Question

In: Economics

The MRSP of car x is $20,000 and is expected to range 25 miles per gallon....


The MRSP of car x is $20,000 and is expected to range 25 miles per gallon.
MRSP of car y is $26,000 and is expected to range 35 mpg. All other costs are same including eventual market value.
1. if you drive 13,000 miles per year, where the average gas cost in $/gallon where you would be indifferent between car x and y? N= 4 years and MARR=9%.
2. Assume gas cost is $2.90 per gallon. Which car would you buy x or y? List any assumptions and justify your decision.

list steps pls no excel.

Solutions

Expert Solution

Answer 1

MRSP of Car X is $20000 and range is 25 miles per gallon.

I drive 13000 miles per year, hence my gas consumption annually will be = 13000/25 = 520 gallons

If price of gas is x per gallon my annual cost will be 520 * x = $520x annually

Present Worth of Gas cost will be given by PV = P * (1- (1+r)^-n) / r , P= -$520x, r = 9%, n= 4 years

Hence PV = -520x * (1-(1+9%)^-4 /9%

= -520x * (1-(1.09)^-4 /0.09

= -520x * (1-0.7084) /0.09

= -520x * 0.2916/0.09

= -$1684.8x

Hence Total Present worth of Car X = Initial cost + Present Worth of Fuel cost = -20000 - 1684.8x

MRSP of Car Y is $26000 and range is 35 miles per gallon.

I drive 13000 miles per year, hence my gas consumption annually will be = 13000/35 = 371.43 gallons

If price of gas is x per gallon my annual cost will be 371.43 * x = $371.43x annually

Present Worth of Gas cost will be given by PV = P * (1- (1+r)^-n) / r , P= -$371.43x, r = 9%, n= 4 years

Hence PV = -371.43x * (1-(1+9%)^-4 /9%

= -371.43x * (1-(1.09)^-4 /0.09

= -371.43x * (1-0.7084) /0.09

= -371.43x * 0.2916/0.09

= -$1203.43x

Hence Total Present worth of Car Y = Initial cost + Present Worth of Fuel cost = -26000 - 1203.43x

I will be indifferent when Present Worth of Car X = Present Worth of Car Y

Hence -20000 - 1684.8x = -26000 - 1203.43x

or, 26000 -20000 = 1684.8x -1203.43x

or, 6000 = 481.37x

or, x = 12.46

Hence at a Gas Price of $12.46 I will be indifferent between Car X and Car Y

Answer 2

At Gas Price of $2.90,

Total Present worth of Car X = -20000 - 1684.8x= -20000 - 1684.8 * 2.9= -20000 - 4885.92 = -$24885.92

Total Present worth of Car Y = -26000 - 1203.43x = -26000 - 1203.43 * 2.90 = -26000 - 3489.947 = -$29489.947

Since the Net Present Worth of Car X is higher at Gas Price of $2.90 Car X shall be purchased


Related Solutions

Your car gets 25 miles per gallon (mpg) at 60 miles per hour (mph) and 18...
Your car gets 25 miles per gallon (mpg) at 60 miles per hour (mph) and 18 mpg at 70 mph. At what speed should you make a 600-mile trip: 1. If gas costs $3 per gallon and your time is worth $12 per hour? 2. If gas costs $4 per gallon and your time is worth $15 per hour? 3. If gas costs $5 per gallon and your time is worth $10 per hour? 4. Build a spreadsheet to calculate...
Your car gets 29 miles per gallon (mpg) at 60 miles per hour (mph) and 25...
Your car gets 29 miles per gallon (mpg) at 60 miles per hour (mph) and 25 mpg a 70 mph. At what speed should you make a 525-mile trip: If gas costs $3 per gallon and your time is worth $18 per hour If gas costs $4 per gallon and your time is worth $12 per hour If gas costs $5 per gallon and your time is worth $9 per hour
you currently drive 300 miles per week in a car that gets 20 miles per gallon...
you currently drive 300 miles per week in a car that gets 20 miles per gallon of gas. you are considering buying a new fuel-efficient car for $12,000 ( after trade-in on your current car) that gets 50 miles per gallon. Insurance premiums for the new and old car are $900 and $500 per year, respectively. you anticipate spending $1300 per year on repairs for the old car and having no repairs on the new car. assume gas costs $3.50...
Suppose gas costs $3 a gallon and the average car gets 28 miles per gallon. If...
Suppose gas costs $3 a gallon and the average car gets 28 miles per gallon. If Congress mandates that cars have to get 36 miles per gallon, by what percentage will this lower the costs of driving? If the elasticity of total miles driven (per year) with respect to the cost of driving is –1, by how much will total miles driven per year increase, assuming it is 10,000 miles at the beginning? How much will total annual gas consumption...
Suppose gas costs $3 a gallon and the average car gets 28 miles per gallon. If...
Suppose gas costs $3 a gallon and the average car gets 28 miles per gallon. If Congress mandates that cars have to get 36 miles per gallon, by what percentage will this lower the costs of driving? If the elasticity of total miles driven (per year) with respect to the cost of driving is –1, by how much will total miles driven per year increase, assuming it is 10,000 miles at the beginning? How much will total annual gas consumption...
Your car gets 22 miles per gallon (MPG) at 55 miles per hour (MPH) and 18...
Your car gets 22 miles per gallon (MPG) at 55 miles per hour (MPH) and 18 MPG at 65 MPH. At what speed should you make a 450-mile trip 1. If gas costs $2.95 per gallon and your time is worth $17/hour? 2. If gas costs $3.80 per gallon and your time is worth $11.5/hour? 3. If gas costs $4.75 per gallon and your time is worth $8.9/hour? 4. Building an Excel spreadsheet to calculate the total trip cost for...
The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the...
The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.5 miles per gallon. ​ (a) What proportion of hybrids gets over 61 miles per​ gallon? (b) What proportion of hybrids gets 52 miles per gallon or​ less? (c) What proportion of hybrids gets between 59 and 62 miles per​ gallon? (d) What is the probability that a randomly selected hybrid gets less...
The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the...
The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.​ (a) What proportion of hybrids gets over 61 miles per​ gallon? (b) What proportion of hybrids gets 51 miles per gallon or​ less? left parenthesis c right parenthesis What proportion of hybrids gets between 59 and 61 miles per​ gallon? (d) What is the probability that a randomly selected...
The average gas mileage of a certain model car is 28.0 miles per gallon. If the...
The average gas mileage of a certain model car is 28.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.4 miles per gallon, find the probability that a car has a gas mileage of between 26.8 and 27.2 miles per gallon.   In addition to the answer, please write out your steps and thoughts that led you to your answer.
The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline...
The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 27.4 mpg and a standard deviation of 12.3 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT