In my five part series analyzing the risk/reward across the five largest US banks, I've saved Bank of America (NYSE:BAC) for last. Using updated prices as of Monday (6/11), * the firm actually has the highest expected IRR across most holding periods (19% on average), but also has the most downside risk, particularly in the short-term, vs other large-cap banks.* The wider range of outcomes reflects my view that, while remote, there is the possibility that the firm may need to do a dilutive capital raise down the road. This wide range unfortunately also makes ranking Bank of America vs its peers more difficult. My bank ranking is thus dependent on your risk tolerance and your view on the likelihood of Bank of America needing to do another dilutive capital raise, see the table below:

Essentially, Bank of America is appropriate for some higher risk investors, but definitely not all. While that's true for BAC, **I believe that Citigroup (****C****) and JP Morgan (****JPM*** ) offer a very compelling combination of return potential and downside protection and are appropriate for most long-term equity investors with the ability to stomach volatility*.

Again, I've done a detailed analysis of the five largest US banks: Bank of America, Citigroup, JP Morgan, Wells Fargo (NYSE:WFC), and US Bancorp (NYSE:USB) and you can read about each of those recommendations and my assumptions in more detail here:

- Own Citi For A 20% IRR With Limited Downside - Most Compelling Large-Cap Bank
- Own JPMorgan For The Second Best Risk/Reward Profile In The Banking Sector
- Wells Fargo: 3rd Best Large-Cap Bank Stock Offering Mid-Teen Returns And Limited Downside
- U.S. Bancorp's Greatness Is Priced In

I've applied a consistent framework to analyze each of these banks which helps me truly judge the difference in risk/reward across the various banks (at least based on my assumptions). This particular article will focus on Bank of America and will serve as an update to my previous recommendations. This article is broken up into the following sections:

- Results
- Methodology
- Assumptions
- Sensitivity Analysis
- Bottom Line

## RESULTS: EXPECT A HIGH-TEENS IRR (HIGHEST IN THE GROUP), BUT THERE'S MORE DOWNSIDE RISK THAN PEERS

In the table below, I show my risk/reward ratio and the Price-to-Tier-1-Common Equity Ratio (P/T1C), stock price, and IRR (Internal Rate of Return) for both my base case and my downside scenario across various holding periods. * So for example, if your holding period is 3 years, I expect the stock to be trading at a 0.9x P/T1C ratio, which implies a 3yr target price of $12.47 and an IRR of 20% including dividends in my base case.* In my downside scenario, I would expect the stock to trade at a 0.5x P/T1C ratio, which implies a 3yr target price of $5.34 or about a negative 9% annualized return (the worst in the peer group).

## METHODOLOGY: A MODIFIED RETURN ON CAPITAL APPROACH TO ESTIMATING LONG-TERM VALUE

For those of you who have read my Citi, JP Morgan, Wells Fargo, and/or US Bancorp write-ups, much of this methodology section will be repetitive, but I have made a few tweaks to my BAC model that are different than the other banks. These tweaks primarily account for the potential for dilutive capital raise and for the dilutive effect associated with the warrants issued to Warren Buffett.

Here's the basic concept; I've built a reasonably simple model, which forecasts Tier 1 Common Equity Per Share (T1C/shr). I arrive at my T1C/shr estimate by projecting a Return on Tier 1 Common Equity (ROT1C), which helps me estimate net income. I then make a few more assumptions around DTA utilization, dividends, buybacks, capital raises, and share count growth to project year-end T1C/shr. Unlike, my other bank models, I've actually produced two sets of forecasts: 1) with very harsh assumptions for the next 3yrs and a $10b dilutive capital raise in 2013 and 2) with less harsh assumptions and no dilutive capital raise (my assumptions will be discussed in more detail below). My T1C/shr and ROT1C forecasts for each scenario are shown below:

I then estimate the stock's value using a range of Price-to-Tier-1-Common Equity Ratios (P/T1C). By multiplying my T1C/shr estimate by a P/T1C ratio, I can generate an estimated price for the stock. Since I don't know what the **right** P/T1C ratio is, I've layered on a probability distribution for each P/T1C ratio across different time periods. I have two general overriding assumptions embedded in my distributions:

- Over time, the base case P/T1C ratio will migrate towards the appropriate P/T1C based on my long-term ROT1C assumption. This is discussed in more detail in the Assumptions section, but for Bank of America, I believe the long-term P/T1C ratio should approach 1.1x (vs. 0.6x today).
- The left tail should generally be fatter than the right tail, which basically implies there more risk of the stock trading at a lower multiple than a higher multiple. This is particularly true in the early years when I believe the risk is highest for the bank.

