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my house sits on two acres of land. i need to make a decision as to whether i mo

ID: 2754039 • Letter: M

Question

my house sits on two acres of land. i need to make a decision as to whether i mow the grass myself or hire someone to do it for me. i have estimated that the law has to be mowed 20 times per year on average. The mowing company offers to mow the grass for $80 a visit. they also offer a contract so that if i agree to let them mow, they will not invrease their price for five years.

If i mow the grass myself i will buy a john deere lawn tractor for $2500. the tractor will last exactly five years and will have noscrap value. gas and maintenance of the tractor will be $250 a year.no interest on tractor.

Assume that these are the only costs. for simplicity, assume i would buy the john deere tractor at the start of the year and that the expensesfor the tractor or payments to the lawn service would be once a year, at the end of the year. Assume that i place no value on my time.

a) If money is worth 7% to me, after tax, what are the present values of the two choices?

b) At what price to mow my lawn would i be indifferent between each choice?

Explanation / Answer

a)

Alternative 1: Hire mowing company

Cost per trip = $80

No. of Trips per year = 20

Annual cost = $80 * 20 = $1,600

Present value of annuity of $1,600 over 5 years = $1,600 * (1 – 1.07-5)/0.07 = $1,600 * 4.100 = $6,560

Alternative 2: Mowing the grass self

Annual cost of the tractor = $250

Present value of annuity of $250 over 5 years = $250 * (1 – 1.07-5)/0.07 = $250 * 4.100 = $1,025

Cost of tractor = $2,500

Present value of proposal = $2,500 + $1,025 = $3,525

b)

In order to be indifferent between each choice, present value of each choice shall be equal.

Let the annual cost to mow the land be P.

P* 4.100 = $3,525

P = $860

Price to be paid to mow = $860 / 20 = $43 per visit