A businessman is considering how many limousines to purchase when he starts up a limousine service.Below are his estimates of the number of limousine rentals the service will make during a year,depending on the number of limousines available.
After paying all non-interest expenses,the owner expects to net $10 per rental.Each limousine costs $50,000.How many limousines should he purchase if the real interest rate is 5.5%?

Question

A businessman is considering how many limousines to purchase when he starts up a limousine service.Below are his estimates of the number of limousine rentals the service will make during a year,depending on the number of limousines available. 
After paying all non-interest expenses,the owner expects to net $10 per rental.Each limousine costs $50,000.How many limousines should he purchase if the real interest rate is 5.5%?

Quizplus · Accepted Answer

To determine how many limousines the businessman should purchase, we need to find the point of diminishing returns, where the cost of an additional limousine outweighs the additional revenue it brings in.

To do this, we calculate the net present value (NPV) of each option, which takes into account the time value of money (i.e. the fact that money is worth more now than it is in the future, due to inflation and the ability to invest it).

Using a discount rate of 5.5% (the real interest rate), we can discount each year's cash flow to its present value, and then sum up those values for each option.

We can then compare the NPV of each option to determine which one has the highest value. The option with the highest NPV is the best choice.

Here are the calculations:

Option 0: 0 limousines
NPV = (-$50,000) + ($10 x 0 rentals x (1/1.055)^1) = -$49,209.78

Option 1: 1 limousine
NPV = (-$50,000) + ($10 x 50 rentals x (1/1.055)^1) + ($10 x 60 rentals x (1/1.055)^2) = $7,150.58

Option 2: 2 limousines
NPV = (-$100,000) + ($10 x 90 rentals x (1/1.055)^1) + ($10 x 120 rentals x (1/1.055)^2) = $21,972.95

Option 3: 3 limousines
NPV = (-$150,000) + ($10 x 120 rentals x (1/1.055)^1) + ($10 x 140 rentals x (1/1.055)^2) = $22,372.08

Option 4: 4 limousines
NPV = (-$200,000) + ($10 x 150 rentals x (1/1.055)^1) + ($10 x 155 rentals x (1/1.055)^2) = $16,521.11

Based on these calculations, Option 2 (purchasing 2 limousines) has the highest NPV of $21,972.95. Therefore, the businessman should purchase 2 limousines to maximize his profits.

A Businessman Is Considering How Many Limousines to Purchase When