Question

You usually go to the theater to see a lot of movies. Now you are considering buying a DVD player and renting movies instead. You currently pay $9 per movie when you go to the theater but if you buy the DVD player you will have to pay only $5 per movie rental. You estimate that the DVD player will cost $400 (at t = 0) and will last 3 years. Except for cost, you are indifferent to seeing movies at home or in the theater. Assume that the cost of theater tickets and rental payments occur at the end of each month and that you use the DVD player only to watch movies. Assume that you watch the same number of movies every month. Your discount rate is 1% per month. Assume that there is no inflation. How many movies per month must you watch for the DVD player purchase to be a smart purchase?

Answer 1

You must watch minimum of 200 movies per month for the DVD player purchase to be a smart purchase.

Step-by-step explanation:

Let assume that you watch 100 movies in a month:

For going to theater:

$9 × 100 = $900

For renting movies and using the DVD Player:

Renting = $5 × 100 = $500

DVD Player cost: $400

Total spent in a month = $500 + $400 = $900

Therefore, in a month, the amount spent going to theater = the amount spent using DVD Player and renting the Film.

Let assume you watch 200 movies in a month:

For going to theater:

$9 × 200 = $1800

For renting movies and using the DVD Player:

Renting = $5 × 200 = $1000

DVD Player cost: $400

Total spent in a month = $1000 + $400 = $1400

Therefore, amount spent using DVD Player and renting movies is cheaper than going to theater to watch movies in a month.

It is safe to conclude that for the DVD Player to be a smart purchase by you, you must watch minimum of 200 movies in a month.