Valuing Hybrid Securities and Noncontrolling Interests  351
If improvements to operations increase enterprise value, it becomes neces-
sary to revalue Square’s convertibles using an option-pricing model. To model 
the value of Square’s convertible debt, disaggregate the value of convertible 
debt into underlying straight debt and the option value to convert. For the 
bond maturing in 2022, the value of straight debt equals the net present value 
of a 0.375 percent coupon bond yielding 2.48 percent (the yield on comparable 
bonds without conversion features), maturing in 3.25 years (the remaining 
life). Without conversion, this bond is valued at 93.45 percent of $211.7 million 
in outstanding principal, or $197.9 million.
To determine the option to convert’s value, you need six inputs: the un-
derlying asset value, the strike price, the volatility of the underlying asset, the 
risk-free rate, the time to maturity, and the dividend rate on the underlying 
asset. For the option embedded in Square’s 2022 convertible bond, the under-
lying asset is 9.23 million shares of Square stock, whose current value equals 
$517.5 million. The strike price, which represents what the investor must pay 
to receive the shares, equals the current value of straight debt, currently val-
ued at $197.9 million. The volatility of Square shares (30.9 percent) is reported 
in the company’s 10-K. The bond’s time to maturity is 3.25 years, and the 
current risk-free rate is 2.48 percent.26 Square does not pay dividends, so the 
dividend yield is set at zero.
Plugging the data into a Black-Scholes estimator leads to an option value 
of $336.9 million. Thus, as illustrated in the third data column of Exhibit 16.4, 
the Black-Scholes value of the convertible debt equals $534.8 million ($197.9 in 
straight debt plus $336.9 in option value). This result is contingent on stabil-
ity of the Black-Scholes inputs, especially volatility. If volatility is expected to 
drop as the company matures, the historical estimate of volatility will overes-
timate the option value. The errant valuation is largest for long-dated options, 
which is often the case for convertible debt.
An alternative to option pricing is the conversion value approach, shown in 
the fourth data column of Exhibit 16.4. The method is easier to implement than 
Black-Scholes but ignores optionality. Under the conversion value approach, con-
vertible bonds are converted immediately into equity. Since Square’s bonds are 
convertible into 20.3 million shares (9.2 million shares from the convertible debt 
due in 2022 and 11.1 million shares from the convertible debt due in 2023), non-
diluted shares are increased from 419.7 million to 440.0 million. This approach 
zeroes out convertible debt and divides the equity value by diluted shares.
In this case, each approach leads to a similar value because the value of 
conversion is much higher than the value of traditional debt (known as being 
in the money). For bonds out of the money, the conversion approach will lead 
to an underestimation of the bonds’ value. Therefore, we recommend using an 
option valuation model, such as Black-Scholes.
26 Square’s convertible debt is not callable, so the remaining maturity can be used in the options 
valuation. If the debt is callable, this must be incorporated into the bond’s valuation.