## Problem Definition

Your client is a very **small consumer packaging** company. One of their **product lines** is **plastic bag**s that are designed to **store food**. They currently have one production machine dedicated to this product.

Since product **demand** currently **exceeds** your client’s **production** **capacity**, they want you to answer two key questions:

1. How can they **best utilize** their current **bag capacity**?

2. Should they **invest** in a **new bag machine**?

## Comments

Since this is an **interviewer-led case**, the interviewer should guide through the interview.

The case is split into **three parts**.

In the **first part,** the interviewee needs to **evaluate** existing **products** and **machine capacity**. The interviewee should **calculate** the client’s most profitable product mix, keeping production capacity in mind.

The **second part** is directed towards answering the **second** key **question** of **investment** in a new **bag machine**. The interviewee must **ask** for **more data** and answer this part mostly **qualitatively**.

The **third part** is optional. It is an extension of the case based on a possible recommendation from the second part. The interviewee must **calculate** the amount of **profit** that the **new product** must generate in order to justify investing in a new machine. The **interviewee** should also **sketch** and interpret the **elasticity curve**.

The **questions** in the big boxes should be read **aloud** to the interviewee.

## Short Solution

- The client can best utilize their current capacity by
**producing 4” and 8” bags** on the roller. This product mix has the **highest yearly profit** ($270K)
- The client should
**not invest** in a **new bag machine** because even if they sell 12” bags in 5 years, their **profits** **cannot cover $150K** in fixed costs.
- However,
**investment** in a **new machine **may make **sense** if our client can meet the **annual** **demand** of 12” bags and u**t**ilize the **surplus capacity** to grow revenue.

## Detailed Solution

Paragraphs highlighted in green indicate diagrams or tables that can be shared in the “Case exhibits” section.

Paragraphs highlighted in blue can be verbally communicated to the interviewee.

Paragraphs highlighted in orange indicate hints for you how to guide the interviewee through the case.

The following structure provides an overview of the case:

### I. Product/Capacity

The interviewee should ask about the following issues:

**Capacity** of the machine
**Demand** for each kind of product
**Revenue / costs** for each product
**Production time** for each product

Share **Diagram 1** with an **overview** of the **capacity** and **Table 1** with an **overview** of the **product mix’s demand/profitability** if asked.

#### 1. What mix of products should our client produce?

**Information** to be shared if the interviewee specifically asks for it

**500 “bag-widths“ **produced **per hou**r per product type
**Machine run time**:
- 20 hours per day
- 5 days a week
- 50 weeks per year

The interviewee should calculate the **total annual profit** and **production time** per **product line**.

**Bags produced per hr**

**Total annual profit**

**Production Time**

**4”** **bags**

# bags produced /hour = 500 x 6 = 3,000

Total annual profit = $0.02 x 9M = $180,000

**8” bags**

# bags produced /hour = 500 x 3 = 1,500

Total annual profit = $0.03 x 3M = $90,000

**12” bags**

# bags made /hour = 500 x 2 = 1,000

Total annual profit = $0.04 x 3M = $120,000

**Machine run time =** 20 hrs/day x 5 days/week x 50 weeks per yr

**= 5000 hrs per yr**

Share **Table 2** with an **overview** of the **solution** when the interviewee is **finished** with the calculation or gets **stuck**.

**Main Conclusion**

Under **current** capacity **constraints** (5000 hours/year), our client should produce **4” and 8” bags**. This product mix generates the **highest** profit ($270k/year)

### II. New Machine

#### 2. Should the client invest in another roller?

**Information** that can be shared if inquired by the interviewee:

- Cost of new roller = $750,000
- Payback needed = 5 yrs
- The roller will add an additional 5,000 hrs of
**machine run time**
**Mature market**, no dramatic changes
**Throughput** growing at **2%** due to **efficiency** of new roller

The **interviewee** should realize that if the **new roller** is able to **meet** the currently-unmet **demand** for **12 bags**, our **client’s profit** would be $**600K** in **5 years**.

**Profit over 5 years **

= Annual profit from 12" bags * 5 yrs = $120,000 * 5 = **$600,000**

However, the client must pay for the roller within 5 years. There is a **profit** **shortfall** of $**150K**.

**Unrecovered investment **

= Profit over 5 yrs - Cost of new roller = $600,000 - $750,000

= **$150,000**

At the current demand level, **2,000 machine production hours** will **NOT** be **used**.

**Annual unused capacity of new roller **

= Machine run time - Capacity needed to meet 12" bags demand

= 5,000 - 3,000 hrs = 2,000 hrs

#### 3. Why might it be a good idea to invest in a new machine?

**Possible answers:**

- The
** demand growth **rate could** exceed 2%**
- Since the current
**market** is **mature**, we could **introduce** a **new** product
- We can
**rent** out **surplus machine production **hours to increase revenue
**Prices** must **increase** to **increase revenue**

### III. New Product

#### 4. If we were to produce a new bag, what annual profit is required in order to justify investing in a new roller?

**Situation:**

The client’s R&D team has just come out with a **new** **bag**. It’s a 2-in-1 bag, one side holds your sandwich and the other side holds your chips or lettuce to keep things from getting soggy. **This bag is 6”. **

**Information** to be shared if inquired by the interviewee:

- There is
**no lag time** between production and market acceptance.
**Unrecovered investment **from new roller = **$150K**
**Payback** period = **5 years**

**Additional profit needed**

**Possible ways **to gain **$30,000 **per year i**n profit **from a new product:

**$0.03 profit** per bag at **1M bags**
**$0.015** **profit** per bag at **2M bags**
**$0.01 profit** per bag at **3M bags**

If the interviewee does **NOT** suggest **combinations**, ask them to **suggest** a **profit** per bag and the corresponding **sales** **volume** required.

#### 5. Draw the graph that represents the different profit/quantity combinations that would justify an investment in a new roller. Does this curve have any end points for our client given that the new machine will produce 6” bags @ 4 bags per bag-width for 2000 hours per year?

Share **Diagram 3** with the interviewee.

**Ke****y Insights**

Yes, there are **two end points**:

- The
**lower limit **of demand depends on **price sensitivity**. A **higher** **profit** margin such as $1 per bag is **not feasible **as production **quantities** wouldn’t be worth it.
- The
**maximum demand **we can serve **depends** on our **production** **capacity**. With the new roller, we can produce up to 4**M of the new type **of bag every year.

**Bags made per hr**

Unused capacity = 2,000 hrs per year

**Maximum production level**

### IV. Conclusion

At the end of the case, the interviewee should come to the following conclusions:

- The client can best utilize their current capacity by producing
**4”** and **8”** **bags** on the **roller** because the combined **profitability** from this product mix is **highest** at $270K per year.
- The client should
**NOT** invest in a **new bag machine** because they **cannot pay for the machine **within 5 years. (They will still owe $150K.)
- However,
**investment** in a **new machine** may **make sense** if we are able to **meet** the **annual demand** of **12” bags** and find a way to **monetize** the machine’s **surplus capacity**.

## Difficult Questions

### If we introduce a new product, what risks should we take into account?

**Possible answer:**

- The new product may
**cannibalize** the **sales** of our **existing** **products**. Thus, it may be **harder** to **achieve** the **profit** **required** to pay for the new machine within 5 years.
- Since the machine produces
**two different kinds of products**, there may be **higher** **operations** and **maintenance** costs.

**More questions to be added by you, interviewer!**

At the end of the case, you will have the **opportunity to suggest challenging questions** about this case (to be asked for instance if the next interviewees solve the case very fast).