Ray owns a gym and he needs equipment for a new workout class. He has two different options:
1. Lease equipment for $1100 per month
2. Purchase new equipment for $24000 which he will finance with a bank loan that charges an interest rate of 7.1%, compounded monthly. He will pay off the loan in 2 years with regular monthly payments. After 2 years, he can sell the equipment for $3800. The workout class runs 3 days a week and he expects to make $285 for each day that the workout class is run.
a) How much profit will Ray make over 2 years if he leases the equipment?
b) How much profit will Ray make over 2 years if he buys the equipment?
a) Well, leasing equipment means you're basically just renting it. So, Ray's profit will be as elusive as finding a parking spot at a busy gym. He'll have to subtract the $1100 monthly leasing cost from the $285 he earns per workout class day. Since there are 3 days in a week, that's 3 times $285, which is $855 a week. Now multiply that by the number of weeks in 2 years, which is approximately 104. (I did the math so you don't have to. You're welcome!) That comes out to be $88,920. But wait, subtract the total leasing cost over 2 years, which is 24 times $1100, or $26,400. Ouch! That means the profit after leasing the equipment for 2 years would be roughly... drumroll please... -$37,480. That's a downside with leasing. No profit, only more clown tears.
b) Now let's look at buying the equipment. Ray will pay $24,000 upfront and finance it with the bank loan. With an interest rate of 7.1% compounded monthly, that's like bench pressing a heavy interest bar. Ray will have to make monthly payments to the bank over 2 years. But hey, there's a silver lining! He can sell the equipment for $3800 after 2 years. So, let's crunch the numbers. The interest rate may be scary, but let's face it, finance is no laughing matter. The monthly payments can be calculated using the compound interest formula, but I'll spare you the details. After some calculations, we find that the monthly payments will be approximately $1129.35. To calculate the profit, we need to subtract the total loan payments from the revenue. Ray earns $855 per week, which we've already calculated. Multiply that by 3 to get the weekly revenue. Multiply it by 104 weeks to get the total revenue over 2 years. That comes out to be $88,920, just like before. But now, let's subtract the loan payments over 2 years, which is 24 times $1129.35... it's approximately $27,104.40. Finally, add the $3800 from selling the equipment. The profit after buying the equipment would be approximately... hold onto your funny bone... $60,615.60. Looks like buying the equipment takes the crown in the profit department. Ray can now juggle his way to success... or maybe leave the juggling to the clowns.
To calculate the profit for each option, we need to consider the cost of the equipment, the income generated from the workout class, and any additional expenses.
a) Profit if Ray leases the equipment:
The monthly lease cost is $1100. Since the workout class runs 3 days a week, Ray will have 12 class days in a month. Therefore, the lease cost per class day is $1100 / 12 = $91.67.
The income Ray will generate from each workout class is $285 per class day.
To calculate the profit, we subtract the lease cost per class day from the income generated per class day:
Profit per class day = Income per class day - Lease cost per class day
Profit per class day = $285 - $91.67 = $193.33
Since there are 12 class days in a month, the monthly profit is:
Monthly profit = Profit per class day * Number of class days in a month
Monthly profit = $193.33 * 12 = $2,320
Since the lease is for 2 years, the total profit over 2 years is:
Total profit = Monthly profit * Number of months
Total profit = $2,320 * 24 = $55,680
b) Profit if Ray buys the equipment:
The cost of the equipment is $24,000.
To calculate the monthly loan payment, we can use the formula for loan payments:
Monthly payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
The interest rate is 7.1% per year, compounded monthly. Therefore, the monthly interest rate is 7.1% / 12 = 0.5917%.
Let's calculate the monthly loan payment:
Monthly payment = ($24,000 * 0.005917) / (1 - (1 + 0.005917)^(-24))
Monthly payment = $1,111.44
The income Ray will generate from each workout class is $285 per class day.
To calculate the profit, we subtract the loan payment per class day from the income generated per class day:
Profit per class day = Income per class day - Loan payment per class day
Profit per class day = $285 - ($1,111.44 / 12) = $196.38
Since there are 12 class days in a month, the monthly profit is:
Monthly profit = Profit per class day * Number of class days in a month
Monthly profit = $196.38 * 12 = $2,356.56
Since the loan is for 2 years, the total profit over 2 years is:
Total profit = Monthly profit * Number of months
Total profit = $2,356.56 * 24 = $56,556.48
b) After 2 years, Ray can sell the equipment for $3800. Let's subtract the selling price from the total profit to calculate the net profit from buying the equipment:
Net profit = Total profit - Selling price of the equipment
Net profit = $56,556.48 - $3800 = $52,756.48
Therefore:
a) Ray will make a profit of $55,680 if he leases the equipment.
b) Ray will make a net profit of $52,756.48 if he buys the equipment.
To calculate the profits in both scenarios, we need to compare the income generated by the workout class with the expenses associated with each option.
a) If Ray leases the equipment, the monthly cost is $1100. Since the workout class runs 3 days a week, he will have 3 workouts per week * 4 weeks = 12 workouts per month.
The income generated by the workout class in one month is 12 workouts * $285 per workout = $3420.
Therefore, the monthly profit is $3420 - $1100 (lease cost) = $2320.
Over 2 years, the total profit obtained by leasing the equipment is $2320 * 24 months = $55,680.
b) If Ray buys the equipment, he will finance it through a bank loan. The principal amount of the loan is $24,000, and the interest rate is 7.1% per year, compounded monthly. The loan duration is 2 years or 24 months.
To calculate the monthly loan payment, we can use the formula for an amortized loan:
Loan Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
- P is the principal amount of the loan
- r is the monthly interest rate
- n is the total number of payments
First, we need to calculate the monthly interest rate:
Monthly interest rate = 7.1% / 12 = 0.59167%
Using the formula, the monthly loan payment is:
Loan Payment = $24,000 * (0.0059167 * (1 + 0.0059167)^24) / ((1 + 0.0059167)^24 - 1) ≈ $1,070.49
To calculate the total loan payments over 2 years, we multiply the monthly payment by the number of months: $1,070.49 * 24 = $25,691.76
After 2 years, Ray can sell the equipment for $3,800.
The total profit obtained by buying the equipment is the sum of the income generated by the workout class, the sale price of the equipment, and the negative value of the loan payments:
$285 * 12 workouts * 24 months + $3,800 - $25,691.76 = $16,508.24
Therefore, Ray will make a profit of $16,508.24 over 2 years if he buys the equipment.