FRM Part I · FRM Exam Part I · Measuring Credit Risk
In a Merton framework, a firm's assets are worth 200 million. It has zero-coupon debt of face value 150 million due in one year, and the continuously compounded risk-free rate is 4%. The value of a one-year European put on the assets with a strike of 150 million is 6 million. What is the value of the firm's equity? (e^-0.04 = 0.960789)
Equity is about 61.88 million. Risky debt equals the discounted face value of 144.12 million minus the 6 million put, giving 138.12 million, and equity is the 200 million of assets minus that. Put-call parity gives the same result.
- AApproximately 61.88 millionCorrect
- BApproximately 56.00 million
- CApproximately 50.00 million
- DApproximately 49.88 million
Explanation
Risky debt = 150×0.960789 - 6 = 144.12 - 6 = 138.12. Equity = 200 - 138.12 = 61.88. Check with put-call parity: C = V - De^(-rT) + P = 200 - 144.12 + 6 = 61.88. Ignoring discounting and adding the put gives 56.00.
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