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Explanation:
The Merton model values the firm's equity as a European call option on the firm's assets. The market value of the debt (D) can be found using the fundamental accounting equation D = V - E, where V is the value of the firm's assets and E is the value of the firm's equity.
The Black-Scholes-Merton formula for equity is: E = V * N(d₁) - K * e^(-rt) * N(d₂)
Given values: V = 85 K = 55 r = 5% = 0.05 t = 2 N(d₁) = 0.9495 N(d₂) = 0.8983
Calculating E: E = 85 * 0.9495 - 55 * e^(-0.05 * 2) * 0.8983 E = 80.7075 - 55 * e^(-0.10) * 0.8983 E = 80.7075 - 55 * 0.904837 * 0.8983 E = 80.7075 - 44.7049 = 36.0026 million
Calculating D: D = V - E D = 85 - 36.0026 = 48.9974 million
Option A (CAD 48.996 million) is the closest estimate.
What is the correct estimate of the market value of the company’s debt using the Merton model?
A
CAD 48.996 million
B
CAD 49.764 million
C
CAD 53.699 million
D
CAD 54.056 million
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