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

Kestrel plc has assets worth $100m now. In one year they will be worth either $140m or $70m. The risk-free rate is 5% and the risk-neutral probability of the up move is 0.5. Kestrel has zero-coupon debt with a face value of $90m due in one year. What is the promised yield on the debt?

The promised yield is 18.1%. Equity is a call worth 0.5 × 50 / 1.05 = $23.81m, so debt is worth $76.19m. The lenders are promised $90m, and 90 divided by 76.19 minus one gives about 18.1%.

  1. A18.1%Correct
  2. B12.5%
  3. C28.6%
  4. D5.0%

Explanation

Equity payoffs are 50 (up) and 0 (down), so equity = 0.5 × 50 / 1.05 = $23.81m. Debt = 100 − 23.81 = $76.19m. Check: debt payoffs of 90 and 70 give an expected 80, and 80/1.05 = 76.19. Promised yield = 90/76.19 − 1 = 18.1%. Using 90/80 gives 12.5%, which is wrong because it ignores the discounting of the risky expected payoff.

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