Below, I show my probability distribution assumptions for each period (I've used the same probability distribution for both my cap raise forecast and my non-cap raise forecast):

To calculate my base-case estimated P/T1C for each period, I multiply my probability assumption by each P/T1C ratio in the range and sum up the results. This creates a weighted average P/T1C for each period, which is my base case assumption. Below, I show a table which walks through this math for the 2014 period in my no cap raise scenario. Note that I use my 2013 year-end T1C/shr estimate of $12.12 to calculate my 2-year holding period target price of $10.47.

Once I have my estimated base-case price, I can add the cumulative dividends I expect to receive over that period ($0.08) to the price and calculate an IRR. As my calculation essentially implies that all dividends are paid at the end of the period, it slightly understates the true IRR. Below, I show the IRR calculation for my base-case assumption in 2014 (2-year holding period).

*IRR = [(Price _{t+n} + Cumulative Dividends) / Price_{t+0}] ^ (1/n) - 1*

- Price
_{t+n}= $10.47 - Cumulative Dividends = $0.08
- Price
_{t+0}= $7.28 - n (holding period) = 2 years

## IRR = 20% in my base case scenario w/ a 2-year holding period

To calculate my downside scenario, I again use my probability distribution graph. With this graph, I can estimate the bottom 10% P/T1C ratio. For Bank of America in 2014, my downside scenario estimates a P/T1C ratio of 0.4x. Said another way, 10% of the time, I expect my P/T1C to be equal to or worse than 0.4x in 2014 (after a 2-year holding period). This analysis is somewhat similar to a VaR calculation in that it doesn't estimate the max downside, but the expected loss at a given probability. Below, I attempt to show where that downside scenario falls on my 2014 probability distribution graph for Bank of America. For my downside scenario, I use my estimated T1C/shr under the dilutive capital raise scenario, which for 2014 is $10.07/shr (vs $12.12 under my scenario that does not include a dilutive cap raise).

Now on to my actual forecast model. To forecast Tier 1 Common Equity growth, my model essentially starts with 2011 year-end Tier 1 Common Equity and then grows it each year as follows:

## Beginning of Period [BOP] T1C

- Add net income
- Add disallowed Deferred Tax Asset [DTA] utilization
- Add capital from dilutive cap raises (if appropriate)
- Subtract dividends
- Subtract buybacks

## End of Period [EOP] T1C

Additionally, I also forecast the average number of diluted shares in each period. I assume that the share count has a natural growth of 1.5% annually from the firm issuing shares to employees. Additionally, in one of my scenarios, I have assumed that the firm does a $10b dilutive capital raise, which results in the issuance of 2.2b shares (roughly a 20% increase in share count). I have also adjusted my model to account for the dilutive affect of the Buffett BAC warrants (option to buy 700m shares at $7.14 through 2021). My model uses the treasury method to account for the warrant's dilutive effect. These increases in share count are partially offset by buyback assumptions. I discuss the assumptions embedded in my forecast model in more detail in the next section.

## ASSUMPTIONS: LOWERED ANALYSTS ESTIMATES BY $15-$25B OVER THE NEXT THREE YEARS

My analysis relies on many, many assumptions, and while I've tried to be conservative in making these assumptions, some readers will disagree with my inputs. For this reason, I've made my model available to anyone who wants to do their own analysis and stress the model or look at how less conservative assumptions affect the outcome (model available for download here). Below, I walk through the biggest drivers of my model.

