Question 1

A car salesperson gives you four alternative ways to pay for your car.The first is to pay $18,000 today.The second is to pay $19,000 one year from today.The third is to pay $20,300 two years from today.The fourth is to pay $21,500 three years from today.If the interest rate is 6 percent,which payment option has the lowest present value and which has the highest?

Accepted Answer

To find the present value of each payment option, we can use 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 years.

1) PV = $18,000
2) PV = $19,000/(1+0.06)^1 = $17,924.53
3) PV = $20,300/(1+0.06)^2 = $17,024.91
4) PV = $21,500/(1+0.06)^3 = $17,067.54

Therefore, the lowest present value is option 3 ($17,024.91) and the highest present value is option 1 ($18,000). Option 2 is the best choice as it has the lowest present value among all the options.

Question 2

Which,if any,of the present values below are correct?

Accepted Answer

The correct formula to calculate present value is: PV = FV / (1 + r)^n, where PV is present value, FV is future value, r is the interest rate, and n is the number of periods. Using this formula for each option, we get:
A) PV = 1000 / (1 + 0.08)^1 = $925.93
B) PV = 1000 / (1 + 0.09)^1 = $917.43
C) PV = 1000 / (1 + 0.10)^1 = $909.09

Therefore, option C is the closest to the given value of $1,000 at 10% interest.

Question 3

HydroGrow is considering building a new building in which to grow tomatoes.The board meets and decides that this is the right thing to do.Before they can put their plans into action,the interest rate increases.The present value of the returns from this investment project

Accepted Answer

An increase in the interest rate will increase the discount rate used to calculate the present value of the returns from the investment project. This will result in a lower present value of the returns, making the project less attractive and reducing the likelihood that HydroGrow will go forward with it.

Question 4

A University of Iowa basketball standout is offered a choice of contracts by the New York Liberty.The first one gives her $100,000 one year from today and $100,000 two years from today.The second one gives her $132,000 one year from today and $66,000 two years from today.As her agent,you must compute the present value of each contract.Which of the following interest rates is the lowest one at which the present value of the second contract exceeds that of the first?

Accepted Answer

The answer of A University of Iowa basketball standout is...

Question 5

The You Look Marvelous! cosmetic company is considering building a new shampoo factory.Its accountants and board of directors meet and decide that its not a good idea to build the factory.If interest rates fall after the meeting

Accepted Answer

When interest rates fall, the present value of future cash flows from the factory increases, making it more financially attractive to build the factory.

Question 6

Other things the same,as the interest rate rises,the present value of future revenues from investment projects

Accepted Answer

As the interest rate rises, the present value of future revenues from investment projects falls, making them less attractive, so investment spending falls.

Question 7

A judge requires Harry to make a payment to Sally.The judge says that Harry can pay her either $10,000 today or $11,000 two years from today.Of the following interest rates,which is the highest one at which Harry would be better off paying the money today?

Accepted Answer

The answer of A judge requires Harry to make a...

Question 8

You have a contract with someone who has agreed to pay you $20,000 in four years.She offers to pay you now instead.For which of the following interest rates and payments would you take the money today?.

Accepted Answer

The present value of $20,000 in four years at 8% is $15,000. The present value of $20,000 in four years at 7% is $16,000. The present value of $20,000 in four years at 6% is $17,000. Therefore, you would take the money today for any of the given interest rates and payments.

Question 9

A firm has four different investment options.Option A will give the firm $10 million at the end of one year,$10 million at the end of two years,and $10 million at the end of three years.Option B will give the firm $5 million at the end of one year,$10 million at the end of two years,and $15 million at the end of three years.Option C will give the firm $15 million at the end of one year,$10 million at the end of two years,and $5 million at the end of three years.Option D will give the firm $21 million at the end of one year,nothing at the end of two years,and $9 million at the end of three years.Which of these options has the highest present value if the rate of interest is 5 percent?

Accepted Answer

To compare the present values of each option, we need to discount each cash flow to its present value using a 5% discount rate. The calculation for each option's present value is as follows:

Option A: PV = $10,000,000 / (1 + 0.05)^1 + $10,000,000 / (1 + 0.05)^2 + $10,000,000 / (1 + 0.05)^3 = $27,103,402.49
Option B: PV = $5,000,000 / (1 + 0.05)^1 + $10,000,000 / (1 + 0.05)^2 + $15,000,000 / (1 + 0.05)^3 = $26,983,024.69
Option C: PV = $15,000,000 / (1 + 0.05)^1 + $10,000,000 / (1 + 0.05)^2 + $5,000,000 / (1 + 0.05)^3 = $25,510,072.79
Option D: PV = $21,000,000 / (1 + 0.05)^1 + $0 / (1 + 0.05)^2 + $9,000,000 / (1 + 0.05)^3 = $27,301,038.61

Option D has the highest present value, so it is the best choice.

