**Investment Banking Charts –** I think the greatest gift of Dan Bricklin (“father” of electronic spreadsheet) and **Bill Gates** to Investment Banking Mankind is the **Excel spreadsheet software** that allows analyst to not only create rock star financial and valuation models but also help present their analysis in some awesome pictorial format (graphs).

With this, I thought why not a tutorial on most popular Investment Banking Graphs and charts. In this article I will discuss the following set of graphs –

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1) Investment Banking Courses 99 Course Bundle, 500+ hours

2) Business and Financial Modeling (University of Pennysylvania)

3) Wharton Business and Financial Modeling Capstone (University of Pennysylvania)

4) Introduction to Finance: Valuation and Investing (University of Michigan)

5) Valuing Projects and Companies (University of Michigan)

Download the Spreadsheet templates for all the graphs here

# 1 – PE Chart

This PE ratio is in essence a payback calculation: it states how many years’ earnings it will take for he investor to recover the price paid for the shares. PE (price to earnings) charts help us to understand the valuation multiple over time. Other things being equal, when comparing the price of two stocks in the same sector the investor should prefer the one with the lowest PE. If you are new to the PE ratios, you may refer to this valuation primer article on Relative Valuations

##### What is a PE Chart

PE chart helps the investors visualize the valuation multiple of Stock or Index over a period of time. For example, the below PE graph of a company named Foodland Farsi is depicted over a period of March’02 until March’07.

##### Interpretation of PE Charts

- Historically Foodland Farsi has traded a an average PE multiple of 8.6x
- The standard deviation of the PE multiple signifies the volatility of the PE multiple.
- We note that Foodland Farsi has traded within the range formed by the
**Upper**(defined as Average PE + 1 Std Dev = 12.2x) and the**Lower**(Average PE – 1 Std Dev = 4.9x) - We note that PE mutiple for period after June’06 has crossed the upper standard deviation line signifying higher valuation multiple.

##### Why it is useful?

- This chart is fairly useful because this provides the historical valuation details in a quick and easy format.
- You may take not more than 30 seconds to interpret such a graph.

##### Dataset for PE Chart

Let us now prepare the PE chart as provided above. Please download the **PE Chart dataset here. **The dataset includes the following –

**Date****Historical Stock Prices****EPS estimate (forward)**– Please note that this data may not be available in the public forum. You may use Bloomberg, Factset, Factiva (all are paid versions) to get access to such data

##### Building a PE Chart

**Step 1 – Calculate the PE Ratio**

Since we already know the Price of the Stock and the Forward EPS, calculate the PE ratio of the stock for each date.

###### Step 2 – Calculate the Standard Deviation of PE

Calculating Standard Deviation is fairly easy in Excel. You can use the formula STDDEV to calculate the standard deviation of the stock. Do not forget to use absolute references so as to display the same standard deviations across the dates.

###### Step 3 – Calculate the Average PE

Calculate the Average PE of the stock using the formula AVERAGE and also use absolute references as the average of the data should remain constant across all the dates.

###### Step 4 – Calculate the UPPER and the LOWER range

Calculate the UPPER and the LOWER range by using the following formula

**UPPER =**Average PE + Standard Deviation**LOWER =**Average PE – Standard Deviation

###### Step 5 – Plot the Graph using the following data –

- Forward PE
- Average PE
- UPPER
- LOWER

###### Step 6 – Format the Graph

This is very important as formatting can really win if you can highlight the important areas and make it more intuitive to comprehend.

Like the PE charts, you can also make** Price to Book Value Chart (P/BV), PEG Graph, Price to Sales or Price to Cash flow Charts.**

**#2 – PE Band Chart**

##### What is PE Band Chart?

Like the PE Ratio Graph, PE Band is also computed from the historical PE ratios for each individual stock/Index.The line plotted from the average highest PE will form the upper PE Band, whereas the average lowest PE will form the lower PE Band. The middle PE Band will be derived from the mean of the Upper and Lower Band.

