Question

Anthony's Inc., has a zero coupon bond that matures in five years with a face value of $1.2M. The current value of the firm is $1.0M, measured at the enterprise level. The standard deviation of the firm's assets returns is 40%. The firm pays no dividends. The risk-free rate is 3.0% per year.

a) What is the value (or price if you prefer) of the zero IF the yield to maturity was the risk-free rate?

b) Using the Black-Scholes methodology, what is the value of the equity of the firm today?

c) Using the Black-Scholes methodology, what is the yield to maturity of the zero?

d) Suppose management is considering a restructuring of the operations. THIS change will NOT affect the average free cash flow of the business in the future, BUT will increase the standard deviation of the firm's assets returns from the current 40% to a new level of 50%:

i. Will the value of the equity change as a result of this proposed change?

ii. How will the zero debt holders react to the planned change?

Answer 1

a). If the YTM is 3% then FV = 1.2 million, N = 5, solve for PV. PV = 1.04 million

b). Black-Scholes model inputs:

Value of the underlying asset (S)	Value of the firm	1
Exercise price (K)	Face value of debt	1.2
Option life (t)	Life of zero bond	5
Volatility (s)	Standard deviation	40%
Risk-free rate ('r)		3%

Using the formulae:

d1 = {ln(S/K) + (r +s^2/2)t}/(s(t^0.5))

d2 = d1 - (s(t^0.5))

N(d1) - Normal distribution of d1

N(d2) - Normal distribution of d2

C = S*N(d1) - N(d2)*K*(e^(-rt))

	d1	0.4111	N(d1)	0.6595
	d2	-0.4834	N(d2)	0.3144
Formula		(In million $ except %)
Using call option	Value of equity ('E)	0.335
(S-E)	Value of debt	0.67
Using RATE function	YTM	12.52%

b). Value of equity today = $0.335 million

c). YTM of the zero = 12.52%

d-i). If standard deviation is increased to 50% then value of equity will increase.

d-ii). Debt holders would react favorably as the YTM of the zero will increase, as well.