The pizza store is expecting a decline in sales for the following year due to an ongoing pandemic. The store owner is considering applying for a loan from a local bank to make up for the expected loss, and you are hired as a consultant to compare the available loan options and recommend the most economical choice.

Part 1

The store operates 8 hours per day, 320 days per year. Each slice of pizza is sold at a price of $1.25. The cost of raw ingredients is roughly $1.00 per slice. The stores rent, utility costs, and other overhead costs add up to $10,000 per month. The cost associated with each employee (salary, benefits, etc.) is $3,000 per month, and the store owner has decided not to make any personnel reduction or increase in the foreseeable future. As an attempt to attract more customers, the store has a promotion day once a month over the next 12 months, where they offer general-purpose $20 gift cards to 3.5% of customers that visit the store on that day to be selected randomly. These gift cards can be used anywhere and do not necessarily have to be used at this store. Moreover, the store will not announce which day of the month will be the promotion day, hence the demand on promotion days is expected to be similar to any other day. The requested loan amount will be equal to the estimated loss over the next 12 months. Therefore, you need to first estimate how much the store will lose in this 1-year period. Due to lack of historical sales data, and given that today is the banks deadline for emergency loan applications, you decide to estimate the loss as follows:

a) Counting the number of customers and pizza slices sold in a 10-minute interval, it was determined that 40 slices of pizza were sold to 20 customers during this time. Estimate: (i) the number of slices sold per month, and (ii) cost of gift cards per month. The assumption is that the sales rate is constant throughout the day and across days over the next 12 months.

b) Given your estimates from part (a), estimate how much the store will lose over the next 12 months.

Part 2

The local bank is offering several 5-year emergency loan options to support small businesses impacted by the pandemic. The bank offers these loans at a 15% annual interest rate. The loan options areas follows:

Option 1: Pay interest each year, but make no principal payment until the end of the loan period.

Option 2: Make equal end-of-year principal payments and pay interest each year on the unpaid balance at the beginning of the year.

Option 3: Make equal end-of-year payments over the loan period.

Option 4: Make no payments until the end of the loan period.

Develop the cash flow diagram for the four plans.

Part 3

The store owner has asked you to develop a decision support tool (e.g., a spreadsheet) that allows the store to compare these four loan options under various interest rates and minimum attractive rate of return (MARR) for the store. In addition to the tool, they expect your report to include the following information:

a) Vary both rates from 5% to 20% in 1% increments and compute the present worth for each loan option under each scenario.

b) What is the most economical loan option if the borrowers MARR is greater than the lenders interest rate?

c) What is the most economical loan option if the borrowers MARR is equal to the lenders interest rate?

d) What is the most economical loan option if the borrowers MARR is less than the lenders interest rate?

e) Clearly explain the reason behind your findings for the three cases in parts (b)-(d).