Debtco's Debt Debate

This week we are looking at different pricing methods for securities. In this case company Debtco has a total enterprise value (1) of $100 million and has issued zero-coupon bonds with an aggregate face value of $80 million (80,000 bonds each with a face value of $1,000) with a one-year maturity date.  The risk free interest rate is 8% and the volatility of the firms’ assets are 30%. Using the Black-Scholes model:

and substituting the call option for Debtco’s equity and the exercise price for the face value of Debtco’s debt, we can use the following formula to find the value of Debtco’s equity:

V= 100

B = 80

T = 1

SD = 0.3

Using this formula we find the value of equity is $28.24 million, making the value of debt (D) worth $71.86 million. Because Debtco issued zero-coupon, one year bonds

the yield-to-maturity will equal the promised rate of interest (R), found in this formula:

The YTM equals: (ln(80/71.86))/1 = 10.87%

This computation can also be done in excel using the options valuing spread-sheet provided at www.mhhe.com/bkm

INPUTS			OUTPUTS
Standard Deviation	0.3		d1	1.1605
Maturity (in years)	1		d2	0.8605
Risk-free rate	0.08		n(d1)	0.8771
Value of Firm	100		N(d2)	0.8052
Bond Value	80		Equity Value	28.2411
Dividend Yield	0		B/S put value	2.0904
Value of Debt	71.7589
YTM	10.87%

The aggregate face value of Debtco’s bond increased to $108.33 million. Using the same formula, the new YTM on Debtco’s debt is 20.70%.

INPUTS			OUTPUTS
Standard Deviation	0.3		d1	0.1500
Maturity (in years)	1		d2	-0.1500
Risk-free rate	0.08		n(d1)	0.5596
Value of Firm	100		N(d2)	0.4404
Bond Value	108.33		Equity Value	11.9230
Dividend Yield	0		B/S put value	11.9242
Value of Debt	88.0770
YTM	20.70%

Assume that the firm's management swaps its assets for riskier assets of the same total value.  How would this asset swap affect the value of its debt and equity?  Explain

Later, Debtco decides to swap its assets for riskier assets of the same total value (100 million). When the volatility of Debtco’s assets increases, the value of the equity must increase to offset lower value of the the debt due to uncertainty in repayment  (lower value, higher yields).

 In the below example, the face value of debt is 80 million and the total value is 100 million, the volatility has increased to 50%. We find that the value of equity has increased to 33.2 million and the value of debt has decreased to 66.8 million. The YTM on the debt has increased to 18.04%. 

INPUTS			OUTPUTS
Standard Deviation	0.5		d1	0.8563
Maturity (in years)	1		d2	0.3563
Risk-free rate	0.08		n(d1)	0.8041
Value of Firm	100		N(d2)	0.6392
Bond Value	80		Equity Value	33.2045
Dividend Yield	0		B/S put value	7.0538
Value of Debt	66.7955
YTM	18.04%

(1) TEV = Market Capitalization + Interest Bearing Debt + Preferred Stock - Excess Cash