Question 1

The payment of a given sum of money each year that continues indefinitely into the future is known as a(n):​

Accepted Answer

A perpetuity is a financial instrument that pays a fixed sum of money at regular intervals for an indefinite period of time. It is commonly used in financial modeling and valuation, especially for the valuation of preferred stock, bonds, and other fixed-income securities that have no maturity date.

Question 2

If the interest rate is 10 percent, the present value of an annual payment of $100,000 to be received indefinitely is:​

Accepted Answer

The present value of an annual payment of $100,000 to be received indefinitely (a perpetuity) is calculated using the formula PV = PMT / i, where PV is the present value, PMT is the annual payment, and i is the interest rate. Here, PMT = $100,000 and i = 10% or 0.10. Thus, PV = $100,000 / 0.10 = $1,000,000.

Question 3

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

Accepted Answer

The procedure of determining the present value of payments to be received in the future is called discounting. To discount future payments, we use a discount rate to determine the present value of those payments. This is the opposite of compounding, which determines the future value of present payments. Amortizing refers to the process of paying off debt over time through regular payments, perpetuating is not a financial term, and nominalizing refers to converting real values into nominal or monetary values.

Question 4

The present value of an education can be computed by:​

Accepted Answer

The present value of an education can be best computed by discounting the earnings based on the level of education and then summing total earnings over the work life. This method takes into account the opportunity cost of the forgone earnings during the years of education and the earning potential after completion of education. It provides a more accurate measure of the economic benefits of education taking into account the time value of money.

Question 5

A $100 annuity means _____.​

Accepted Answer

A $100 annuity means $100 is received each year for a certain number of years. An annuity is a series of payments made at equal intervals.

Question 6

The present value of a given payment will be lower _____.​

Accepted Answer

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

Question 7

Andre runs a company that yields a profit of $40,000 per year, and this profit stream is expected to continue indefinitely. If the interest rate equals 8 percent, he will be willing to sell the company at a price of:​

Accepted Answer

The answer of Andre runs a company that yields a...

Question 8

When David Palmisano won the Powerball lottery, he could choose between getting annual installments and taking a lump-sum amount. An economist suggested that David should think about _____.​

Accepted Answer

The economist is suggesting that David should consider the present value of his income stream. This is because if David chooses the annual installments, the payments would be spread out over time and may not have the same value in the future due to inflation or changes in the economy. Calculating the present value would give David a better understanding of the current worth of his future payments and help him make an informed decision.

Question 9

Suppose Penny will receive $2,000 per year forever from her local bank when the prevailing interest rate is 7 percent. The present value of that income stream is approximately _____.​

Accepted Answer

The present value of a perpetuity is calculated using the formula PV = P / r, where P is the payment per period and r is the interest rate per period. Here, P = $2,000 and r = 0.07. Thus, PV = $2,000 / 0.07 = $28,571.

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 at a market interest rate of 5 percent, the present value of this income stream is:​

Accepted Answer

We can use the formula for the present value of an annuity:

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

where PV is the present value, C is the payment per period, r is the interest rate, and n is the number of periods.

Plugging in the given values, we get:

PV = $200 * [(1 - (1 + 0.05)^-1) / 0.05] + $250 * [(1 - (1 + 0.05)^-2) / 0.05]
PV = $200 * 0.9524 + $250 * 0.9070
PV = $190.48 + $226.75
PV = $417.23

Therefore, the present value of the income stream is $417.23, which corresponds to choice B.

Question 11

If the market interest rate is 5 percent, the present value of $200 to be paid to you at the end of two years is _____.​

Accepted Answer

PV = FV / (1 + r)n
PV = 200 / (1 + 0.05)2
PV = 200 / 1.1025

PV = $181.41

Question 12

​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,...

