Question

The Hendersons have just bought a home that requires some monthly yard maintenance. They are trying to decide if they should hire a professional lawn care service to maintain the property or do it themselves. Below are the costs associated with both options:

Professional Service Option
Do-It-Yourself Option
$75 for the first month
$250 lawnmower
$45 per month after initial visit
$135 edger
Includes mowing and edging the lawn, trimming the bushes, and raking the leaves.
$69 hedge trimmer

$25 rake

How long would it take before the Hendersons would recover their costs if they chose to do it themselves over the professional service?

Answer 1

Total DIY startup cost = 250 + 135 + 69 + 25 = $479.

Professional total after n months = 75 + 45(n − 1).

Set them equal: 75 + 45(n − 1) = 479
45(n − 1) = 404
n − 1 = 404/45 ≈ 8.9778
n ≈ 9.98 months.

So in practice they recover their costs at about 10 months. (After 9 months the pro has cost $435; after 10 months the pro has cost $480, just $1 more than the DIY total.)