Question 1

The present value of a promise to pay $100 one year from now would be greater if the interest rate were higher.

Accepted Answer

The present value of a future payment decreases as the interest rate increases. Therefore, the present value of a promise to pay $100 one year from now would be lower if the interest rate were higher.

Question 2

The present value of receiving M dollars in year t when the prevailing interest rate is i is equal to

Accepted Answer

The formula for present value is M divided by (1 + i)^t, where M is the future value, i is the interest rate, and t is the number of years in the future. This aligns with option C, which is the only choice with that formula.

Question 3

A firm is considering the purchase of a piece of equipment that will add $200 per year to the firm's revenue forever.If the interest rate is 10 percent,the firm will purchase the equipment so long as it costs less than

Accepted Answer

The present value of an infinite cash flow can be calculated by dividing the annual cash flow by the discount rate.

In this case, the annual cash flow is $200 and the discount rate is 10%, so the present value of the cash flow is:

PV = $200 / 0.1 = $2,000

Therefore, the firm should purchase the equipment as long as it costs less than $2,000.

The only answer choice that is less than $2,000 is B, which is $2,000, so the answer is B.

Question 4

The present value of receiving M dollars two years from now when the prevailing interest rate is i is equal to

Accepted Answer

The present value formula for receiving M dollars two years from now when the prevailing interest rate is i is M/(1 + i)^2. Multiplying both numerator and denominator by (1 + i) gives M/(1 + i)*(1 + i), which simplifies to M/(1 + i)*². Therefore, the correct answer is E.

Question 5

The present value of a promise to pay $100 one year from now is approximately $90.91 if the interest rate is 10 percent.

Accepted Answer

The answer of The present value of a promise to...

Question 6

The present value of an annuity that pays $100 each year indefinitely (i.e. ,a perpetuity) is $2,000 if the interest rate is 5 percent.

Accepted Answer

The formula for the present value of a perpetuity is (annual payment)/(interest rate). Plugging in the values given, we get ($100)/(0.05) = $2,000. Therefore, the statement is true.

Question 7

The present discounted value of $100 to be received in one year and with an interest rate of 10 percent is closest to

Accepted Answer

The present discounted value of $100 to be received in one year with a 10 percent interest rate is calculated as: $100/(1+0.1) = $90.91 which is closest to $91. Therefore, the correct choice is D.

Question 8

You buy a bond for $1,000 from the federal government,which guarantees that you will receive $70 a year forever.Thus,7 percent was the market rate of interest when you bought the bond.Suppose that immediately after you buy the bond,the market rate of interest goes to 10 percent.The market value of your bond

Accepted Answer

When the market rate of interest increases from 7% to 10%, the present value of the bond decreases as the future cash flows of $70 a year are worth less in today's dollars. Therefore, the market value of the bond will be less than $1,000.

Question 9

If the interest rate is 8 percent,$54 next year is worth _____ today.

Accepted Answer

The answer of If the interest rate is 8 percent,$54...

Question 10

If you are to receive a payment of $200 at the end of the first year and a payment of $250 at the end of the second year and the market interest rate is 5 percent,the present value of this income stream is

Accepted Answer

To find the present value of the income stream, we need to discount each future payment back to its present value using the formula:

Present Value = Future Value / (1 + Interest Rate)^n

Where n is the number of years from the present to the future payment.

Using this formula, we can calculate the present value of the first payment:

PV(year 1) = $200 / (1 + 0.05)^1 = $190.48

And the present value of the second payment:

PV(year 2) = $250 / (1 + 0.05)^2 = $223.75

The total present value of the income stream is then:

PV(total) = PV(year 1) + PV(year 2) = $190.48 + $223.75 = $414.23

Therefore, the best choice is B, $417.23, as it is the closest option to the calculated present value.

Question 11

If the market interest rate is 5 percent,the opportunity cost of $100 worth of present consumption

Accepted Answer

The answer of If the market interest rate is 5...

Question 12

The present value of $200 to be paid to you at the end of two years,if the market interest rate is 5 percent,is

Accepted Answer

The present value can be calculated using the formula PV = FV/(1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. 
Substituting the given values, we get PV = 200/(1 + 0.05)^2 = $181.41. Therefore, the best choice is A.

Question 13

If Mike gets $3,000 three years from today,for an interest rate of 8%,what is its present value?

Accepted Answer

The present value is calculated using the formula PV = FV / (1 + r)^n. Plugging in the values: PV = $3,000 / (1 + 0.08)^3 = $2,381.50.

Question 14

If the discount rate is 5 percent,the present value of annual $100,000 payments in perpetuity (i.e. ,continued indefinitely into the future) is

Accepted Answer

The answer of If the discount rate is 5 percent,the...

Question 15

The present value of receiving $200 one year from now when the prevailing rate of interest is 8 percent is

Accepted Answer

The present value can be calculated using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. Plugging in the numbers, we get:
PV = 200 / (1 + 0.08)^1
PV = 200 / 1.08
PV = $185.19
Therefore, the best choice is B with the calculated present value of $185.19.

Question 16

The procedure of determining the present value of payments to be received in the future is known as

Accepted Answer

The process of determining the present value of future payments is known as discounting. This involves calculating the value of payments in the present day, based on the time value of money and a chosen discount rate. This is different from compounding (which involves determining the future value of present investments) and amortizing (which involves spreading out payments over time). Perpetuating and nominalizing are not relevant processes in this context.

Question 17

If the interest rate is 6%,the present value of receiving $300 next year is approximately:

Accepted Answer

The formula to calculate the present value of a future payment is:

Present Value = Future Value / (1 + interest rate)^n

where n is the number of years in the future.

In this case, we have:

Present Value = $300 / (1 + 0.06)^1 = $283.02

Rounding to the nearest dollar gives us Choice C as the best answer.

Question 18

The present value of a given payment will be lower

Accepted Answer

The answer of The present value of a given payment...

Question 19

There is an inverse relationship between the present value of a future amount and the interest rate used for discounting.

Accepted Answer

As the interest rate used for discounting increases, the present value of a future amount decreases, and vice versa.

Question 20

If you will receive $5,000 two years from today,what is its present value if the discount rate is 5 percent?

Accepted Answer

We can use the present value formula: PV = FV / (1 + r)^n
PV = 5,000 / (1 + 0.05)^2
PV = 4,535.03
Therefore, the present value is $4,535.03, which is closest to option D ($4,535).

Quiz 13: Capital, interest, and Corporate Finance