Question 1

If the discount rate increases, then the present value of a potential investment would fall.

Accepted Answer

The discount rate is used to calculate the present value of future cash flows. If the discount rate increases, the present value of those cash flows decreases, making the investment less valuable. Therefore, if the discount rate increases, the present value of a potential investment would fall.

Question 2

The present value is simply the current value of a future cash flow that has been discounted at the relevant discount rate.

Accepted Answer

This is the definition of present value - it is the current value of a future cash flow that has been discounted using the appropriate discount rate.

Question 3

The future value factor for 10 years at 15% with annual compounding is calculated as (1 + 0.15)¹⁰.

Accepted Answer

The formula for calculating the future value with annual compounding is (1+r)^n, where r is the interest rate and n is the number of years. Therefore, the future value factor for 10 years at 15% with annual compounding is (1 + 0.15)^10, which simplifies to 4.046.

Question 4

The lower the discount rate, the lower the present value of a future cash flow.

Accepted Answer

A lower discount rate increases the present value of a future cash flow because it reduces the rate at which future cash flows are discounted back to their present value.

Question 5

The process of calculating the present value of a future cash flow is called compounding.

Accepted Answer

The process of calculating the present value of a future cash flow is called discounting. Compounding is the process of calculating the future value of an investment.

Question 6

If the discount rate falls, then the present value of a potential investment would also fall.

Accepted Answer

If the discount rate falls, the present value of a potential investment would increase. This is because a lower discount rate means lower future cash flows are discounted less heavily, leading to a higher present value.

Question 7

The more frequently the interest payments are compounded, the larger the future value of $1 for a given time period.

Accepted Answer

When interest payments are compounded more frequently (such as monthly instead of annually), the interest is earned on a larger principal amount each time. This results in a higher overall return on investment and a larger future value of $1 for a given time period.

Question 8

The present value technique uses discounting to find the present value of each cash flow at the beginning of a project.

Accepted Answer

The present value technique involves discounting future cash flows to their present value at the beginning of the project. This helps to determine the value of the project and evaluate whether it is worthwhile or not. Therefore, the given statement is true.

Question 9

To calculate the present value of a future amount, we divide the future value by the future value factor.

Accepted Answer

The present value of a future amount is calculated by dividing the future value by the present value factor, not the future value factor.

Question 10

William invested $5,000 in an account earning 10 percent for one year. If he had left his investment in that account for another two years, he would expect the total interest earned over the three years to be higher by exactly $1,000.

Accepted Answer

The interest earned in the first year would be $500 (10% of $5,000). If left for another two years with compound interest, the interest earned would be more than $1,000 due to the interest compounding annually, not just an additional $500 per year.

Question 11

The present value of $3,000 to be received in two years at a discount rate of 10 percent is $3,630.

Accepted Answer

The present value formula is PV = FV / (1 + r)^n, where PV is present value, FV is future value, r is the discount rate, and n is the number of years. Plugging in the given values, we get:
3,630 = 3,000 / (1 + 0.1)^2
This equation is not true, so the answer is false.

Question 12

The farther in the future a dollar will be received, the less it is worth today.

Accepted Answer

This is due to the concept of time value of money, which suggests that the value of money decreases over time due to factors such as inflation, opportunity cost, and risk. Therefore, a dollar received in the future is worth less than a dollar received today.

Question 13

The higher the interest rate on an investment, the more money that is accumulated for any time period.

Accepted Answer

This is true because a higher interest rate means that the investment is earning more money over time, which will accumulate to a greater total amount.

Question 14

If Bank A pays interest on a monthly basis and Bank B pays the same interest rate, but on a quarterly basis, then investing $1,000 in Bank B will result in a higher future value compared to investing the same amount in Bank A.

Accepted Answer

Interest compounded more frequently (monthly in this case) will result in a higher future value due to the effect of compounding interest on the principal more often.

Question 15

The future value of an investment of $5,000 earning an interest rate of 10 percent compounded annually equals $6,000 at the end of one year.

Accepted Answer

The future value of an investment is calculated using the formula FV = PV(1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years. For a $5,000 investment at 10% interest compounded annually for one year, the future value would be $5,000 * (1 + 0.10)^1 = $5,500, not $6,000.

Question 16

The higher the discount rate, the lower the present value of a future cash flow.

Accepted Answer

This is the concept of time value of money, where the higher the discount rate (or cost of capital), the lower the present value of a future cash flow.

Question 17

Suppose Randy plans to invest $1,000. He can earn an annual rate of 5% on Security A, while Security B has an effective annual rate of 10%. After 11 years, the compounded value of Security B should be somewhat less than double the compounded value of Security A.

Accepted Answer

Using the compound interest formula, the compounded value of Security A after 11 years is:

A = 1000(1 + 0.05)^11 = $1,629.72

The compounded value of Security B after 11 years is:

B = 1000(1 + 0.10/12)^(12*11) = $2,134.99

So, B is indeed more than double A. However, the problem states that B should be "somewhat less" than double A, which is not the case. Therefore, the statement is false.

Question 18

The future value in three years of $5,000 invested today at a discount rate of 10 percent is $6,655.

Accepted Answer

This statement is true.

Question 19

The present value factor increases as the number of period decreases.

Accepted Answer

The present value factor, which is used to discount future cash flows to their present value, increases as the number of periods decreases because there is less time for the discount rate to apply, thus reducing the amount of discounting.

Question 20

You need $5000 in five years. If you could choose a discount rate of 8 percent or 10 percent, you should always choose the higher rate because you would need a higher starting amount.

Accepted Answer

The statement is false. A higher discount rate means the value of your money would increase at a higher rate, but it also means that the future value of your money would decrease. Therefore, the rate you choose depends on your specific financial situation and goals. Some people may prefer a higher discount rate if they want to take more risks and potentially earn higher returns, while others may prefer a lower discount rate if they prioritize safety and stability. Ultimately, it depends on your individual preferences and circumstances.

Quiz 5: The Time Value of Money