Question 1

Which is greater,the present value of a five-year ordinary annuity of $300 discounted at 10%,or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?

Accepted Answer

The present value of a five-year ordinary annuity of $300 discounted at 0% will simply be $300 multiplied by the number of periods, which is 5, for a total of $1,500. However, the first cash flow does not occur until six years from today, which means it will not be discounted at all. This gives us a present value of $1,500 for the second annuity. On the other hand, the present value of the first annuity will be calculated at a discount rate of 10%, which will decrease the value of the cash flows. Therefore, the second annuity is greater in value than the first.

Question 2

What is the future value in year thirty-five of an ordinary annuity cash flow of $4,000 per year at an interest rate of 11.0% per year?

Accepted Answer

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

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

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

Plugging in the given values, we get:

FV = 4,000 x [(1 + 0.11)^35 - 1] / 0.11

FV ≈ $1,366,358.22

Therefore, the best choice is A.

Question 3

Autorola plans to invest $5,000 per year in equal end-of-the-year amounts at an interest rate of 6% compounded annually.How much will the firm have at the end of four years?

Accepted Answer

The answer of Autorola plans to invest $5,000 per year...

Question 4

You are presented with two cash flow options: Option Near,a $5,000 annuity for three years,with the first cash flow one year from today,or Option Far,a $5,000 annuity for six years with the first cash flow ten years from today.Assuming an interest rate of 7.0%,which set of cash flows has a greater present value?

Accepted Answer

To compare the present value of the two options, we need to calculate the present value of each cash flow and add them up. Using the formula for the present value of an annuity, we find that the present value of Option Near is $13,121.58 and the present value of Option Far is $12,963.41. Therefore, Option Near has a greater present value and is the better choice.

Question 5

A trend among universities is to guarantee tuition to incoming freshmen for a four-year period.Further,the annual amount due is collected in equal payments collected every three months.Although the payments are equal as well as equally spaced,this is NOT an example of an annuity because the payments are made every three months rather than on a monthly or annual basis.

Accepted Answer

An annuity is a series of equal payments made at equal intervals, which can be monthly, quarterly or annually. In this case, the payments are made every three months, which is not a standard interval for an annuity. Therefore, the given statement is false.

Question 6

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

Accepted Answer

The formula for the Future Value Interest Factor of an Annuity (FVIFA) is indeed $\frac { ( 1 + r ) ^ { n } - 1 } { r }$, where $r$ is the interest rate per period, and $n$ is the number of periods.

Question 7

Which of the following is greater (answers rounded to the nearest cent)?

Accepted Answer

The present value of all three choices is $248.69 when using an interest rate of 10% per year.

Question 8

You estimate that the drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $120,000 per year for the next ten years.If you discount these cash flows at an annual rate of 11%,what is the present value of your expected cash flows?

Accepted Answer

The present value of an ordinary annuity can be calculated using the formula PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual cash flow ($120,000), r is the annual discount rate (11% or 0.11), and n is the number of periods (10 years). Plugging these values into the formula gives a present value of approximately $706,707.84.

Question 9

You are paid to teach graduate-level classes for the university and want to determine how much money the university makes from your graduate-level classes.Based on historical data,you estimate that your graduate classes for the next six years will generate an average annual revenue of $99,850.If you discount these cash flows at an annual rate of 7.30%,what is the present value of the expected cash flows?

Accepted Answer

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

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

PV = present value
C = average annual revenue = $99,850
r = discount rate = 7.30% = 0.073
n = number of periods = 6

Plugging in the values, we get:

PV = $99,850 * [(1 - (1+0.073)^-6)/0.073]
PV = $471,562.95

Therefore, the present value of the expected cash flows is $471,562.95.

Choice C is the best choice.

Question 10

The furniture store offers you no-money-down on a new set of living room furniture.Further,you may pay for the furniture in three equal annual end-of-the-year payments of $750 each with the first payment to be made one year from today.If the discount rate is 5%,what is the present value of the furniture payments?

Accepted Answer

The present value of the furniture payments is $2,042.44. This is calculated by multiplying the annual payment of $750 by the present value factor for an annuity of 3 years at 5%, which is 2.72325.

Question 11

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

Accepted Answer

This is because the interest earned on each cash flow will accumulate over time, resulting in a higher future value of the annuity.

Question 12

What is the future value in year four of an ordinary annuity cash flow of $6,000 per year at an interest rate of 12.00% per year?

Accepted Answer

The answer of What is the future value in year...

Question 13

You have the opportunity to purchase mineral rights to a property in Wyoming with expected annual cash flows of $8,000 per year for ten years.If you discount these cash flows at a rate of 12% per year,what are these cash flows worth today if the cash flows occur at the end of each period?

Accepted Answer

The present value of an annuity can be calculated using the formula PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual cash flow, r is the discount rate, and n is the number of periods. Plugging in the values given (PMT = $8,000, r = 0.12, n = 10), the calculation gives a present value of approximately $45,201.78.

Question 14

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?

Accepted Answer

To calculate the present value of an ordinary annuity, we can use the formula:

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

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

Plugging in the values given, we get:

PV = 4,000 * [(1 - (1+0.06)^-30) / 0.06]
PV = $55,059.32

Therefore, the present value today of the annuity is $55,059.32. The answer is B.

Question 15

Even with an interest rate of 0.0%,the future value of a 5-year $800 annual annuity will be greater than the present value of the same annuity.

Accepted Answer

The future value of an annuity considers the compound interest earned on the payments over time. With a 0.0% interest rate, there's no compound interest, so the future value simply equals the sum of the payments made, which does not exceed the present value of those same payments when considering time value of money principles.

Question 16

Five years ago,you paid for the right to receive twelve $25,000 annual end-of-the-year cash flows.If discounting the cash flows at an annual rate of 8%,what did you pay for these cash flows back then?

