The article focuses on eight of the largest businesses that issued crisis era warrants: American International Group (NYSE:AIG), General Motors (NYSE:GM), JPMorgan Chase (NYSE:JPM), Bank of America (NYSE:BAC), Citigroup (NYSE:C), Wells Fargo (NYSE:WFC), Capital One Financial (NYSE:COF), and PNC Financial (NYSE:PNC). Below is a list of crisis era warrants issued by these businesses along with their key characteristics - Expiry, Float, Current Warrant & Common Stock Pricing, Warrant Price Premium, Nominal Leverage, Anti-Dilution Dividend Adjustment Threshold, and Warrant Type (Troubled Asset Relief Program - TARP & auto/insurance bailouts):

As can be seen, the warrant price premium, nominal leverage, and dividend adjustment threshold are all over the place. Those statistics are vital to valuing warrants although they are not very meaningful on their own. Leverage is not free and the cost of leverage is influenced by the warrant price premium and the dividend adjustment threshold. Finding cost-of-leverage helps determine:

- Whether the warrant price premium paid is reasonable, and
- Whether there exists any mispricing compared to call option leaps with the same strike.

One approach to measuring cost-of-leverage involves splitting the cost into two components:

- Cost attributable to the dividend paid to common holders that are exempt from any anti-dilution provisions in the warrant. It can be calculated by dividing the annual dividend exempt from anti-dilution provisions by the strike price, and
- Cost attributable to the warrant price premium. It can be calculated as the rate that will result in (Strike Price - Price Premium) reaching Strike Price at expiry.

The details of the calculation using the General Motors warrants (GM-WT-B) as an example follow:

Strike Price (SP): $18.33

Annual Dividend (AD): $1.20**

Annual cost attributable to the dividend (X): AD/SP = 1.20/18.33 = 6.5%

**For GM, there is no anti-dilution provision for ordinary dividends and so the entire dividend amount is exempt.

To determine the annual cost attributable to warrant price premium (denoted by Y) -

Current Price (CP): $29.94

Warrant Price (WP): $12.91

Warrant Price Premium (PP): WP + SP - CP = 12.91 + 18.33 - 29.94 = $1.30

Warrant Time Period Remaining in Years (T): 4.7

Solve for Y in,

(SP-PP)*(1+Y)^T = SP

(18.33-1.30)*(1+Y)^4.7 = 18.33

Y = 1.58%

Annual cost of leverage (Z): X + Y = 8.08%

Below is a list showing cost of leverage for the warrants associated with the eight businesses:

Annual cost of leverage varies widely although it roughly parallels the nominal leverage. An educated judgment can be made about this cost by comparing it to the cost of leverage of the security's call option leaps with the closest strike price to the warrant strike. For example, applying the same method to GM Jan 2016 Calls with Strike 18 yield an annual cost of leverage of 8.27%. The rate is comparable but higher for what is in effect a shorter-term loan - there is a modest amount of mispricing in GM-WT-B.

The spreadsheets show a nominal leverage of 2.30 for GM-WT-B. If cost-of-leverage (the effect of dividend payments and the warrant price premium) is ignored, the warrants would return 2.3x the returns of the common stock (upside or downside). Also, the common stock price at expiry at which warrant holders and common stock holders would both have the same return would be the current price (in this hypothetical case, it is obvious that the securities will both breakeven if the price is the same at expiry). The actual common stock price at expiry where both GM warrant & common stock holders will show same return will be higher as $1.48 (calculated as SP*Z) in annual leverage costs have to be accounted for.

Below is an approach to identifying that price-point and measuring sensitivity of General Motors warrant (GM-WT-B) price to common stock price:

To determine stock price on expiry date (7/10/2019) where warrant and stock returns will equal (denoted by X) -

Current Price - $29.94

Warrant Price (NYSE:WP) - $12.91

Strike Price - $18.33

Maximum dividends through expiry exempted from anti-dilution (D) = 0.30*19 = $5.70

Stock Return (SR) = (X - CP + D) / CP**

Warrant Return (WR) = (X - SP - WP) / WP

** The calculation is not exact as the time value of ongoing dividend payments is not considered. Nevertheless, the adjustment required would be relatively minor and so is ignored.

Solve for X where SR=WR:

(X - CP + D) / CP = (X - SP - WP) / WP

X = (WP * D + CP * SP) / (CP - WP)

= (12.91 * 5.70 + 29.94 * 18.33) / (29.94 - 12.91) = $36.55

If the stock trades above $36.55, the warrant (GM-WT-B) will have a better return. Otherwise, the common stock will have a better return.

Sensitivity of GM-WT-B relative to GM stock price can then be measured as:

Expiry price-point where returns are even : $36.55

Stock & Warrant return, if stock price is $36.5 at expiry: 41.12%**

** Either SR or WR formulas apply

Expiry price @ X+25%: $45.60,

Stock return: (45.60 - 29.94 + 5.70) / 29.94 = 71.34%,

Warrant return: (45.60 - 18.33 - 12.91) / 12.91 = 111.23%

Expiry price @ X-25%: $27.41,

Stock return: (27.41 - 29.94 + 5.70) / 29.94 = 10.59%,

Warrant return: (27.41 - 18.33 - 12.91)/12.91 = (29.67%)

Below is a sensitivity analysis that shows the performance of the warrants relative to the performance of the corresponding common stock at expiry for the eight businesses:

The analysis is not exact in certain cases as it makes the assumption that the dividend thresholds where anti-dilution takes effect has already reached for all the warrants. This is not yet true for the following securities and so the future warrant performance relative to common stock price is slightly understated in those cases: AIG-WT, BAC-WT-B, COF-WT, and PNC-WT.

Conclusion:

The analysis shows a clear picture of how the warrant performance will compare to common stock performance at different price points at expiry. The negative effect of cost-of-leverage on warrant price performance diminishes at higher price-points of the common stock as cost-of-leverage is a fixed cost. In general, if you estimate a high probability for the price at expiry of the common stock to exceed the equal-return price-point, the warrants are a better bet compared to common stock and vice-versa.

Reference: The formulas used in this article were based on a discussion here.

**Disclosure:** The author is long GM. The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I am long GM through GM-WT-B warrants