**Net Income**

To forecast Net Income in 2012-2014, I start with the street's GAAP EPS estimates from Thomson Reuters of $0.60, $1.01, and $1.40, respectively. I then layer on additional losses to help compensate for my view that The Street tends to be overly optimistic in its earnings projections. My additional losses for my cap raise and no cap raise scenarios are shown below:

For 2015-2020, I forecast a Return of Tier 1 Common Equity (ROT1C) for each year to estimate net income. **For Bank of America, I believe the firm's long-term sustainable ROT1C is 10.5% and I eventually build to that return by 2019.**

To arrive at my 10.5% long-term sustainable ROT1C, I use history as my guide and perform a modified DuPont Analysis. I look at the last 10yrs of data unmodified (i.e. I leave the 2008-2009 financials losses in without making any adjustments). This assumption essentially assumes that a traditional credit cycle tends to include a crash like we saw in 2008, a reasonably conservative assumption, but not insane considering we have Europe hanging over our heads and Bank of America still has a host of legal settlements to get through. My modified DuPont Equation is as follows:

*ROT1C = Profit Margin x Asset Turnover / Regulatory Capital*

- Profit Margin = Net Income / Revenue (pre-provisions)
- Asset Turnover = Revenue (Pre-provisions) / RWA
^{1} - Regulatory Capital = Tier 1 Common Equity
^{2}/ RWA^{1}

^{1} RWA = Risk-weighted Assets as defined under Basel 1

^{2} Tier 1 Common is calculated under Basel 1 for all periods

In the table below, I show the historical average, one standard deviation up and down, and median for the full history and the last four quarters for each component of my DuPont analysis. The full data series is available as part of the model and was constructed using both CapIQ and Bloomberg data.

Using this table as my historical guide, I then make estimates for what each of these components can be going forward, taking into account the many, many regulatory changes that are being implemented across the industry. The biggest change I'm forecasting is that regulatory capital will need to increase almost 67% above the 10yr historical average. Below, I show my estimates and my forecast for long-term sustainable ROT1C of 10.5% based on these estimates.

**Long-term Appropriate P/T1C Ratio**

Next, using the dividend discount model and making a few adjustments, I can back into the appropriate P/T1C, given an assumed payout ratio, discount rate, and ROT1C. The math works as follows:

*Dividend Discount Model: Price = Dividend _{t+1} / (r_{equity} - g)*

- where g = ROT1C x (1 - PayOut)
- where Dividend
_{t+1}= Dividend_{t+0}x (1 + g) - where Dividend
_{t+0}= T1C x ROT1C x PayOut

*P/T1C = ROT1C x PayOut x (1 + g) / (r _{equity} - g)*

Making the following assumptions:

- PayOut Ratio = 60% (includes both dividends and buybacks)
- Discount rate = 10% (my standard hurdle rate)
- ROT1C = 10.5% as calculated above

* I arrive at a long-term sustainable P/T1C ratio of 1.1x plugging in the assumptions above.* In my analysis, I forecast that by 2018, Bank of America should trade right around that level in my base case (the stock currently trades around 0.6x P/T1C).

**Dividends**

I have forecast two different dividend profiles for my two different scenarios. Under my capital raise scenario, I have assumed that the firm does not increase its dividend payout until 2015. Under my less harsh scenario, I have assumed that the firm is able to increase its dividend payout by 2014. In both scenarios, I forecast that Bank of America will eventually target a 30% payout ratio. My assumptions are shown below:

**Stock Buybacks**

Similar to my dividend assumptions, I have forecast two different stock buyback profiles for my two different scenarios. Under my dilutive capital raise scenario, I don't have the firm repurchase any shares until 2016 and I forecast a large $10b dilutive capital raise in 2013. Under my less harsh scenario, I assume that the firm begins making small stock repurchases in 2014. Under both scenarios, I assume the bank will eventually target a combined dividend/stock-buyback payout ratio of about 60%. My buyback assumptions and buyback payout assumptions are shown below.

**Disallowed Deferred Tax Asset Utilization**

I have assumed the firm is able to utilize between $0.5b to $6b per year of its $19b of disallowed DTA. Bank of America has $32b of DTAs sitting on its balance sheet, but for regulatory purposes the DTA component of Tier 1 Common Equity can not exceed 10%. This essentially excludes approximately $19b from the firm's T1C calculation. However, as the firm generates positive net income it can offset some of its tax expense by utilizing its DTA. This essentially has the effect of allowing T1C to grow at a faster rate than would be expected by net income alone.

**Probability Distributions for P/T1C Ratios**

As I discussed above, I've made a series of assumptions around the likelihood of each P/T1C ratio being the correct future ratio. I generally assumed that the weighted average P/T1C would migrate toward the appropriate sustainable long-term P/T1C of 1.1x that I calculated using the dividend discount model above. I also assumed that the left-tail of the distribution would be fatter essentially implying that the risks were weighted to the downside. If you disagree with any of my probability distributions, please feel free to change them as you see fit.

