Period and Interest Rates

With compounding periods of less than one year, the period and interest rate must be consistent. # of periods: m periodic interest rate for m periods: r/m

***Lesson 2 Questions***

Work through them! For problem 3: when finding the future value of years 1,2,3,4 to be summed at year 4..... the n value of year 1 will be 3. The n value of year 2 will be 2, the n value of year 3 will be one, and year 4 will be treated as a present value.

Periodic Rate

r/m With monthly compounding of an annual interest rate of 18%, the periodic interest rate is 1.5% 18%/12 = 1.5

The more frequent the compounding period.....

the larger the future value.