Question

Each year you need to power wash your deck. You can rent a power washer for $38 per day. If you go with this option, you will pay $38 each year starting today up to and including year 5 . If you buy the power washer, you will pay $100 today and the power washer will last up to and including year 5 . If your investments earn 4% compounded annually, how much does it save you in present value terms to own the power washer?

Answer 1

If you buy the power washer, you will pay $100 today and the power washer will last up to and including year 5

Therefore present value of buy the washer = $100

If you rent a power washer for $38 per year for 5 years; present value can be calculated in following manner –

We can use formula of the present value (PV) of annuity due calculation as payment is at beginning of the year

PV = PMT * [1- (1+i) ^-n / i] * (1+i)

Where,

Present value PV =?

Annual payments PMT = $34

Interest rate I/Y = 4% per year

Time period n = 5 years

Therefore,

PV = $34 * [1- (1+4%) ^-5 / 4%] * (1+4%)

OR PV = $157.42

Therefore present value of renting a power washer is $157.42

Saving in present value terms to owning the power washer = PV of renting – PV of buying

= $157.42 - $100

= $57.42