exam 1

What is an annuity?

A series of payments of a fixed amount for a specified number of equal periods. OR A series of equal payments at fixed intervals for a specified number of periods. · Annuity payments, which are given the symbol PMT or Pmt, can occur at the beginning or end of each period.

What is a perpetuity?

An annuity that lasts forever (has no maturity date) OR An annuity that goes on indefinitely, or perpetually, hence the name.

Why does an investment have an opportunity cost rate even when the funds employed have no explicit cost?

Because it is affected by time and interest rates/inflation rates over the time period of the investment.

What are a few real-world situations that may require you to solve for interest rate or time?

Car loans, car payments, mortgages.

When constructing an amortization schedule, how is the periodic payment amount calculated?

Consists partly of interest and partly of repayment of principle

Differentiate between dollar return and rate of return.

Dollar Return- To measure the dollar return on the investment, the cost of the (subject) must be compared to the present value of the expected benefits (the cash inflows).. · Note that this measure of dollar return incorporates time value, and hence opportunity costs, through the discounting process. · Excess return= net present value · If the expected present value is more than would result if it has a smaller percent return, that is opportunity cost rate. Rate of Return (percentage return)- This measure the interest rate that must be earned in the investment outlay to generate the expected cash inflows. · In other words, this measure provides the expected periodic rate of return on the investment. · If the cash flows are annual, the rate of return is an annual rate. · When solving for i- the interest rate that equates the sum of the present values of the cash inflows to the dollar amount of the cash outlay. · NOTE, that the rate of return on an investment, particularly an investment in plant or equipment, typically is called the internal rate of return (IRR)

How does the effective annual rate differ from the stated rate?

Effective Annual Rate (EAR)- used to compare rates of return on investments that have different compounding periods. · the interest rate that, under annual compounding, produces the same future value as was produced by more frequent compounding. · The rate that produces the same ending (future) value under annual compounding. · Can be found, given the stated rate and number of compounding periods per year. State Rate (Nominal Rate)- the rate that is stated in the contract with the bank. OR Annual rate normally quoted in financial contracts.

1. How is it (discounting) related to compounding?

Finding present values is called discounting, and it is simply the opposite of compounding. · If the PV is known, compound to find the FV; if the FV is known, discount to find the PV. · The equations show us that compounding problems are solved by multiplication, while discounting problems are solved by division.

What changes must be made in the calculations to determine the future value of an amount being compounded at 8 percent semiannually versus one being compounded annually at 8 percent?

For a future value being compounded semiannually instead of annually you need to take N, the periods, and multiply by 2 and take the I, interest rate, and divide by 2.

1. Why is sign convention important in time value analyses?

In complicated analyses, it is essential to use the proper signs to designate whether a cash flow is an inflow or an outflow.

What does the term ROI mean?

In most investments, an individual or a business pends cash today with the expectation of receiving cash in the future. The financial attractiveness of such investments is measured by the return on investment (ROI), or just return. · There are two basic ways of expressing ROI: in dollar terms and in percentage terms.

How does the present value of a lump sum to be received in the future change as the time is extended and as the interest rate increases?

It decreases in value because of TVM + as interest rates increases, the value of the lump sum decreases.

What is meant by net present value?

Net present values means the sum or net of the present values of a cash flow stream. Often the stream will consist of both inflows and outflows. OR A project return-on-investment (ROI) metric that measures the time value adjusted expected dollar amount. · The NPV function calculates the present value of a stream, called a spreadsheet range, of cash flows The NPV function assume that cash flows occur at the end of each period, so NPV is calculated as of the beginning of the period of the first cash flow specified in the range, which is one period before that cash flow occurs

Do the principal and interest components remain constant over time? Explain your answer.

No, the interest component is the largest in the first year, and it declines as the outstanding balance if the loan is reduced over cost.

Does the opportunity cost rate depend on the source of the investment funds?

No, the opportunity cost rate does not depend on the source of the funds to be invested. Rather, the primary determinant of this rate is the riskiness of the cash flows being discounted.

