Question 1

By choosing to attend college today,you have agreed to pay $17,000 per year in tuition and fees for the next five years.(What… you really thought that you would graduate in four years?)In addition to the tuition and fees,you have also given up the ability to work full time and earn $23,000 per year for the next five years.If your required rate of return is 5% (the U.S.long-run average rate of inflation plus an average real rate of return),what is the total cost in today's dollars of your college degree,assuming that all of the aforementioned cash flows are ordinary annuities?

Accepted Answer

The answer of By choosing to attend college today,you have...

Question 2

When solving for present value,we use the term compounding of cash flows rather than the term discounting of cash flows.

Accepted Answer

When solving for present value, we use the term discounting of cash flows, not compounding of cash flows. Compounding refers to the process of calculating future values by adding interest to the initial investment, while discounting refers to the process of calculating present values by subtracting interest from future cash flows.

Question 3

You have just won the Publisher's Clearinghouse lottery of $50,000 per year for twenty years,with the first payment today followed by nineteen more start-of-the-year cash flows.At an interest rate of 4%,what is the present value of your winnings?

Accepted Answer

We need to calculate the present value of an annuity. Using the formula PV = PMT*((1 - (1 + r)^-n)/r), where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of payments, we can calculate the present value. Plugging in the given values, we get: PV = 50,000*((1 - (1 + 0.04)^-20)/0.04) = $706,696.97. Therefore, the best choice is B.

Question 4

A never-ending stream of equal periodic,end-of-the-period cash flows is called a/an ________.

Accepted Answer

A perpetuity is a series of equal cash flows that continues forever, unlike an annuity which has a finite number of cash flows over a certain period of time. An annuity due is an annuity where the payments are due at the beginning of each period instead of at the end, and amortization refers to the process of paying off a debt over time with regular payments that include principal and interest.

Question 5

What is the present value today of an ordinary annuity cash flow of $4,000 per year for thirty years at an interest rate of 6.0% per year if the first cash flow is six years from today?

Accepted Answer

The present value of an ordinary annuity can be calculated using the formula for the present value of an annuity. First, calculate the present value of the annuity as of year 5 (since the first payment is at year 6) and then discount it back to today (year 0) using the formula: PV = PMT × [(1 - (1 + r)^-n) / r] and then discount this value back to present value today. The correct calculation results in approximately $41,143.53.

Question 6

Your firm wishes to purchase a financial contract that provides equal end-of-the-year cash flows of $18,000 per year for the next seven years.What is the present value of these cash flows if you choose to discount them at a rate of 8% per year?

Accepted Answer

The answer of Your firm wishes to purchase a financial...

Question 7

You dream of endowing a chair in finance at the local university that will provide a salary of $250,000 per year forever,with the first cash flow to be one year from today.If the university promises to invest the money at a rate of 4% per year,how much money must you give the university today to make your dream a reality?

Accepted Answer

The present value of a perpetuity is calculated as the annual cash flow divided by the interest rate. Here, $250,000 / 0.04 = $6,250,000.

Question 8

Plimpton has an annuity due that pays $800 per year for 11 years.What is the present value of the cash flows if they are discounted at an annual rate of 7.50%?

Accepted Answer

The present value of an annuity due can be calculated using the formula for the present value of an ordinary annuity and then multiplying by (1 + r) to account for the payments occurring at the beginning of each period. Using the formula: PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r), where Pmt = $800, r = 0.075, and n = 11, the present value is approximately $6,291.26.

Question 9

Which of the following is NOT a form of perpetuity?

Accepted Answer

All of the given options are examples of perpetuities.

Question 10

What is the present value of a lottery paid as an annuity due for twenty years if the cash flows are $150,000 per year and the appropriate discount rate is 7.50%?

Accepted Answer

The answer of What is the present value of a...

Question 11

You have just turned 27 and may now spend a portion of the trust fund your parents established for you.The terms of the trust fund allow you to withdraw 50 beginning-of-the-year cash flows of $40,000 each.An investment firm has offered to pay you cash for all of the fund today.If the rate they use to discount the cash flows is 14% per year,what is their offer price today for your pension fund?

Accepted Answer

The answer of You have just turned 27 and may...

Question 12

The formula for the Present Value Interest Factor of an Annuity (PVIFA)is $\frac { ( 1 + r ) ^ { n } - 1 } { r }$ .

Accepted Answer

The correct formula for PVIFA is $\frac{1 - (1 + r)^{-n}}{r}$, which calculates the present value of a series of annuities.

