you work for a medium$-$sized company in the financial services sector, contemplating offering a new lending product to new and existing customers. Your department was tasked with evaluating the opportunity and creating a report for the Management Team addressing your findings.

The market segment is a subset of the financially underserved population, often characterized by limited access to financial services institutions and low or no credit score information. This underserved segment includes diverse communities and individuals from various socioeconomic backgrounds who, despite their potential and aspirations, are often excluded from the financial opportunities that can help them improve their financial well$-$being. Addressing the needs of this segment is crucial for promoting financial inclusion and ensuring that everyone has an equal chance to build a more secure and prosperous future.

Part I: Market Analysis and Competition

One of the existing market players is a cash$-$advance store, providing short terms loans to individuals in need of immediate funds. They offer two products to their customers:

two$-$week loans charging a $$75$ fee for each $$1,000.$ At the end of the two$-$weeks, the customers may pay back the total outstanding loan with the added fee or sign up for a new loan $($with new fees assessed$).$

a four$-$week variation of the above loan in which you are assessed the two $$75$ fees at the beginning of the loan, and pay back weekly installments for $4$ weeks. That is$,$ for each $$1000$ borrowed, you keep $$1000-$ $$150=$ $$850$ and make weekly payments of $$250$ for the following four weeks

Analyze this competitor$$s offerings by determining the APR and EAR of each of the products above $($assume a year consists of exactly $52$ weeks$).$ What are your observations about their business model and the products they offer?

Part II: NPV and IRR

After discussing the details of the market segment you are targeting with your Marketing and Risk Departments, your team learned that consumers would prefer access to longer loan terms. The Risk Department also mentioned that, historically, customers in this segment default on average at the following rates:

Month $123456$

Default Rate $10\%5\%4\%3\%2\%1\%$

That is$,$ we expect $10\%$ of loans to default before any payment takes place $($at month $1),5\%$ of the loans that were active after one month to default during the second month, and so on$.$

Your company also informed your team that they secured $$10$MM to provide $6-$month loans to customers and determined that the typically desired loan amount is $$1,000.$ In order to secure this amount, the company estimated that investors will require an annualized return of $18\%$ to compensate them for the inherent risk of this opportunity.

For the rest of your analysis, assume that the segment is large enough, costumers are keen on using your product, and that this opportunity is just a one$-$time program. In particular, this means that the company will be able to exhaust generate all the loans immediately and run this product only for the following $6$ months. Additionally, assume additional costs of $$250,000$ for each month until the program ends, starting today.

One of your team members suggested an APR of $36\%$ for this product. What's the maximum number of loans you will be able to provide using only the investor funds mentioned above? Note that the initial cost of this program is the cost of setting up the program plus the total principal of the loans generated. What is the IRR for this project at this APR? Are you able to offer the product at this rate? What is the breakeven APR for which you would be able to offer this product? That is$,$ what is the minimum APR you can charge your customers so the product generates the required returns?

After your analyses, the company decided to charge customers the breakeven APR plus $10\%.$ What are the new IRR and the NPV you expect this project to generate at this APR, taking into account the required return above? What are the expected accounting profits?

Part III: Scenario and Sensitivity Analysis

To get a better handle of this product, management asked your team to assess the sensitivity of this product to increases in each month's default rates. Namely, management wants to understand the impact on the NPV of a $1\%$ increase to each of the rates in the table above $($independently$).$ Plot a graph with the numbers you determined and explain your observations and what conclusions you can draw from this graph.

Additionally, management asked you to compute the impact to the NPV for the following stress scenarios in order to understand the impact an economic crisis can have on this product:

All default rates increase $1\mathrm{.}5$x

All default rates increase $2$x

What are your observations from the numbers you obtained?