You and one of your classmates are considering setting up a prescription delivery service for local residents in Mount Pearl. In order to start the business you will need to purchase a car for $7,200 which you expect you will be able to sell for $3,600 at the end of every two years (you'll have to purchase a new equivalent car at that time). Insurance costs are $560 for each six months of operation, starting immediately, and advertising costs (flyers, newspaper ads, etc.) are estimated to be $110 per month. All calculations are performed using 4 significant figures. The big question is how many customers you will have, but you figuring on setting a fee of $2 per delivery, which will be payable by your clients at the end of each month. Assuming a stable interest rate of 6% per year, compounded monthly what is the break even number of deliveries per month?
You and one of your classmates are considering setting up a prescription delivery service for local residents in Mount Pearl. In order to start the business you will need to purchase a car for $7,200 which you expect you will be able to sell for $3,600 at the end of every two years (you'll have to purchase a new equivalent car at that time). Insurance costs are $560 for each six months of operation, starting immediately, and advertising costs (flyers, newspaper ads, etc.) are estimated to be $110 per month. All calculations are performed using 4 significant figures. The big question is how many customers you will have, but you figuring on setting a fee of $2 per delivery, which will be payable by your clients at the end of each month. Assuming a stable interest rate of 6% per year, compounded monthly what is the break even number of deliveries per month?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![You and one of your classmates are considering setting up a prescription delivery service
for local residents in Mount Pearl. In order to start the business you will need to purchase
a car for $6000, which you expect you will be able to sell for $3000 at the end of every two
years (you'll have to purchase a new equivalent car at that time). Insurance costs are $600
for each six months of operation, starting immediately, and advertising costs (flyers,
newspaper ads, etc.) are estimated to be $100 per month. The big question is how many
customers you will have, but you are figuring on setting a fee of $2 per delivery, which will
be payable by your clients at the end of each month. Assuming a stable interest rate of
8% per year, compounded monthly, what is the break-even number of deliveries per
month? (NOTE: All calculations should be performed using 4 significant figures.)
Solution:
Let D = the number of deliveries per month; % monthly interest is i = 8%/12 = 0.6667%
{interest factors for 0.6667% are attached}
Using the Capital Recovery Formula for the vehicle cost, set up an equation for the
Equivalent Monthly Worth (EMW) of the project as:
EMW = (Monthly Revenues) - (Monthly Costs)
=($2. D)-(vehicle cost+ advertising cost + insurance cost)
= ($2.D)-([(P-S)(A/P, I, N) + Si] + ad. cost + insurance cost)
where the vehicle cost is: (P-S)(A/P, i, N) + Si
= (6000-3000)(A/P, 0.6667%, 24) + 3000(0.006667)
= (3000)(0.04523) +20= 135.69 + 20 = 155.69
and the Monthly Costs are: (vehicle cost + ad. cost + insurance cost)
= 155.69 + 100+600(A/P, 0.6667%, 6)
= 255.69 + 600(0.17058) = 255.69 + 102.35 = 358.04
Now the EMW = ($2. D) - (vehicle cost + ad. cost + insurance cost) = ($2D) - ($358)
Next, we set the EMW equal to 0 and solve for D: 0 = 2D - 358
2D = 358
The break-even number of deliveries per month is D = 179.
or: D= 358/2 = 179
NOTE: The Maple TA solution shows a table of values and suggests plotting a curve or using linear
interpolation to come up with the solution to the EMW equation formed. However, we can
calculate the factors for (A/P, 1, 24) and (A/P, i, 6) to make this solution much easier.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96ed4f2e-a0e5-40d5-9d9a-4e9c33f2cc14%2Fb4e05a5a-156f-46e2-acbd-a7f9a7f79ad4%2F88imocc_processed.png&w=3840&q=75)
Transcribed Image Text:You and one of your classmates are considering setting up a prescription delivery service
for local residents in Mount Pearl. In order to start the business you will need to purchase
a car for $6000, which you expect you will be able to sell for $3000 at the end of every two
years (you'll have to purchase a new equivalent car at that time). Insurance costs are $600
for each six months of operation, starting immediately, and advertising costs (flyers,
newspaper ads, etc.) are estimated to be $100 per month. The big question is how many
customers you will have, but you are figuring on setting a fee of $2 per delivery, which will
be payable by your clients at the end of each month. Assuming a stable interest rate of
8% per year, compounded monthly, what is the break-even number of deliveries per
month? (NOTE: All calculations should be performed using 4 significant figures.)
Solution:
Let D = the number of deliveries per month; % monthly interest is i = 8%/12 = 0.6667%
{interest factors for 0.6667% are attached}
Using the Capital Recovery Formula for the vehicle cost, set up an equation for the
Equivalent Monthly Worth (EMW) of the project as:
EMW = (Monthly Revenues) - (Monthly Costs)
=($2. D)-(vehicle cost+ advertising cost + insurance cost)
= ($2.D)-([(P-S)(A/P, I, N) + Si] + ad. cost + insurance cost)
where the vehicle cost is: (P-S)(A/P, i, N) + Si
= (6000-3000)(A/P, 0.6667%, 24) + 3000(0.006667)
= (3000)(0.04523) +20= 135.69 + 20 = 155.69
and the Monthly Costs are: (vehicle cost + ad. cost + insurance cost)
= 155.69 + 100+600(A/P, 0.6667%, 6)
= 255.69 + 600(0.17058) = 255.69 + 102.35 = 358.04
Now the EMW = ($2. D) - (vehicle cost + ad. cost + insurance cost) = ($2D) - ($358)
Next, we set the EMW equal to 0 and solve for D: 0 = 2D - 358
2D = 358
The break-even number of deliveries per month is D = 179.
or: D= 358/2 = 179
NOTE: The Maple TA solution shows a table of values and suggests plotting a curve or using linear
interpolation to come up with the solution to the EMW equation formed. However, we can
calculate the factors for (A/P, 1, 24) and (A/P, i, 6) to make this solution much easier.
![You and one of your classmates are considering setting up a prescription delivery service for local residents in Mount Pearl. In
order to start the business you will need to purchase a car for $7,200 which you expect you will be able to sell for $3,600 at the
end of every two years (you'll have to purchase a new equivalent car at that time). Insurance costs are $560 for each six months
of operation, starting immediately, and advertising costs (flyers, newspaper ads, etc.) are estimated to be $110 per month.
All calculations are performed using 4 significant figures.
The big question is how many customers you will have, but you figuring on setting a fee of $2 per delivery, which will be payable
by your clients at the end of each month.
Assuming a stable interest rate of 6% per year, compounded monthly what is the break even number of deliveries per month?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96ed4f2e-a0e5-40d5-9d9a-4e9c33f2cc14%2Fb4e05a5a-156f-46e2-acbd-a7f9a7f79ad4%2Furr34r_processed.png&w=3840&q=75)
Transcribed Image Text:You and one of your classmates are considering setting up a prescription delivery service for local residents in Mount Pearl. In
order to start the business you will need to purchase a car for $7,200 which you expect you will be able to sell for $3,600 at the
end of every two years (you'll have to purchase a new equivalent car at that time). Insurance costs are $560 for each six months
of operation, starting immediately, and advertising costs (flyers, newspaper ads, etc.) are estimated to be $110 per month.
All calculations are performed using 4 significant figures.
The big question is how many customers you will have, but you figuring on setting a fee of $2 per delivery, which will be payable
by your clients at the end of each month.
Assuming a stable interest rate of 6% per year, compounded monthly what is the break even number of deliveries per month?
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