Ray owns a gym and he needs equipment for a new workout class. He has two different options:
• Lease equipment for $1100 per month.
• Purchase new equipment for $24 000 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?
To calculate the profit, we need to subtract the expenses from the revenue.
a) If Ray leases the equipment for $1100 per month, the total expense for 2 years would be:
Monthly expense = $1100
Total expense = 12 months/year * 2 years * $1100/month = $26,400
The revenue from the workout class would be:
Revenue per class = $285
Number of classes per week = 3
Number of weeks in 2 years = 52 weeks/year * 2 years = 104 weeks
Total revenue = $285/class * 3 classes/week * 104 weeks = $88,920
Profit = Total revenue - Total expense = $88,920 - $26,400 = $62,520
Therefore, Ray will make a profit of $62,520 if he leases the equipment over 2 years.
b) If Ray buys the equipment for $24,000 financed by a bank loan with an interest rate of 7.1% compounded monthly, he will make monthly payments over 2 years. To calculate the monthly payment, we can use the formula for a fixed loan payment:
Loan amount = $24,000
Interest rate per month = 7.1% / 12 months = 0.5917%
Number of months = 2 years * 12 months/year = 24 months
Monthly payment = (Loan amount * Interest rate) / (1 - (1 + Interest rate)^(-Number of months))
Monthly payment = ($24,000 * 0.5917%) / (1 - (1 + 0.5917%)^(-24)) = $1068.16
The total amount paid over 2 years would be:
Total payments = Monthly payment * Number of months = $1068.16/month * 24 months = $25,636.64
After 2 years, Ray can sell the equipment for $3800. Therefore, his total revenue from the workout class and selling the equipment would be:
Total revenue = $3800 + $88,920 = $92,720
Profit = Total revenue - Total payments = $92,720 - $25,636.64 = $67,083.36
Therefore, Ray will make a profit of $67,083.36 if he buys the equipment over 2 years.
To calculate the profit in each scenario, we need to consider the expenses and revenue generated over the 2 years.
a) If Ray leases the equipment, the monthly expense will be $1100. Over 2 years, the total expense will be:
Total Expense = Monthly Expense x Number of Months
Total Expense = $1100 x 12 x 2
Total Expense = $26,400
Now, let's calculate the revenue. The workout class runs 3 days a week, so the number of workouts per month is:
Workouts per Month = 3 workouts/week x 4 weeks/month
Workouts per Month = 12 workouts/month
The revenue generated per month will be:
Monthly Revenue = Workouts per Month x Revenue per Workout
Monthly Revenue = 12 workouts/month x $285/workout
Monthly Revenue = $3,420
Over 2 years, the total revenue will be:
Total Revenue = Monthly Revenue x Number of Months
Total Revenue = $3,420 x 12 x 2
Total Revenue = $82,080
To calculate the profit, we subtract the total expense from the total revenue:
Profit = Total Revenue - Total Expense
Profit = $82,080 - $26,400
Profit = $55,680
Therefore, if Ray leases the equipment, his profit over 2 years will be $55,680.
b) If Ray buys the equipment, he will have an upfront expense of $24,000. He will also have to pay interest on the bank loan for 2 years, with monthly payments.
The amount financed is $24,000, and the interest rate is 7.1% compounded monthly. To calculate the monthly payment, we can use a loan payment formula or a financial calculator.
Using a loan payment formula, the monthly payment (P) can be calculated as:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
r = monthly interest rate (7.1% / 12)
PV = present value (loan amount) = $24,000
n = number of periods (months) = 2 years x 12 months/year
Using these values, we can calculate the monthly payment:
r = 7.1% / 12 = 0.00592
n = 2 years x 12 months/year = 24 months
P = (0.00592 * $24,000) / (1 - (1 + 0.00592)^(-24))
P ≈ $1,083.19
Now, let's calculate the total loan payments over 2 years:
Total Loan Payments = Monthly Payment x Number of Months
Total Loan Payments = $1,083.19 x 24
Total Loan Payments = $25,996.56
However, at the end of 2 years, Ray can sell the equipment for $3,800. So, his net cost after selling the equipment will be:
Net Cost = Total Loan Payments - Selling Price
Net Cost = $25,996.56 - $3,800
Net Cost = $22,196.56
The revenue generated per month will be the same as in the lease scenario:
Monthly Revenue = $3,420
Over 2 years, the total revenue will be:
Total Revenue = Monthly Revenue x Number of Months
Total Revenue = $3,420 x 12 x 2
Total Revenue = $82,080
To calculate the profit, we subtract the net cost from the total revenue:
Profit = Total Revenue - Net Cost
Profit = $82,080 - $22,196.56
Profit = $59,883.44
Therefore, if Ray buys the equipment, his profit over 2 years will be $59,883.44.
In conclusion, Ray will make a higher profit of $59,883.44 over 2 years if he buys the equipment compared to leasing it for $55,680.