##### Interpretation of PE Band Chart

The above chart can be interpreted as follows

- Currently, the Price Line (colored in GREEN) is touching the Maximum PE Band Line of 20.2x. This implies that the stock is trading at its maximum PE and may be overvalued!
- The upper band reflects the Historical Maximum Price of the stock if the stock would have traded at its Maximum PE. For example, If we trace backwards the Maximum PE Band Line till March’02, we find that the stock would have traded at Rs600/- if the PE during that period would was 20.2x
- Also, we note that the stock has touched the lowest PE Band of 5.0x many a times in the last 5 years period. It denotes an ideal opportunity to buy the stock.

##### Why PE Band Chart is Useful?

- The advantage of the PE Band is its consideration for both the fundamental factor (i.e. profitability) and the historical trading pattern of a stock.
- The use of PE Band is especially meaningful for listed companies, which have profitable track records.
- For a stock with stable earnings, its price tends to move within the PE Band. In other words, the stock price in one extreme tends to move to the other extreme within the Band
- Also, note that PE Band Chart is different from PE ratio graph as we note that the Y axis represents the price of the stock rather than the PE multiple.
- This PE Band Chart is effective because this graph is able to denote both the PE Bands (valuation) and the corresponding Prices. Along with the PE ratio graphs, this makes a case for taking a valuation call on stocks.

##### PE Band Chart Data set

The PE Band Chart Data Set is no different from the one that we used earlier. Infact, is the same! We require the following –

- Historical Stock Prices
- Dates
- Forward EPS

##### Building a PE Band Chart

###### Step 1 – Calculate the Forward PE Ratio for the Historical Dataset

###### Step 2 – Calculate the average, maximum and the minimum of the PE ratios

###### Step 3 – Find the Implied Prices using the following formula

Calculate the implied prices using the formula below

**Price (corresponding to Average)**= Average PE x (Historical EPS)**Price (corresponding to maximum)**= Maximum PE x (Historical EPS)**Price (corresponding to minimum)**= Minimum PE x (Historical EPS)

###### Step 4 – Plot the graph using the following

- Stock Price
- Implied Average Price
- Implied Maximum Price
- Implied Minimum Price

###### Step 5 – Format the Graph 🙂

You can make Band Charts for other set of valuation multiples like EV/EBITDA (Enterprise Value to EBITDA), P/CF etc

## #3 – Football Field Graph

##### What is Football Field Chart?

Sometimes it is easier for us to represent the data in floating columns or bars in which columns (or bars) float spanning a region from minimum to the maximum values. Below is a sample Football Field column chart.

##### Interpretation of the Football Field Chart (above)

- The data represents fair valuation (Price/Share) of the company under different assumptions and valuation methods.
- Using DCF the valuation of the firm comes out to be $30/share (pessimistic case) and $45 under (most optimistic case).
- The highest fair valuation of the company is $50/share when using Replacement Cost method of valuation
- However, the lowest fair valuation comes out to be $20/share when using M&A Transaction Comp valuation.

##### Data for Football Field Chart

Let us assume that you have been provided with the following set of data. You want to represent the below data in the best possible graphical format.

There can different ways of making graphs on such a data, however, they may not provide great insights when we make a regular line graph or the bar graphs. Below are the representation (poor) of these regular graphs –

###### Line Graph

The problem with this representation is that it is very difficult to interpret this data.

###### Column Graph

Again the same problem that it is very difficult to interpret such data.

With this it is now easy to understand that the solution lies in making the floating column or the bar chart.

##### Building a Football Field Chart

**Step 1 – Create the Two series with Minimum and Range**

The first series represents the minimum and the second represents the range (maximum – minimum). Please see below the two series on which we create our graph.

**Step 2 – Choose Stacked Column Chart**

The secret to making the floating chart is to use the column chart in an effective way by selecting the “stacked column chart” using two series.

You will get the below chart

###### Step 3 – Make the “minimum” columns Invisible!

Select the minimum column bars (blue color) and from the top menu change the color to **“No Fill”**

With this you will get the graph below

###### Step 4 – Format the graph and make it awesome!

- Change the x axis to reflect the valuation methodology
- Remove the Legends on the right hand side (Range and Minimum)
- Change the color of the bars to suit your color taste (please don’t make the columns as pink, its Investment Banking you know!)

