### Calculated value of the investment

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Basic Financial Tools: A Review

Directions: Answer the following five questions on a separate document. Explain how you reached the answer or show your work if a mathematical calculation is needed, or both.

1. Which of the following statements is CORRECT?

a. Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.

b. A time line is not meaningful unless all cash flows occur annually.

c. Time lines are not useful for visualizing complex problems prior to doing actual calculations.

d. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.

e. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities.

2. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

a. The discount rate decreases.

b. The cash flows are in the form of a deferred annuity, and they total to \$100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for \$20,000 rather than for \$10,000.

c. The discount rate increases.

d. The riskiness of the investment's cash flows decreases.

e. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.

3. Which of the following statements is CORRECT?

a. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.

b. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.

c. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.

d. The cash flows for an annuity due must all occur at the ends of the periods.

e. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.

4. Your bank account pays a 5% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

a. The periodic rate of interest is 5% and the effective rate of interest is also 5%.

b. The periodic rate of interest is 1.25% and the effective rate of interest is 2.5%.

c. The periodic rate of interest is 5% and the effective rate of interest is greater than 5%.

d. The periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%.

e. The periodic rate of interest is 2.5% and the effective rate of interest is 5%.

5. A \$250,000 loan is to be amortized over 8 years, with annual end-of-year payments. Which of these statements is CORRECT?

a. The proportion of interest versus principal repayment would be the same for each of the 8 payments.

b. The annual payments would be larger if the interest rate were lower.

c. If the loan were amortized over 10 years rather than 8 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 8-year amortization plan.

d. The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower.

e. The last payment would have a higher proportion of interest than the first payment.

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