Question 13

You have accumulated $1,200,000 for your retirement.How much money can you withdraw in equal annual beginning-of-the-year cash flows if you invest the money at a rate of 5% for thirty years?

Accepted Answer

Using the formula for present value of an annuity:
PV = PMT * [(1 - (1 + r)^-n)/r]
where PV = present value, PMT = payment, r = interest rate per period, n = number of periods
we can solve for PMT:
PMT = PV / [(1 - (1 + r)^-n)/r]
Plugging in the given values:
PV = $1,200,000
r = 0.05 (5%)
n = 30
PMT = $74,344.50 (rounded to the nearest cent)
Therefore, the answer is A.

Question 14

Given positive equal annual cash flows and a positive interest rate,the present value of an annuity will be greater than the sum of the cash flows.

Accepted Answer

The present value of an annuity, given positive equal annual cash flows and a positive interest rate, will be less than the sum of the cash flows because the present value calculation discounts future cash flows back to their value in today's dollars, accounting for the time value of money.

Question 15

A wealthy man just died and left his pet dogs the following estate: $20,000 per year for the next 11 years with the first cash flow today.At a discount rate of 4.2%,what is the doggy estate worth in today's dollars?

Accepted Answer

We can use the formula for present value of an annuity to calculate the value of the doggy estate:
PV = C x [(1 - (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 years.

Plugging in the given values, we get:
PV = 20,000 x [(1 - (1 / (1 + 0.042)11)) / 0.042]
PV = $180,614.80

Therefore, the doggy estate is worth $180,614.80 in today's dollars.

Question 16

A series of equal periodic finite cash flows that occur at the beginning of the period are known as a/an ________.

Accepted Answer

An annuity due is a series of equal periodic finite cash flows that occur at the beginning of the period. An ordinary annuity has cash flows that occur at the end of each period, while a perpetuity has a never-ending stream of equal cash flows. Amortization refers to the process of reducing the value of an asset or liability over time through regular payments.

Question 17

Severson has an annuity due that pays $400 per year for 20 years.What is the value of the cash flows 20 years from today if they are placed in an account that earns 7.50%? Note: You are asked to find the FV one year after the last cash flow is realized.

Accepted Answer

To find the future value of an annuity due, we use the formula for the future value of an annuity due, which is FV = P * [((1 + r)^n - 1) / r] * (1 + r), where P is the payment amount, r is the interest rate per period, and n is the number of periods. Here, P = $400, r = 7.50% or 0.075, and n = 20. Plugging these values into the formula gives us the future value one year after the last cash flow is realized, which calculates to $18,621.01.

Question 18

The future value three years from today of a $200 three-year annuity due compounded at a rate of 10% is equal to ________.

Accepted Answer

The formula for the future value of an annuity due is:

FV = PMT x [(1 + r)^(n+1) - 1] / r

where PMT is the payment, r is the interest rate, and n is the number of periods.

In this case, PMT = $200, r = 10%, and n = 3. Plugging these values into the formula, we get:

FV = $200 x [(1 + 0.10)^(3+1) - 1] / 0.10
   = $200 x [1.4641 - 1] / 0.10
   = $728.20

Therefore, the future value of the annuity due is $728.20, so the best choice is C.

Question 19

The present value of a $100 three-year annuity due (first cash flow occurs today)discounted at a rate of 10% is equal to ________.

Accepted Answer

An annuity due means the first payment occurs immediately. The present value of an annuity due can be calculated using the formula for the present value of an ordinary annuity and then multiplying by (1 + r) to account for the immediate payment. The present value of a $100 annuity due for 3 years at 10% is $273.55.

Question 20

Your neighbor owns a perpetuity of $100 per year that has a discount rate of 6% per year.He offers to sell to you all but the next 20 cash flows (the first to be received one year from today)for $500.In other words,he keeps the first 20 cash flows of his perpetuity and you get all of the rest.Is this a good price for you if the appropriate discount rate is 6%?

Accepted Answer

The present value of a perpetuity is calculated using the formula PV = C / r, where C is the cash flow per period and r is the discount rate. The entire perpetuity is worth $100 / 0.06 = $1,666.67. The present value of the first 20 cash flows can be calculated using the formula for the present value of an annuity: PV = C * [1 - (1 + r)^-n] / r, where n is the number of periods. For the first 20 cash flows, this is $100 * [1 - (1 + 0.06)^-20] / 0.06 = $1,147.01. The value of the remaining cash flows is the difference between the total perpetuity and the first 20 cash flows: $1,666.67 - $1,147.01 = $519.66. Since you are buying them for $500, it's a good price.

Quiz 4: The Time Value of Money Part 2

When solving for present value,we use the term compounding of cash flows rather than the term discounting of cash flows.

