You are the financial manager at Best Buy where a certain TV set is normally sold for $2,500 and the full purchase price is financed for 30 monthly payments at 24% per year compounded monthly, with the payments made at the end of each month. During Christmas Best Buy is planning to run a zero-interest financing sale during which you will offer the customers to finance the TV set over 30 months at 0% interest. How much do you need to charge for the TV set during the Christmas sale in order to earn your usual combined return on the sale and the financing?
How would I do this question? thanks
Facts:
PV= $2,500
APR= 24%
30 months payment
compounded monthly (every 12 months)
Step 1- Find EPR:
(1+APR/m)^m = (1+EPR)^f
(1+0.24/12)^12 = (1+EPR)^12
(1.268241795) = (1+EPR)^12
(1.268241795)^(1/12) = (1+EPR)
(1.02-1)= EPR
0.02= EPR
Step 2 - Find the PMT
PV= PMT (1 - (1/(1+EPR)^t))/EPR
2500 = PMT (1 - (1/1.02)^30))/0.02
2500/22.39565 = PMT
PMT = 111.63
Step 3 -
Customers pay $2500 so without interest they should be paying 2500/30 = 83.33
However they pay 111.63 every month which is 111.63-83.33= $28.3 of interest every month
So in 30 months total interest payed is $28.3*30= $849
Therefore if the manager wants to get the same amount of money but with 0% of interest he would have to charge $849+$2,500= $3,349
3349
To determine how much you would need to charge for the TV set during the Christmas sale in order to earn your usual combined return on the sale and financing, you can follow these steps:
Step 1: Calculate the present value (PV) of the monthly payments using the original financing terms.
PV = [Payment × (1 - (1 + interest rate)-number of periods)] / interest rate
where:
Payment = $2,500 / 30 (monthly payments)
Interest rate = 24% per year / 12 (compounded monthly)
Number of periods = 30 (monthly payments)
Step 2: Calculate the combined return on the sale and financing.
Combined Return = PV of the monthly payments + Purchase price
Step 3: Since the financing is zero-interest during the Christmas sale, the combined return on the sale and financing remains the same.
Step 4: Determine the new purchase price that would yield the same combined return.
Purchase price = Combined Return - PV
Now let's calculate the values:
Step 1:
Payment = $2,500 / 30 = $83.33 (rounded to the nearest cent)
Interest rate = 24% / 12 = 2% per month (as it's compounded monthly)
Number of periods = 30
PV = [$83.33 × (1 - (1 + 0.02)^-30)] / 0.02
PV ≈ $1,727.97 (rounded to the nearest cent)
Step 2:
Combined Return = PV + Purchase price
Step 3:
Since the financing is zero-interest during the Christmas sale, the Combined Return remains the same.
Step 4:
Purchase price = Combined Return - PV
Now, to find the purchase price during the Christmas sale:
Purchase price = Combined Return - PV
Purchase price = $1,727.97 + $2,500
Purchase price ≈ $4,228.04 (rounded to the nearest cent)
Therefore, in order to earn your usual combined return on the sale and financing, you would need to charge approximately $4,228.04 for the TV set during the Christmas sale.
To find out how much you need to charge for the TV set during the zero-interest financing sale, you will have to calculate the combined return on the sale and the financing. Here's how you can approach this problem:
1. Calculate the monthly payment amount: Since the purchase price is financed for 30 monthly payments, you need to find out the fixed payment amount. To do this, you can use the present value of an ordinary annuity formula:
PV = PMT x [1 - (1 + r)^(-n)] / r
Where:
PV = Present value or purchase price ($2,500 in this case)
PMT = Monthly payment amount (to be calculated)
r = Interest rate per period (24% per year compounded monthly, which is 2% per month)
n = Number of periods (30 months)
Substituting the given values into the formula, you can solve for PMT:
2,500 = PMT x [1 - (1 + 0.02)^(-30)] / 0.02
2. Calculate the total payments made over the 30-month period: Now that you have the monthly payment amount, multiply it by 30 to find the total payments made over the entire financing period.
Total Payments = Monthly Payment Amount x Number of Periods
3. Calculate the usual profit from financing: In the normal scenario where the TV set is sold for $2,500 and financed at 24% per year compounded monthly, calculate the interest earned on the financing.
A. Calculate the interest rate per month: 24% per year compounded monthly is equivalent to 2% per month.
B. Calculate the interest earned over the 30-month period using the formula for compound interest:
Interest Earned = PV x [(1 + r)^n - 1]
Substituting the values, you get:
Interest Earned = 2,500 x [(1 + 0.02)^30 - 1]
4. Add the usual profit from financing and profit from the sale: The usual combined return on the sale and financing is obtained by adding the interest earned from the financing and the profit from the sale.
Combined Return = Interest Earned + Profit from Sale
Now that you have the combined return, you can set it equal to what you want to earn during the zero-interest financing sale. Assuming you want to earn the same combined return as before, you can set up the equation:
Combined Return = Usual Combined Return
Solve the equation for the sale price, and you will have the amount you need to charge for the TV set during the Christmas sale to achieve your desired return.