Question

The following facts have been assembled to facilitate an analysis of an option to abandon a project currently being considered by Xiaomi Group ltd:

Risk-free rate of return	8%
Time until decision to abandon is taken	0.64 years
PV of cash flows if the project is not abandoned	Ksh.415 million
Salvage value if abandoned	Ksh.480 million

The variance of the projects rate of return is being considered at different levels as follows:

Var-1	3%
Var-2	6%
Var-3	9%
Var-4	12%

Required:

Assess the effect of a change in the variance on the Value of the Abandonment Option Using black-Scholes options valuation model.

Answer 1

The value of the abandonment option is the put option value.

	Inputs:
	Current stock price (S)	415.00	415.00	415.00	415.00
	Strike price (K)	480.00	480.00	480.00	480.00
	Time until expiration(in years) (t)	0.640	0.640	0.640	0.640
	Variance (v)	3.00%	6.00%	9.00%	12.00%
v^0.5	volatility (s)	17.3%	24.5%	30.0%	34.6%
	risk-free rate (r)	8.00%	8.00%	8.00%	8.00%
Formula	Output:
{ln(S/K) + (r +s^2/2)t}/(s(t^0.5))	d1	(0.6113)	(0.3833)	(0.2729)	(0.2017)
d1 - (s(t^0.5))	d2	(0.7499)	(0.5792)	(0.5129)	(0.4789)
Normal distribution of -d1 using NORMDIST function	N(-d1)	0.7295	0.6492	0.6076	0.5799
Normal distribution of -d2 using NORMDIST function	N(-d2)	0.7733	0.7188	0.6960	0.6840
K*(e^(-rt))*N(-d2) - S*N(-d1)	Put premium (P)	49.9299	58.3608	65.2738	71.2506

Note: Volatility in a Black-Scholes model is measured by standard deviation so variance^0.5 has been taken as volatility.

As volatility increases, the value of the abandonment option increases, as well. This is logical since with increase in uncertainty of the project, the option to be able to abandon the project at a later date becomes more valuable.