# Case Study – Chapter 4

Morden Shapiro

## Leverage

Leverage

1. use borrowed capital for (an investment), expecting the profits made to be greater than the interest payable.
“without clear legal title to their assets, they own property that cannot be leveraged as collateral for loans”
2. use (something) to maximum advantage.
“the organization needs to leverage its key resources”

[Source: Oxford dictionary]

Most business make decisions that involve the concept of leverage. For example,

“Can I borrow dollars at a cost of  dollars and then use those borrowed dollars in some way that will generate an amount greater than  dollars AND enable me to repay the original borrowing of  dollars?”

Caution: In this case we will ignore the following reality:

If the business already has the $x$ dollars, then the “cost” of those funds can be considered to be what those funds would have earned if used elsewhere. The already available / owned funds are never considered to be “free”.

### Background

Jim’s friends Mary and Robert need cash for the next year in order to renovate a live-in apartment in their house for their parents. They are confident that they will be able to repay the debt in one year from Robert’s annual Christmas bonus. Jim has the borrowing power to obtain the funds from his Chartered Bank at a preferred customer borrowing rate. Mary and Robert have asked Jim if he would be able to help them out. They don’t want to get into a negotiation with Jim and so they have said they would want to pay an interest rate that is 3 percentage points greater than Jim would have to pay his bank in order to borrow the funds.

If Jim borrows these funds at his bank and lends the funds to Mary and Robert at their offered rate of interest, then Jim is said to have “leveraged” his borrowing. His “gain” is the 3% by which Mary’s and Robert’s interest payment exceeds Jim’s borrowing cost.

### Assignment 1

1. In mathematical terms express the calculation that expresses how Jim’s gain on this borrowing / lending transaction arises.
2. Create an Excel spreadsheet that demonstrates the relationship between Jim’s preferred customer borrowing rate and Mary’s and Robert’s interest payment.

### Assignment 2

Assume that Jim has the opportunity to purchase a new piece of equipment for his manufacturing plant for the sole purpose of manufacturing a new item to be identified as SuperMonster in his Toys for Kids product line. The machine is capable of producing x units per month. The total cost for the machine is y dollars (including the cost of funds). The machine is estimated to have a usable lifetime at full capacity of 5 years. Jim is confident of the following:

• Each unit of SuperMonster produced by this machine will cost $z$ dollars to manufacture and deliver. All other costs will be “piggy-backed” on top of Jim’s business’s existing costs.
• Jim will be able to sell all of the production that this machine is capable of generating for the next 5 years.
• The delivered selling price of each unit manufactured by this machine will be $8z$ dollars which Jim estimates will reduce by 20% (of the original selling price) per year for the next 5 years.
1. Given Jim’s assumptions and using the concept of leverage, express in mathematical terms the calculation that Jim must make in order to decide whether or not to seize this opportunity.
2. Identify and explain any relationships amongst the elements of your response to Assignment 2 which must exist for Jim to achieve a “gain” should he choose to proceed with this new piece of equipment.
For example: “Sales in a given year must exceed costs in that same year.”

Attribution: Case study by Morden Shapiro (Ontario Tech University), published under Creative Commons Attribution-NonCommercial-ShareAlike licence (CC-BY-NC-SA)

Any modifications to this case study may affect its solvability and caution is advised.