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

Using the option view of corporate capital structure, Zeta Co has assets worth $100m and zero-coupon debt with a face value of $100m due in one year. The risk-free rate is 25%, so the present value of the debt face value at the risk-free rate is $80m. Equity is valued as a European call on the assets at $30m. What is the value of the put option implicit in the risk of default, that is, the shareholders' limited-liability put on the assets?

The put is worth $10m. Put-call parity gives put = call - assets + present value of debt = 30 - 100 + 80 = $10m. This is confirmed because risky debt is worth 100 - 30 = $70m, which is risk-free debt of $80m less the $10m default put.

  1. A$10mCorrect
  2. B$20m
  3. C$30m
  4. D$70m

Explanation

Parity: P = C - S + PV(X) = 30 - 100 + 80 = $10m. Check: risky debt = assets - equity = $70m, which equals risk-free debt $80m less the put $10m. Option 2 uses the undiscounted face value (30 - 100 + 100 would be 30, and 20 results from other mishandling), and $70m is the value of the risky debt, not the put.

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