# Applying Black-Scholes to valuation of real options

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• massif
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Hello again.

My question refers to the P4 sample question (Allegro Technologies Co.) and Question 2(iii) of the June 2010 paper( AggroChem).

I want to know what is the appropriate proxy to use for Pe – the exercise price when valuing a real option? And if the proxy will change depending on whether we are valuing a put option or a call option?

1. June 2010 is valuing a call option ( an acquisition/expansion). The proxy for Pe is the value of the outstanding debt calculated as the present value of a zero coupon bond offering the same yield as the current debt.
[ \$3M X 1.08 to the power -5 = \$2.04175M]

Allegro is valuing a put option( a possible disposal/abandon).But it uses the purchase price that Staccato Innovations Co (SIC) is willing to pay Allegro (\$113,000,000) instead of present valuing SIC’s outstanding debt.I’m puzzled at the two different methods being used. Would it be wrong to calculate Pe (exercise price) as the present value of SIC’s loan notes to give
[ (\$92M X 1.02) X 1.05 to the power -3 = \$81,062,520.25 ?

Why are the two methods different? The sample question, Allegro, provides all the necessary information to be able to PV SIC’s debt ( the debt, the interest rate, the time period 2016 – 2018) so why was this method not used? Is it because one is a put option and the other is a call?

maoxuanyan
Member
• Topics: 0
• Replies: 3

BSOP can be used in many situations such as share price,valuation of company or real option.
As for sample jun,2010,BSOP are used to valution the value of company,so they assum present value of bond as Pe.
AS for sample Allegro,this is real option-option to abandon,in this situaiton,Pe =disposal amount
so when use of BSOP,we must understand the stuation which BSOP is applicable first.
Hope this can explain.

coscos
Participant
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what are the rules for determining Pa, Pe and t for the following options: delay, expand, redeploy and abandon? for example: Pa is always PV of cash inflows from now until t? Pe is sell price, Pe is investment/capex?

John Moffat
Keymaster
• Topics: 3
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massif: In the exam do not expect to be told to use a proxy for Pe. Allegro was written by the examiner who is no longer there and was very unusual – you had to use a proxy because you were told to.
Almost certainly with the current examiner the idea of a proxy will not be mentioned (but if it is you do what you are told to do) and Pe will either be the investment required or the disposal amount (depending on the whether it is option to delay, abandon etc..)

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