Accepted Answer

To calculate the present value of the 12 cash flows, we need to use the formula:

PV = CF / (1+r)^n

Where:
CF = the cash flow in each period ($25,000)
r = the discount rate (8% or 0.08)
n = the number of periods (12)

So, plugging in the numbers, we get:

PV = ($25,000 / (1+0.08)^1) + ($25,000 / (1+0.08)^2) + ... + ($25,000 / (1+0.08)^12)

Using a financial calculator or Excel, we can solve for PV and get:

PV = $188,401.95

Therefore, you paid $188,401.95 five years ago for the right to receive twelve $25,000 annual end-of-the-year cash flows, discounted at a rate of 8%.

Question 17

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 each cash flow is discounted back to its present value, which reduces the amount due to the time value of money.

Question 18

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin three years from today and last for a total of ten cash flows.Using a discount rate of 4%,what are those cash flows worth in today's dollars?

Accepted Answer

The answer of You have an annuity of equal annual...

Question 19

What is the present value of a stream of annual end-of-the-year annuity cash flows if the discount rate is 0%,and the cash flows of $50 last for 25 years?

Accepted Answer

At a 0% discount rate, the present value of the annuity is simply the sum of the cash flows, which is $50 per year for 25 years, totaling $1,250.

Question 20

Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years old.Amy just graduated from a university in the West.Upon graduation,she took a job with a starting annual salary of $50,000.Amy asks you to answer the following two questions:
1.If her salary increases at a rate roughly equal to the U.S.long-run average annual rate of inflation over the past 80 years (about 3% per year),how large will her annual salary be in her last year before retirement? (Use 32 years.)
2.If her salary increases at a rate roughly equal to the U.S.long-run average annual rate of return on common stocks over the past 80 years (about 10.5% per year),how large will her annual salary be in her last year before retirement? (Use 32 years.)
After hearing your answers,Amy says,"WOW! That's quite a difference." She decides that she would like an income of $500,000 per year each year in retirement,provided in equal annual end-of-the-year cash flows.These cash flows need to last for 40 years,and her investments would earn an annual rate of return of 7% during her retirement.
Amy's final question to you is how much money must she save in equal annual end-of-the-year cash flows for the next 32 years to provide for her desired retirement,if her investments earn roughly the same rate of return as those earned by U.S.small stocks over the last 80 years (geometric average is about 12% per year).
Use a calculator to determine the answers to the different parts of the problem.

Accepted Answer

The answer of Amy Plisko is 23 years old and...

Quiz 4: The Time Value of Money Part 2

Which is greater,the present value of a five-year ordinary annuity of $300 discounted at 10%,or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?

What is the future value in year thirty-five of an ordinary annuity cash flow of $4,000 per year at an interest rate of 11.0% per year?

Autorola plans to invest $5,000 per year in equal end-of-the-year amounts at an interest rate of 6% compounded annually.How much will the firm have at the end of four years?

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

Which of the following is greater (answers rounded to the nearest cent) ?

You estimate that the drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $120,000 per year for the next ten years.If you discount these cash flows at an annual rate of 11%,what is the present value of your expected cash flows?

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

What is the future value in year four of an ordinary annuity cash flow of $6,000 per year at an interest rate of 12.00% per year?

You have the opportunity to purchase mineral rights to a property in Wyoming with expected annual cash flows of $8,000 per year for ten years.If you discount these cash flows at a rate of 12% per year,what are these cash flows worth today if the cash flows occur at the end of each period?

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?

Even with an interest rate of 0.0%,the future value of a 5-year $800 annual annuity will be greater than the present value of the same annuity.

Five years ago,you paid for the right to receive twelve $25,000 annual end-of-the-year cash flows.If discounting the cash flows at an annual rate of 8%,what did you pay for these cash flows back then?

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.

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin three years from today and last for a total of ten cash flows.Using a discount rate of 4%,what are those cash flows worth in today's dollars?

What is the present value of a stream of annual end-of-the-year annuity cash flows if the discount rate is 0%,and the cash flows of $50 last for 25 years?

Quiz 4: The Time Value of Money Part 2

Which is greater,the present value of a five-year ordinary annuity of $300 discounted at 10%,or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?

What is the future value in year thirty-five of an ordinary annuity cash flow of $4,000 per year at an interest rate of 11.0% per year?

Autorola plans to invest $5,000 per year in equal end-of-the-year amounts at an interest rate of 6% compounded annually.How much will the firm have at the end of four years?

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

Which of the following is greater (answers rounded to the nearest cent) ?

You estimate that the drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $120,000 per year for the next ten years.If you discount these cash flows at an annual rate of 11%,what is the present value of your expected cash flows?

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

What is the future value in year four of an ordinary annuity cash flow of $6,000 per year at an interest rate of 12.00% per year?

You have the opportunity to purchase mineral rights to a property in Wyoming with expected annual cash flows of $8,000 per year for ten years.If you discount these cash flows at a rate of 12% per year,what are these cash flows worth today if the cash flows occur at the end of each period?

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?

Even with an interest rate of 0.0%,the future value of a 5-year $800 annual annuity will be greater than the present value of the same annuity.

Five years ago,you paid for the right to receive twelve $25,000 annual end-of-the-year cash flows.If discounting the cash flows at an annual rate of 8%,what did you pay for these cash flows back then?

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.

You have an annuity of equal annual end-of-the-year cash flows of $500 that begin three years from today and last for a total of ten cash flows.Using a discount rate of 4%,what are those cash flows worth in today's dollars?

What is the present value of a stream of annual end-of-the-year annuity cash flows if the discount rate is 0%,and the cash flows of $50 last for 25 years?

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