## SENSITIVITY ANALYSIS: RETURNS ARE MORE SENSITIVE TO THE LONG-TERM SUSTAINABLE ROT1C THAN THE SIZE OF ANY FUTURE DILUTIVE CAPITAL RAISE

**Lower Terminal ROT1C Estimate to 8.5% (vs 10.5% Currently)**

In the table below, I show my updated return profile if I cap my sustainable long-term ROT1C at 8.5% (vs 10.5% previously). I have updated by P/T1C distribution tables by shifting my probabilities 0.35x to the left. This essentially targets a long-term P/T1C of 0.8x, which is roughly what you'd expect the multiple to be if the ROT1C drops. My average base-case IRR over all time periods falls to 2% (vs 19% previously). While this is a significantly lower IRR, investors with a long-term time horizon can still expect a low double-digit return with a low single-digit negative IRR in my bottom 10% scenario. While I can't say for sure what the bank would do in this scenario, I wouldn't be surprised to see the bank shrink by selling off businesses to lower their capital requirements and thus increase their potential long-term sustainable ROT1C.

**A $20b Dilutive Capital Raise At $4.50 (vs $10b Currently)**

In the table below, I show my updated return profile if I double the firm's capital raise to $20b instead of the $10b I'm currently forecasting. A $20b capital raise at $4.50 increases the firm's share count by about 40%. It's unclear how a capital raise this large would actually get done as Bank of America would likely be tapping the capital markets at a point of severe stress and the government might need to be involved. So in a sense, this is more of a theoretical exercise than what may actually play out in real life. Having said that, My average downside IRR over all time periods falls to negative 7% (vs negative 6% previously). One thing to note, my capital raise scenario only affects my bottom 10% scenario, the base case remains unchanged as it does not assume any capital raise.

**2x Larger Additional Losses in 2012-2014**

In the table below, I show how my returns are affected if I double my additional losses for each of the next three years. As I'm forecasting two scenarios 1) with harsh losses and a dilutive capital raise and 2) with less harsh losses, I've double each one from its respective original value. In my no-cap raise scenario, I'm forecasting additional losses in 2012-2014 of $6b, $16b, and $8b, respectively (vs $3b, $8b, and $4b previously). In my cap raise scenario, I'm forecasting additional losses in 2012-2014 of $10b, $30b, and $10b, respectively (vs $5b, $15b, and $5b previously). Again, my loss estimates are deducted from the street consensus estimates. My average base-case IRR over all time periods falls to 15% (vs 19% previously).

**Eliminate Benefit from disallowed DTA Utilization**

In the table below, I show what the return profile would look like if I entirely eliminated the benefit I anticipate the firm will get from utilizing its disallowed deferred tax assets. My average base-case IRR over all time periods falls to 17% (vs 19% previously).

**Bottom 5% Expected Returns**

In the table below, I update my return analysis looking at the bottom 5% of expected returns (my previous downside scenario was the bottom 10%). This provides some perspective on what kind of returns investors should expect if things really get ugly. In a really bad scenario, I don't expect shareholders to breakeven until year six, a pretty bad outcome.

**Upside--Stock Trades At Top 10% Of My Probability Distribution**

While I'm much more concerned with downside risk than I am with upside potential, it is still helpful to have an understanding of the return possibilities in a very bullish upside scenario. Using the same methodology I used to forecast the potential outcome in the bottom 10% scenario, I can alternatively look at the top 10% scenario. The table below looks at this outlier scenario to the upside. Under this very bullish scenario, the stock could generate IRRs in the high-twenties over a 3 year period.

## BOTTOM LINE--BANK OF AMERICA OFFERS, THE HIGHEST RETURN POTENTIAL, BUT ALSO THE WORST DOWNSIDE IF THINGS GET BAD.

Bank of America is only really an appropriate stock for investors with a relatively high risk tolerance and a reasonably strong belief that the firm will not need to do another dilutive capital raise. For the best combination of potential return and downside protection, I recommend that investors stick with Citigroup and JP Morgan.

I've written two previous articles on BAC. While I stand behind both of these pieces, I think my current model and analysis is a bit more comprehensive and thus does a better job estimating the potential outcomes for BAC shareholders. Having said that, I do believe that the stock still offers a much more compelling risk/reward trade-off than the warrants as the implied volatility of those warrants is still quite high.