## # 4 – Scenario Graphs

##### What are Scenario Graphs?

Sometimes It is important for us to accept the fact that understand that valuation is not a very scientific approach. It depends on assumptions and scenarios. While we value a stock, you may make a different set of assumptions while preparing a financial model – projecting income statement, balance sheet and cash flows. While it is important for us to take the most expected case while we do the valuation, it is equally important to show the impact of different cases like what if the tax rates go down or what if the production moves up more than expected etc. These scenarios can be easily built using Financial Models.

You can use the following financial models for your reference –

Please see below a sample Scenario Graph –

##### Interpretation of Scenario Graph

- We note from above that the base case valuation for the stock XYZ is $300
- The scenario graphs provide us with additional inputs on downsides with respect to the following
- If price of the product decreases then the fair price of the stock would go down by $17.
- If corporate taxes are higher, then the fair price of the stock would move further down by another $28
- If raw material prices move up, then fair prices of the stock would move down even more by another $25.
- If we consider all the pessimistic cases (an event when all three negative events happen together), then the fair valuation of the stock would drop to
**$230 per share**

- Likewise, you can find the additional inputs on the upsides – If we consider all the optimistic cases (Higher prices, higher taxes and lower raw material costs), the fair price of the stock would move up to
**$410 per share**

##### Dataset for the Scenario Graphs

The dataset required for this graph is shown as below. The table below is arrived at after inputting new assumptions in your Financial Model and recalculating the fair share price.

##### Building a Scenario Graph

We will assume that you already have the data like the one above. With this let us look at the steps involved to build the Scenario Graphs –

###### Step 1 – Add two columns X and Y in the data-set (tricky and most important)

- This graph builds on the Football Field Graph (#3) that we earlier made.
- In this we again use the Column Stacked Graph where Y data gets stacked over the X data.
- In addition to this we make the X dataset as invisible so that we get the floating Y dataset.
- For example, If you closely observe the scenario graph – downside scenario – Price decrease shows a floating visible data of $17 (Y data) and immediately below this dataset is the invisible $283 (X Data).

###### Step 2 – The completed X and Y dataset should look something like below

###### Step 3 – Prepare the Column Stacked Graph on the two dataset X and Y

Please note that we are not preparing the chart on the original set of data. We are preparing the chart on the converted dataset (X and Y)

###### Step 4 – Make the X dataset hidden

Hide the X dataset by selecting the columns and choosing “No Fill” from the Formatting options in the menu

###### Step 5 – Format the Graph and be awesome!

## Conclusions

As we note above that there can be a different graphical representation of stock valuation. The primary reason we use such graphs is to comply save time for the clients and make the research report or pitch book a time saving and effective document. You will find the four types of valuation graphs in a majority of the tier-1 brokerage firm research reports. I had worked earlier at JPMorgan as an equity research analyst and found the Football field graph and Scenario graph to be most useful representation for clients. You can use these in Ratio analysis Graphs too.

## What’s Next?

If you learned something new or enjoyed the post, please leave a comment below. Let me know what you think. Many thanks and take care.

Jadranka says

Thanks for sharing this. I am happy that your blog reached me.

You have the gift to share your knowledge on very simple ,concise and understandable way.

Dheeraj Vaidya says

Thanks Jadranka 🙂 Glad you know that you find these resources useful.

Best,

Dheeraj

Abhinav Kaul says

Hi Dheeraj,

Can you mail me the video of this tutorial

Dheeraj Vaidya says

Hi Abhinav, I don’t have the video tutorials of these charts as of now.

Aditya says

i stumbled upon this blog when i look for PE Band formula, thanks for the awesome tutorial sir! it helps me a lot in building a similar template for myself.

but i have a question. why do you “limit” the max PER to 50 and the min PER to 0.001?

=(MIN(50;MAX($G$6:$G$267)))

=MAX(0.001;MIN($G$6:$G$267))

your explanation would be much appreciated

Dheeraj says

Hi Aditya,

not much logic here. You can change the limits so to accommodate your stock PER fluctuations.

