## 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 interviewee should perform a back-of-envelope calculation which answers two key questions:

- (1) What will be the size of my cellar (in number of bottles) over time?
- (2) What are the economics of the cellar over time in terms of money earned and money spent?

## I. Background

**Warm-up question:** What sorts of things do you need to know from me to answer these two questions?

At this point the interviewee should ask the right questions in order to have all the information needed to answer the initial questions.

#### 1. What does the wine cost?

Interviewer’s answer: $30 per bottle to drink, $100 per bottle to invest

2. How much am I willing / able to spend?

Answer: Initial kick-start $1,500 (to drink), $12,000 (to invest), $300 (to drink) $600 (to invest) per month thereafter

3. What is my own consumption?

Answer: 2 bottles per week to drink, plus 2 per month to give away as gifts

4. How does the investment wine appreciate?

Answer: 20% p.a.

5. How / when do I sell the investment wine?

Answer: Always after exactly 5 years, no cost of sale, always a buyer, no discounting

6. Are there costs to build / maintain the cellar?

Answer: $200 p.m. (optional)

## II. Analysis

### Key question 1: What will be the size of my cellar (in number of bottles) over time?

To answer this question, first the interviewee should draw a chart of the number of bottles in the cellar over time. Important note: The following diagrams are based on the assumption, that the bottles initially purchased are as old as the bottles being bought in the first year.

The graph should look something like above. The interviewee should keep things simple, e.g. calculating and charting in years, and the interviewee should make a reasonable assumption about how many years need to be charted to show the dynamics. How the interviewee does the annual accounting (does the up-front kick-start count as year “0” or year 1, etc.) should not matter… It’s the shape that counts. Many interviewees start trying to make use of the “revenue” numbers (e.g. appreciation of investment wine) at this stage — it’s clearly not yet relevant.

Share **Diagram 1** with interviewee after he or she accurately described the graph to the interviewer.

**Calculation and Conclusion**

There should be a **kick-start of 170 bottles**: 1500/30=50 from the drinking cellar, and 12000/100=120 from the investment cellar.

The **monthly consumption of 10 bottles** in the drinking cellar (here the interviewee should make the reasonable simplifying assumption, e.g. that a month has ca. 4 weeks) **equals my purchases** for this cellar (300/30=10), so the drinking section is a **steady-state** cellar of 50 bottles. In the first five years, given the investment strategy, I **sell nothing** from the investment cellar and **only purchase wine** at the rate of (600/100=6*12=**72**) **bottles per year**.

Thus at the end of year one, I should have 120+72=**192 bottles in the investment section** or **242 bottles in the total cellar**. **After 5 years** (in my time accounting), I **sell the kick-start of 192 bottles**, and the stock drops significantly. In **subsequent years**, I always buy the same amount of investment wine as I sell (72 bottles per year), and therefore I always have exactly 5*72=360 bottles of investment wine in my cellar in years 6+: the 72 bottles from each of the last five “vintages” I've purchased. This makes a **total long-term steady-state cellar of** 360+50=**410 bottles**.

### Key question 2: What are the economics of the cellar over time in terms of money earned and money spent?

Now let’s look at the **economics over time**. In fact, let’s plot cumulative return (total revenues minus total costs) over at least these 10 years.

Here the interviewee should present something like the following. Again, the details of time accounting (“did you sell at the beginning or end of the year?”) are not important.

Share **Diagram 2** with interviewee after he or she accurately described the graph to the interviewer.

**Calculation and Conclusion**

You have the **kick-start of $13,500** and then only **costs for the first 5 years**. **After 5 years**, you **sell the kick-start of 120 investment bottles** and get a **big push in revenue** of 120*$250=**$30,000**.

The interviewee should be able to estimate the fact that **$100*(1 + 20%)^5 is something like $250 off the cuff**. **Without compounding**, it’s obviously **$200 exactly**, so the **answer “something a bit more than $200” is good**. Many people answer $200 exactly and, when prompted “is it more or less than $200” choose “less”, which is clearly madness.

In these first 5 years, you of course also have the **cost of** 12*$300 for purchase of drinking wine, 12*$600 for investment wine, and 12*$200 for maintenance of the cellar, so 12*$1100**=$13,200 per year**.

As of **year 6**, you continue to have the **above costs in addition to the revenue** of 72*$250**=$18,000 from selling 72 bottles**. This means that there is a “net return” in these years of $4,800, which is the slope of the above curve in years 6+. You **break even after ca. 15 years**, and only then does the cellar **“pay for itself” and even make a slight return**.

## III. Concluding observations

**So it takes something like 15 years to break even and recoup your initial investments. **Nonetheless, we’ve obviously made a lot of simplifying assumptions and painted some rosy scenarios:

- (1) the investment wine always appreciates at 20% p.a.,
- (2) you can fund a cumulative outlay of ca. $80,000 after 5 years out of your own pocket,
- (3) you can always find a buyer for your wine, etc.

**Does the 20% p.a. strike one as a credible return on an investment-grade wine? **Why or why not? How does it compare to other returns you know?

Well, yes, it’s extremely aggressive but not completely implausible. It’s certainly not a sustainable return!

The interviewer is not looking for any particular answer here, but the candidate should state a coherent opinion. To answer why or why not, the candidate should be prepared to offer some benchmark returns from own experience (NYSE, real estate, term deposits, etc).