VALUATION OF A PUT OPTION

NOTE – I had asked a similar question previouly this one is different previous question was valuation of call option this i valuation of put option

SCENARIO –
Company X is a considering an investment in a joint venture to develop high quality office blocks
to be let out to blue chip corporate clients. This project has a 30-year life, and is expected to cost
Company X $90 million and to generate an NPV of $10 million for Company X.
The project manager has argued that this understates the true value of the project because the
NPV of $10 million ignores the option to sell Company X’s share in the project back to its partner
for $40 million at any time during the first ten years of the project.
The standard deviation is 45% p.a. and the risk-free rate is 5% p.a

QUESTION

identify the basic variables that are needed to complete the call option formula.

Pa = PV of cash inflow
Pe = cost of investment

ANSWER IN THE TEXT

Pa = 100m Assuming that this is in 10 years’ time, then 20 years of the project remain so Pa is estimated as 20/30 × 100 = $66.7m.

Pe = 40m

DOUBT

1) should’t the cost of investment (Pe) be 90 million since they have invested 90m ? why is it 40 m

2) should’t the PV of cash inflow (Pa) be 100 million since 90M+10M(NPV) ? how have they arrived at the figure 66.7M could you please explain in detail