Give two examples of financial decisions that typically involve uneven cash flows.

One example would be the financial evaluation of a proposed outpatient clinic or MRI facility rarely involves constant cash flows.

How are opportunity cost rates established?

Opportunity cost rates are obtained by looking at rates that could be earned—or more precisely, rates that are expected to be earned—on securities such as stocks or bonds.

What is the difference between an ordinary annuity and an annuity due?

Ordinary (regular) Annuity- Payments that occur at the end of each period, as they typically do. · Because ordinary annuities are far more common in time value problems, when the term annuity is used in the book or in general, payments are assumed to occur at the end of each period. Annuity due- Payments are made at the beginning of each period.

How does the periodic rate differ from the stated rate?

Periodic interest rate- in time value of money analysis, the interest rate per period. For example, 2 percent quarterly interest, which equals an 8 percent stated (annual) rate. · The periodic rate equals the stated rate divided by the number of compounding periods per year State Rate (Nominal Rate)- the rate that is stated in the contract with the bank. OR Annual rate normally quoted in financial contracts.

What are three techniques for solving lump sum discounting problems?

Regular Calculator solution, financial calculator solution, spreadsheet solution.

Describe how present values of uneven cash flow streams are calculated using a regular calculator, using a financial calculator, and using a spreadsheet.

Regular Calculator- The PV of each lump sum cash flow can be found using a regular calculator, and then these values are summed to find the present value of the stream Financial Calculator- · Input the individual cash flows, in chronological order, into the cash flow register, where they usually are designated as CF0 and CFj (CF1, CF2, CF3, and so on) or just CF0, CF1, CF2, CF3, and so on). · Enter the discount rate · Push the NPV key

1. Why is semiannual compounding better than annual compounding from an investor's standpoint?

Semiannual compounding means that interest is paid every 6 months, so interested is earned more often than under annual compounding that is paid once a year.

What is lump sum?

Single value or single starting amount

Which annuity has the greater future value: an ordinary annuity or an annuity due? Why?

The future value of an annuity due because all the cash flows of an annuity due are compounded for one additional period. Hence the future value of an annuity due is greater than the future value of a similar ordinary annuity by (1+i).

Which annuity has the greater present value: an ordinary annuity or an annuity due? Why?

The present value of an annuity due is larger than that of a similar regular annuity because the payments are shifted to the left, each one is discounted for one less year.

what is discounting?

The process of finding the current (present) value of a lump sum, an annuity, or a series of unequal cash flows. · Discounting is moving left along the timeline, as we move left along the time line, values get smaller, or discount, over time.

what is confounding

The process of finding the future value of a lump sum, an annuity, or a series of unequal cash flows. OR The process of going from today's values, or present value (PV), to future values. · Moving right along the timeline

Explain the Rule of 72.

The rule of 72 give a simple and quick method for judging the effect of different interest rates on the growth of a lump sum deposit. To find the number of years required to double the value of a lump sum, merely divide the number 72 by the interest rate paid. · In a similar manner, the rule of 72 can be used to determine the interest rate required to double the money in an account in a given number of years.

what are three solution techniques for solving lump sum compounding problem?

They can be solved with a regular calculator, a financial calculator, or a spreadsheet.

1. What happens to the value of an perpetuity when interest rates increase or decrease?

When interest rates decrease the perpetuities value would increase When interest rates increase the perpetuities value would decrease

1. What role does the opportunity cost rate play in calculating financial returns?

When the expected present value is more than what would result if it had only a (given % in problem) return, that would result in an opportunity cost rate

what is interest on interest?

When the interest you made in year one is now being interested in year 2, and the interest you made in years one and two are now being interested in year 3, and so on.

Does the periodic payment remain constant over time?

Yes, if they are doing it in equal installments.

1. Is the calculation of financial return an application of time value analysis? Explain your answer.

Yes, you can always incorporate TVM when calculating returns.

how does the future value of a lump sum change as the time is extended as the interest rate increases?

increases as time is extended and as the increased rate increases

1. Can financial calculators and spreadsheets easily solve for interest rate or time?

yes