Question

A professional photographer who specializes in wedding-related activities paid $48,500 for equipment that will have a $2000 salvage value after 5 years. He estimates that his costs associated with each event amount to $65 per day. If he charges $300 per day for his services, how many days per year must he be employed in order to break even at an interest rate of 9% per year?

The number of days required for break even is determined to be_____ per year.

Answer 1

Initial Cost of equipment=Co=-$48500

Salvage value=S=$2000

Interest rate=i=9%

Useful life=n=5

Let photographer is employed for X days per year

Annual Cost=AOC=65X

Annual Revenue=AR=300X

Net Revenue per year=AR-AOC=(300-65)*X=235X

In the case of break even

0=PW of Initial Cost+PW of net revenue+PW of salvage

0=-48500+235X*(P/A,9%,5)+2000*(P/F,9%,5)

Let us calculate interest factors

(Interest factors can also be directly be held from interest factors tables given in books)

(I shall calculate the interest factors rounded up to 6 decimal places for better accuracy)

(P/F,0.09,5)=1/(1+0.09)⁵=0.649931

Now, we plug in interest factors

0=-48500+235X*(P/A,9%,5)+2000*(P/F,9%,5)

0=-48500+235X*3.889651+2000*0.649931

X=(48500-2000*0.649931)/(235*3.889651)=51.64 days