Question

A professional photographer who specializes in wedding-related activities paid $47,500 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 $200 per day for his services, how many days per year must he be employed in order to break even at an interest rate of 10% per year? The number of days required for break even is determined to be 82 Incorrect per year.

Answer 1

At year 0 the present value of equipment or cash outflow = PV of purchasing equipment - PV of salvage value of equipment

= 47500 - 2000*PVIF(10%,5)

= 47500 - 2000*0.620921

= 47500 - 1241.841

= 46258.16 or 46258

Profit in a day = revenue service - cost

= 200 - 65

= 135

Now the Present value of ordinary annuity = P*[1 - (1+i/m)^(-n*m)]/(i/m)

where - P - Periodic payment 135

I - rate of interest 10%

m- no. of compounding in a period

n - No. of periods (suppose X) = ?

46258 = 135*[1 - (1+0.10/365)^(-n)]/(0.10/365)

(46258*0.10/365*1/135) = [1 - (1 + 0.000274)^(-n)]

0.093878 = 1 - 1.000274^(-n)

1 - 0.093878 = 1.000274^(-n)

0.906122 = 1.000274^(-n)

take log of both sides

log(0.906122) = log(1.000274)^(-n)

-0.04281 = -n log(1.000274) ---------------{ logm^n = n logm}

-0.04281 = -n * 0.000119

n = -0.04281/-0.000119

=359.84 days

Please check with your answer and let me know.