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ACCA Strategic Professional · Advanced Financial Management · Application of option pricing theory in investment decisions

Zeta Ltd has an option to expand into a new market in two years. The present value of the expansion's cash inflows is $8m and the cost of expansion is $9m, so the expansion has a negative NPV today. Zeta values the option as a European call using Black-Scholes with risk-free rate 5% (e^-0.10 = 0.9048) and volatility 30%. The calculations give d1 = 0.17 and d2 = -0.25, with N(d1) = 0.5675 and N(d2) = 0.4013. What is the value of the expansion option?

The expansion option is worth about $1.27m. It is valued as a call: 8m x 0.5675 gives 4.54m, less the discounted cost 9m x 0.9048 x 0.4013 which is 3.27m. A negative current NPV does not make the option worthless because future project value is uncertain.

  1. A$1.27mCorrect
  2. B$0.93m
  3. C$1.42m
  4. DNil, because the expansion has a negative NPV

Explanation

Call = 8 x 0.5675 - 9 x 0.9048 x 0.4013 = 4.540 - 3.268 = $1.27m. Not discounting the exercise price gives 4.540 - 3.612 = $0.93m. $1.42m is the put value from parity, not the call. The option has value because the future value of the project is uncertain, despite the negative NPV today.

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