You have just won the Publisher's Clearinghouse lottery of $50,000 per year for twenty years,with the first payment today followed by nineteen more start-of-the-year cash flows.At an interest rate of 4%,what is the present value of your winnings?

A never-ending stream of equal periodic,end-of-the-period cash flows is called a/an ________.

What is the present value today of an ordinary annuity cash flow of $4,000 per year for thirty years at an interest rate of 6.0% per year if the first cash flow is six years from today?

Your firm wishes to purchase a financial contract that provides equal end-of-the-year cash flows of $18,000 per year for the next seven years.What is the present value of these cash flows if you choose to discount them at a rate of 8% per year?

Plimpton has an annuity due that pays $800 per year for 11 years.What is the present value of the cash flows if they are discounted at an annual rate of 7.50%?

Which of the following is NOT a form of perpetuity?

What is the present value of a lottery paid as an annuity due for twenty years if the cash flows are $150,000 per year and the appropriate discount rate is 7.50%?

The formula for the Present Value Interest Factor of an Annuity (PVIFA)is $\frac { ( 1 + r ) ^ { n } - 1 } { r }$ .

You have accumulated $1,200,000 for your retirement.How much money can you withdraw in equal annual beginning-of-the-year cash flows if you invest the money at a rate of 5% for thirty years?

Given positive equal annual cash flows and a positive interest rate,the present value of an annuity will be greater than the sum of the cash flows.

A wealthy man just died and left his pet dogs the following estate: $20,000 per year for the next 11 years with the first cash flow today.At a discount rate of 4.2%,what is the doggy estate worth in today's dollars?

A series of equal periodic finite cash flows that occur at the beginning of the period are known as a/an ________.

Severson has an annuity due that pays $400 per year for 20 years.What is the value of the cash flows 20 years from today if they are placed in an account that earns 7.50%? Note: You are asked to find the FV one year after the last cash flow is realized.

The future value three years from today of a $200 three-year annuity due compounded at a rate of 10% is equal to ________.

The present value of a $100 three-year annuity due (first cash flow occurs today) discounted at a rate of 10% is equal to ________.

Quiz 4: The Time Value of Money Part 2

When solving for present value,we use the term compounding of cash flows rather than the term discounting of cash flows.

You have just won the Publisher's Clearinghouse lottery of $50,000 per year for twenty years,with the first payment today followed by nineteen more start-of-the-year cash flows.At an interest rate of 4%,what is the present value of your winnings?

A never-ending stream of equal periodic,end-of-the-period cash flows is called a/an ________.

What is the present value today of an ordinary annuity cash flow of $4,000 per year for thirty years at an interest rate of 6.0% per year if the first cash flow is six years from today?

Your firm wishes to purchase a financial contract that provides equal end-of-the-year cash flows of $18,000 per year for the next seven years.What is the present value of these cash flows if you choose to discount them at a rate of 8% per year?

Plimpton has an annuity due that pays $800 per year for 11 years.What is the present value of the cash flows if they are discounted at an annual rate of 7.50%?

Which of the following is NOT a form of perpetuity?

What is the present value of a lottery paid as an annuity due for twenty years if the cash flows are $150,000 per year and the appropriate discount rate is 7.50%?

The formula for the Present Value Interest Factor of an Annuity (PVIFA)is (1+r)n−1r\frac { ( 1 + r ) ^ { n } - 1 } { r }r(1+r)n−1​ .

You have accumulated $1,200,000 for your retirement.How much money can you withdraw in equal annual beginning-of-the-year cash flows if you invest the money at a rate of 5% for thirty years?

Given positive equal annual cash flows and a positive interest rate,the present value of an annuity will be greater than the sum of the cash flows.

A wealthy man just died and left his pet dogs the following estate: $20,000 per year for the next 11 years with the first cash flow today.At a discount rate of 4.2%,what is the doggy estate worth in today's dollars?

A series of equal periodic finite cash flows that occur at the beginning of the period are known as a/an ________.

Severson has an annuity due that pays $400 per year for 20 years.What is the value of the cash flows 20 years from today if they are placed in an account that earns 7.50%? Note: You are asked to find the FV one year after the last cash flow is realized.

The future value three years from today of a $200 three-year annuity due compounded at a rate of 10% is equal to ________.

The present value of a $100 three-year annuity due (first cash flow occurs today) discounted at a rate of 10% is equal to ________.

The formula for the Present Value Interest Factor of an Annuity (PVIFA)is $\frac { ( 1 + r ) ^ { n } - 1 } { r }$ .