Thanks,

Dheeraj

Oketak says

I know that you get the estimated eps from bloomberg or similiar services, but can you explain how is it that the eps data is not quarterly in your example but weekly? Thanks

Dheeraj says

Hi Oketak,

Each week, Bloomberg and many other service providers release the annual/quarterly EPS estimated for companies. This EPS which is released each week is an average of the estimates provided by different equity research analyst (jpmorgan, nomura, merrill etc). If even one of the analyst changes their EPS estimate, then then the average estimate would change.

Thanks,

Dheeraj

Alex Lee says

Hi,

I see that in the excel file you provide you have fwd EPS filled in for every weekly entry. But is that practical when applying this? I see companies only have the Est EPS per quarter, and this will greatly affect the standard deviation afterwards.

Thanks.

Dheeraj says

HI Alex, you can get the data of fwd EPS every week from databases like bloomberg etc. it is not readily available publicly.

Thanks,

Dheeraj

Chern yi says

THIS IS A GEM! So glad I found this 🙂 Thank you so much for sharing!

Dheeraj says

Thank you Chern!

adeel says

Well explained! Btw how are you coming up with weekly epsforecasts?

Piyush Arora says

Hi Dheeraj,

Informative and insightful piece.

Quick question, where are we supposed to download Indian-based historical P/E and per share prices?

You wrote, “Please download the PE Chart dataset here. ”

But the hyperlink (if it was intended to be there) doesn’t seem to work.

Really want this data, paid or not.

Looking forward to hearing from you soon.

Regards,

Piyush

Fellow U.S based analyst !

mahendra edunoori says

what a great things that i am learning from your articles….

Rohitesh says

Extremely well explained sir. I have been a fan of your teaching…since my IICM days, when you had taught us Financial Modelling..way back in 2008-09.

Refreshing to read your articles Sir.

Regards,

Wall Street Mojo says

Thank you Rohitesh for your kind words.

Madhu says

thank you. it is really a useful stuff. thanks once again.

Wall Street Mojo says

Hi Madhu,

I am glad you found this article on Investment Banking Charts to be useful.

Best,

Dheeraj

Joseph says

Great stuff especially twisting Excel around for optimal results. Keep the good work and I impatiently await your next issue.

Amrit V says

Amazing and all free. Thanks very much for sharing

MUHAMMAD NAWAZ says

sir i am glad to see your publication sir i want your help in making my project proposal for COL (MBA) in H.R.M.

will you please help me in this matter i shall be very greateful to you in this matter if you help me

Pravin says

Its really really great Sir..

Kindly keep posting to me for all such post.

Thank you.

henning says

Nicely done – thank you

Mona says

Awesome.. Thanks for sharing this..

Kinshook Chaturvedi says

One of the best practical article on stock valuation. But where is the Excel sheet model which is downloadable ?

Wall Street Mojo says

Hi Kinshook,

Please look at the first set of paragraphs for “Download the Spreadsheet templates for all the graphs here”. You should be able to download the associated template.

Thanks, Dheeraj

Vishey says

Hello Sir,

I have one question? Do we need to know VBA for building financial models?

Wall Street Mojo says

Hi Vishwantha, You will not require VBA for building financial models for Investment Banks. However, if you are doing lot of scenario analysis and data download and anlaysis, one can make efficient use of VBA for automating mundane tasks

James says

Can you give all this stuff in pdf form so that we can download .

Mahesh says

What an exciting and intelligent way of explaining. Language is very simple and easy to understand. Please continue to do so.

Thanks,

Mahesh

Wall Street Mojo says

Thank you Mahesh for your kind words!

Arinjay says

Great Knowledge sharing process Sir !

Neeraj says

Awesome financial stuff. Amazing Work. Waiting for new IPO valuations.

Raushan says

Thanks …..

Rajan says

Thank you sir for sharing this knowledge. When are you going to write on DCF?

Wall Street Mojo says

I am glad you liked the tutorials. A lot of subscribers want me to write on DCF. Will write about it soon.

Thanks, Dheeraj