Business, 10.09.2019 00:30 afosburgh20

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?
a. 5 percent
b. 6 percent
c. 7 percent
d. 8 percent

Answers: 3

Show answers

Answers

Answer from: hany90

The sum of the present value of the revenues from buying a bicycle is the closest to the price of a bicycle when we use an interest rate of:

d. 8 percent.

Explanation:

Making use of the present value concept is a useful way to compare cases where money is to be received in the future. The higher the present value, the better.

In this case, we don't know the sum of the present value of the revenues from buying one bicycle, so we have to determine it by using different interest rates (a. 5%, b. 6%, c. 7%, and d. 8%).Each time we determine a present value, we will compare it with the price of a bicycle ($249.66), to see at which interest rate is the present value closest to the price of the bicycle.Since we can sell the used bike for $25 at the end of the second year, we can add this money to the revenues of the second year ($115), to simplify calculations. We should then get a total of $115+$25=$140 by the end of the second year.The following formula is the one that we are going to use to determine our present value for each interest rate:

$P=\frac{C}{(1+r)^{n} }\\$

Where P: Present value (what we are going to determine),

C: Cash flow at a given period of time (what we are going to receive by the end of a given year; in this case, $140 for the first year, C₁, and another $140 for the second year, C₂),

r: Interest rate (we will use the different mentioned options of 5%, 6%, 7%, and 8%, or 0.05, 0.06, 0.07, and 0.08, respectively, until we get a present value that is the closest possible to the price of a bicycle), and

n: Number of periods of time (in this case, n=1 for the first year, and n=2 for the second year).

Now, since we are getting money twice (each year for two years), we can add the term for the second year to the formula, and we will get something like this:

$P=\frac{C_{1}}{(1+r)^{1} }+\frac{C_{2}}{(1+r)^{2} }\\\\P=\frac{C_{1}}{1+r }+\frac{C_{2}}{(1+r)^{2} }\\\\P=\frac{140dollars}{1+r }+\frac{140dollars}{(1+r)^{2} }\\\\P=140dollars*[\frac{1}{1+r }+\frac{1}{(1+r)^{2} }]$

We could further simplify our formula but it's better not complicate ourselves so much.

-------------------------------------------------------------------------------------------------------

Let's now start determining our present value of the revenues with the interest rate of 5%, or 0.05:

$P_{r:0.05}=140dollars*[\frac{1}{1+0.05}+\frac{1}{(1+0.05)^{2} }]\\\\P_{r:0.05}=140dollars*[\frac{1}{1.05}+\frac{1}{1.1025}]\\\\P_{r:0.05}=140dollars*[0.95238+0.90703]\\\\P_{r:0.05}=140dollars*1.85941\\\\P_{r:0.05}=260.31733dollars$

So we got a present value of P=$260.32 while using an interest rate of 5%, which is pretty close to the price of $249.66, but maybe not close enough. We should determine the difference between the present value and the price like this:

$Difference=260.32dollars-249.66dollars\\Difference=10.66dollars$

The less difference there is, the closer we get to the price of the bicycle. Let's use the following interest rate now.

-------------------------------------------------------------------------------------------------------

6%, or 0.06:

$P_{r:0.06}=140dollars*[\frac{1}{1+0.06}+\frac{1}{(1+0.06)^{2} }]\\\\P_{r:0.06}=140dollars*[\frac{1}{1.06}+\frac{1}{1.1236}]\\\\P_{r:0.06}=140dollars*[0.94340+0.89000]\\\\P_{r:0.06}=140dollars*1.83340\\\\P_{r:0.06}=256.67550dollars$

In the 6% interest rate case, our present value is of P=$256.68, which got us closer to the price of $249.66. We should calculate its difference with the price:

$Difference=256.68dollars-249.66dollars\\Difference=7.02dollars$

-------------------------------------------------------------------------------------------------------

7%, or 0.07:

$P_{r:0.07}=140dollars*[\frac{1}{1+0.07}+\frac{1}{(1+0.07)^{2} }]\\\\P_{r:0.07}=140dollars*[\frac{1}{1.07}+\frac{1}{1.1449}]\\\\P_{r:0.07}=140dollars*[0.93458+0.87344]\\\\P_{r:0.07}=140dollars*1.80802\\\\P_{r:0.07}=253.12262dollars$

The 7% case gave us a present value of P=$253.12. Its difference with the price is:

$Difference=253.12dollars-249.66dollars\\Difference=3.46dollars$

-------------------------------------------------------------------------------------------------------

8%, or 0.08:

$P_{r:0.08}=140dollars*[\frac{1}{1+0.08}+\frac{1}{(1+0.08)^{2} }]\\\\P_{r:0.08}=140dollars*[\frac{1}{1.08}+\frac{1}{1.1664}]\\\\P_{r:0.08}=140dollars*[0.92593+0.85734]\\\\P_{r:0.08}=140dollars*1.78327\\\\P_{r:0.08}=249.65763dollars$

This time, by using an interest rate of 8%, we got to the present value of P=$249.66, which is exactly the price of a bicycle. The difference in this case is therefore 0.

-------------------------------------------------------------------------------------------------------

So the sum of the present value of the revenues from buying a bicycle is the closest to the price of a bicycle when we use an interest rate of:

d. 8 percent.

Answer from: Quest

answer( isp );

Answer from: Quest

Gamma-rays can kill living cells, a fact which medicine uses to its advantage, using gamma-rays to kill cancerous cells.

Another question on Business

Business, 22.06.2019 00:10

Which of the following is a problem for the production of public goods?

Answers: 2

Answer

Business, 22.06.2019 01:30

The gomez company, a merchandising firm, has budgeted its activity for december according to the following information: • sales at $500,000, all for cash. • merchandise inventory on november 30 was $250,000. • the cash balance at december 1 was $20,000. • selling and administrative expenses are budgeted at $50,000 for december and are paid for in cash. • budgeted depreciation for december is $30,000. • the planned merchandise inventory on december 31 is $260,000. • the cost of goods sold represents 75% of the selling price. • all purchases are paid for in cash. the budgeted cash disbursements for december are:

Answers: 3

Answer

Business, 22.06.2019 16:00

What impact might an economic downturn have on a borrower’s fixed-rate mortgage? a. it might cause a borrower’s payments to go up. b. it might cause a borrower’s payments to go down. c. it has no impact because a fixed-rate mortgage cannot change. d. it has no impact because the economy does not affect interest rates.

Answers: 1

Answer

Business, 23.06.2019 00:40

Skathy lee berggren, a professor of oral communication at cornell university, indicates “a lot of my students really [only] scratch the surface with the type of research they’re doing.” according to andy guess, at inside higher ed, “just because students walk in the door as ‘digital natives’, doesn’t mean they’re equipped to handle the heavy lifting of digital databases and proprietary search engines that comprise the bulk of modern, online research techniques.” students erroneously think a google search is research. as you read through the reasons that should stimulate your interest in studying research methods or evaluate the nine factors that guarantee good research, what actions do you propose to narrow the gap between students’ research competence and what’s required of a modern college graduate about to become a manage

Answers: 1

Answer

You know the right answer?

Happy trails, a bicycle rental company, is considering purchasing three additional bicycles. each bi...

Questions