Question 1

Assume that an investor owns TKB preferred stock, which pays an annual dividend of $4.50. What is the present value of the stock if the investor's discount rate is six percent?

Accepted Answer

The present value of a perpetuity is calculated as the annual dividend divided by the discount rate. Therefore, the present value = $4.50 / 0.06 = $75.

Question 2

Use the following to answer questions
Bob Lower wants to retire in 10 years. At that time he wants to have a lump sum accumulated that would allow him to withdraw $35,000 a year for the next 20 years. Assume that Bob earns an after-tax return of eight percent. Ignore the inflation in these calculations.
- Suppose an investor invests $2,000 in a Certificate of Deposit which earns eight percent compounded quarterly. What is the value of the CD in five years?

Accepted Answer

Using the formula A = P(1 + r/n)^(nt), where A is the ending amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years, we can solve for the value of the CD:
A = 2000(1 + 0.08/4)^(4*5) = $2,972.48 (rounded to the nearest cent)
Therefore, the answer is D, $2,972.

Question 3

Use the following information for questions
Mary needs $145,000 in 15 years to buy her son a new Ferrari. Assume that she can earn an 8% after-tax return on her investment. You may ignore inflation in these calculations.
-How much ignore cents) will Mary need to invest today?

Accepted Answer

The answer of Use the following information for questions
Mary needs...

Question 4

Suppose an investor invests $2,000 at the beginning of each year. What will be the value of the investment at the end of ten years if he earns ten percent?

Accepted Answer

This is a case of annuity compounded annually. The formula for the future value of an annuity is FV = PMT * [(1+i)^n - 1]/i, where PMT is the payment made each period, i is the interest rate, and n is the number of periods.
In this case, PMT = $2,000, i = 10% and n = 10. Plugging these values into the formula, we get:
FV = $2,000 * [(1+0.1)^10 - 1]/0.1 = $35,062. Therefore, the best choice is B.

Question 5

Use the following information for questions
Mary needs $145,000 in 15 years to buy her son a new Ferrari. Assume that she can earn an 8% after-tax return on her investment. You may ignore inflation in these calculations.
-How much will Mary need to invest each year for the next 15 years if investments are made at the end of each year?

Accepted Answer

Mary needs to calculate the annuity payment using the future value of an annuity formula. The correct annual investment is approximately $5,340.

Question 6

Which of the following definitions of "Present Value of an Uneven Payment Series" is true?

Accepted Answer

The correct definition of "Present Value of an Uneven Payment Series" involves calculating the present value for each individual payment separately, considering their unique timing and amount, and then summing up these individual present values. This approach accounts for the fact that each payment has a different value in present terms due to the time value of money.

Question 7

Use the following information for questions
Mary needs $145,000 in 15 years to buy her son a new Ferrari. Assume that she can earn an 8% after-tax return on her investment. You may ignore inflation in these calculations.
- If you calculate "Future Value of an Annuity":

Accepted Answer

The future value of an annuity calculation will provide the total value of the fund at the end of the annuity period, which in this case is 15 years.

Question 8

Use the following information for questions
Mary needs $145,000 in 15 years to buy her son a new Ferrari. Assume that she can earn an 8% after-tax return on her investment. You may ignore inflation in these calculations.
-How much does Bob need to invest for each of the next ten years to fulfill his needs?

Accepted Answer

To find the annual investment needed, we use the future value of an annuity formula. Solving for the annual investment, we find that Mary needs to invest approximately $23,721 each year for 10 years at an 8% return to reach $145,000 in 15 years.

Question 9

Assume that an investor expects to receive the following dividends: year 1: $8, years 2-7: $10, and years 11-12: $12. If the investor's discount rate is 5 percent, what is the present value of this dividend stream?

Accepted Answer

The present value of the dividend stream is calculated by discounting each dividend to its present value using the formula PV = D / (1 + r)^n, where D is the dividend, r is the discount rate, and n is the year. Summing these present values gives $69.66.

Question 10

Present Value of a Perpetuity implies that

Accepted Answer

Perpetuity refers to an annuity that continues indefinitely. Therefore, to calculate the present value of a perpetuity, one needs to determine the present value of the payments that will last indefinitely. The formula to calculate the present value of a perpetuity is PV = PMT / r, where PV is the present value, PMT is the constant payment, and r is the discount rate.

Question 11

Mr. Hall wants to receive $45,000 at the end of each year in today's dollars for the next 15 years. He is concerned about inflation and wants you to determine the lump sum he would need if the annual rate of inflation averages four percent and he could earn nine percent on his investment.

Accepted Answer

To determine the lump sum Mr. Hall would need to receive $45,000 at the end of each year for the next 15 years, we can use the present value of an annuity formula:

PV = C [(1 - (1 + r)^-n) / r]

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of periods.

First, we need to calculate the inflation-adjusted cash flow for each year. The first year's payment is already given as $45,000, but we need to adjust it for inflation in the following years. In year two, this payment will be worth $45,000 / (1 + 0.04) = $43,269.23 in today's dollars. In year three, it will be worth $43,269.23 / (1 + 0.04) = $41,870.69, and so on. We can create a table to calculate the inflation-adjusted cash flow for each year:

Year	Cash Flow	Inflation-adjusted Cash Flow
1	$45,000	$45,000
2	$45,000	$43,269.23
3	$45,000	$41,870.69
4	$45,000	$40,758.16
5	$45,000	$39,889.54
6	$45,000	$39,229.65
7	$45,000	$38,748.09
8	$45,000	$38,419.19
9	$45,000	$38,220.98
10	$45,000	$38,136.23
11	$45,000	$38,150.41
12	$45,000	$38,251.63
13	$45,000	$38,430.54
14	$45,000	$38,679.34
15	$45,000	$38,991.76

Next, we can use the formula to calculate the present value of these cash flows. We'll use a discount rate of 9%, since Mr. Hall could earn 9% on his investment:

PV = $45,000 [(1 - (1 + 0.09)^-15) / 0.09] = $470,094.70

However, this is the present value of the cash flows without considering inflation. We need to adjust this amount for inflation by dividing it by (1 + 0.04)^15:

Inflation-adjusted PV = $470,094.70 / (1 + 0.04)^15 = $495,967.26

Therefore, Mr. Hall would need a lump sum of approximately $495,967 in today's dollars to receive $45,000 at the end of each year for the next 15 years, given an average inflation rate of 4% and an investment return of 9%. The best choice is B.

Question 12

Which of the following statements are true?

Accepted Answer

Interest payment frequencies can vary, but it's common for banks to pay interest daily, monthly, or quarterly, rather than annually, making A incorrect. Bonds often pay interest semi-annually, making C correct. Dividends for stockholders are commonly paid quarterly, making D correct. Therefore, E, which includes both C and D, is the correct choice.

Question 13

What is the effective interest rate on a bank savings account which pays six percent, compounded semi-annually?

Accepted Answer

To calculate the effective interest rate, we need to take into account the compounding period. In this case, the interest is compounded semi-annually, which means twice a year.

The formula for effective interest rate is:

Effective rate = (1 + (nominal rate / n))^n - 1

Where:
- n is the number of times the interest is compounded per year
- nominal rate is the interest rate stated as an annual percentage

Plugging in the values for this savings account, we get:

Effective rate = (1 + (0.06 / 2))^2 - 1
Effective rate = 0.0609 or 6.09%

Therefore, the answer is B.

Quiz 3: Time Value of Money: The Universal Tool