Question 13

If the market interest rate is 5 percent, the opportunity cost of $100 spend on the purchase of goods:​

Accepted Answer

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

Question 14

Suppose Peter expects to receive $5,000 three years from today. If the interest rate is 4 percent, the present value of $5,000 is approximately _____.​

Accepted Answer

The present value of a future sum of money is calculated using the formula:PV = FV / (1 + r)^nwhere:PV is the present valueFV is the future valuer is the interest raten is the number of yearsIn this case, we have:FV = $5,000r = 4% = 0.04n = 3Plugging these values into the formula, we get:PV = $5,000 / (1 + 0.04)^3PV = $5,000 / 1.1255PV = $4,444.44Therefore, the present value of $5,000 three years from today is approximately $4,444.

Question 15

Suppose an investment will yield $1,000 after one year and $2,000 after two years. The present value of this investment at a discount rate of 8 percent is:​

Accepted Answer

To calculate the present value of the investment, we need to discount the future cash flows to their present value using the discount rate of 8%. We can use the formula:

PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2

Where PV is the present value, CF1 is the cash flow after one year, CF2 is the cash flow after two years, and r is the discount rate.

Substituting the values, we get:

PV = 1000 / (1 + 0.08)^1 + 2000 / (1 + 0.08)^2
PV = 925.93 + 1,714.67
PV = $2,640.60

Therefore, the present value of the investment is $2,640.60. Choice B is the correct answer.

Question 16

Discounting involves:​

Accepted Answer

Discounting involves converting future dollar amounts into present value. This is typically done to evaluate the current value of an investment or project, taking into account the time value of money and potential inflation. By discounting future cash flows, investors can determine the expected return on investment and make more informed decisions about where to allocate their resources.

Question 17

The present value of receiving M dollars in year t when the prevailing interest rate is i is given by the formula _____.​

Accepted Answer

The formula for present value is M/(1+i)^t, which is equivalent to choice C.

Question 18

If you own a perpetuity of $500 and if the interest rate is 4 percent, then its present value:​

Accepted Answer

The answer of If you own a perpetuity of $500...

Question 19

​A given sum of money received each year for a specific number of years is called a(n):

Accepted Answer

An annuity is a sum of money received each year for a specific number of years. Bonds are typically loans that have a fixed term and interest rate, while perpetuities are payments that continue forever. Debt and dividends are not specific to a set number of years.

Question 20

The present value of $200 received one year from now when the prevailing interest rate is 8 percent is _____.​

Accepted Answer

To find the present value, we need to discount the future value by the interest rate. 
PV = FV / (1 + r) 
where PV is the present value, FV is the future value, and r is the interest rate. 
In this question, 
FV = $200 
r = 8% = 0.08 
PV = $200 / (1 + 0.08) 
PV = $185.19 
Therefore, the best choice is B.

Quiz 13: Capital, Interest, Entrepreneurship, and Corporate Finance

The payment of a given sum of money each year that continues indefinitely into the future is known as a(n) :

If the interest rate is 10 percent, the present value of an annual payment of $100,000 to be received indefinitely is:

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

The present value of an education can be computed by:

A $100 annuity means _____.

The present value of a given payment will be lower _____.

Andre runs a company that yields a profit of $40,000 per year, and this profit stream is expected to continue indefinitely. If the interest rate equals 8 percent, he will be willing to sell the company at a price of:

When David Palmisano won the Powerball lottery, he could choose between getting annual installments and taking a lump-sum amount. An economist suggested that David should think about _____.

Suppose Penny will receive $2,000 per year forever from her local bank when the prevailing interest rate is 7 percent. The present value of that income stream is approximately _____.

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 at a market interest rate of 5 percent, the present value of this income stream is:

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

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

If the market interest rate is 5 percent, the opportunity cost of $100 spend on the purchase of goods:

Suppose Peter expects to receive $5,000 three years from today. If the interest rate is 4 percent, the present value of $5,000 is approximately _____.

Suppose an investment will yield $1,000 after one year and $2,000 after two years. The present value of this investment at a discount rate of 8 percent is:

Discounting involves:

The present value of receiving M dollars in year t when the prevailing interest rate is i is given by the formula _____.

If you own a perpetuity of $500 and if the interest rate is 4 percent, then its present value:

A given sum of money received each year for a specific number of years is called a(n) :

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