Question 10

A firm has three different investment options,each costing $10 million.Option A will generate $12 million in revenue at the end of one year.Option B will generate $15 million in revenue at the end of two years.Option C will generate $18 million in revenue at the end of three years.Which option should the firm choose?

Accepted Answer

The best investment option depends on the present value of future cash flows, which requires knowing the rate of interest to discount future revenues.

Question 11

Dobson Construction has an investment project that would cost $150,000 today and yield a one-time payoff of $167,000 in two years.What is the highest interest rate at which Dobson would find this project profitable?

Accepted Answer

The project is profitable if the present value of the payoff is greater than the initial investment. The present value of $167,000 in two years at 5% interest is $151,200, which is greater than $150,000. At 6%, the present value is $148,305, which is less than $150,000. Therefore, the highest interest rate at which the project is profitable is 5%.

Question 12

Which of the following has a present value of $100?

Accepted Answer

We can use the present value formula to determine which option is worth $100 today. The formula is: Present Value = Future Value / (1 + r)^n, where r is the interest rate and n is the number of periods. Plugging in the values for each option, we get:

A) Present Value = 110 / (1 + 0.05)^2 = $100.00 (rounded to the nearest penny)
B) Present Value = 112.36 / (1 + 0.06)^2 = $100.00 (rounded to the nearest penny)
C) Present Value = 117.49 / (1 + 0.07)^2 = $100.00 (rounded to the nearest penny)

So, option B is the best choice because it has a future value of $112.36 in two years but is worth $100 today.

Question 13

Which of the following is correct if the interest rate is 6 percent?

Accepted Answer

According to the compound interest 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.
Using this formula, we can calculate the present values for both options:
PV1 = 215 / (1+0.06)^1 = $203.77 (rounded)
PV2 = 420 / (1+0.06)^1 = $396.23 (rounded)
Option B is correct because PV1 > $200 and PV2 < $400. The other options are incorrect because they either have both values above their respective thresholds (Option A and C) or both values below their respective thresholds (Option D).

Question 14

You have a choice among three options.Option 1: receive $900 immediately.Option 2: receive $1,200 one year from now.Option 3: receive $2,000 five years from now.The interest rate is 15% per year.Rank these three options from highest present value to lowest present value.

Accepted Answer

First, we need to calculate the present value of each option, given the interest rate of 15% per year:

Option 1: $900
Option 2: $1,200/(1+0.15) = $1,043
Option 3: $2,000/(1+0.15)^5 = $952

Therefore, the ranking from highest present value to lowest present value is: Option 2, Option 3, Option 1.

The best choice would be Option 2, since it has the highest present value among the three options.

Question 15

The K-Nine dog food company is considering the purchase of additional canning equipment.They expect that adding the equipment will yield $200,000 at the end of the first year and $250,000 at the end of the second year and then nothing after that.At which of the following prices and interest rates would K-Nine buy the equipment?

Accepted Answer

The answer of The K-Nine dog food company is considering...

Question 16

A firm has three different investment options.Option A will give the firm $10 million at the end of one year,$10 million at the end of two years,and $10 million at the end of three years.Option B will give the firm $15 million at the end of one year,$10 million at the end of two years,and $5 million at the end of three years.Option C will give the firm $30 million at the end of one year,and nothing thereafter.Which of these options has the highest present value?

Accepted Answer

The answer of A firm has three different investment options.Option...

Question 17

Dobson Construction has an investment project that would cost $150,000 today and yield a one-time payoff of $167,000 in three years.What is the highest interest rate at which Dobson would find this project profitable?

Accepted Answer

The answer of Dobson Construction has an investment project that...

Question 18

Happy Trails,a bicycle rental company,is considering purchasing three additional bicycles.Each bicycle would cost them $249.66.At the end of the first year the increase to their revenues would be $140 per bicycle.At the end of the second year the increase to their revenues would be $115 per bicycle and they can sell each used bike for another $25.At which of the following interest rates is the sum of the present value of the revenues from buying a bicycle closest to the price of a bicycle?

Accepted Answer

The answer of Happy Trails,a bicycle rental company,is considering purchasing...

Question 19

Heart's Restaurants is considering building a restaurant in a new location.The owners and their accountants decide that this is not the profitable thing to do.However,soon after both the interest rate and the cost of building the restaurant change.In which case do these changes both make it more likely that they will now build the restaurant?

Accepted Answer

If both interest rates and the cost of building the restaurant fall, it reduces the overall cost of financing and constructing the restaurant, making it more likely to be a profitable venture.

Question 20

Mixster Concrete Company is considering buying a new cement truck.The owners and their accountants decide that this is the profitable thing to do.Before they can buy the truck,the interest rate and price of trucks change.In which case do these changes both make them less likely to buy the truck?

Accepted Answer

If both interest rates and the price of trucks rise, it will increase the cost of borrowing to buy the truck and also increase the cost of purchasing the truck. This would make it less likely for Mixster Concrete Company to buy the truck.

Quiz 27: The Basic Tools of Finance