
Explanation:
(Note: The original text incorrectly stated 'Correct Answer B' and 'Explanation B is correct' in a typo, but the mathematical derivation and the explicit statement 'B is incorrect' within the same explanation confirm that A is the correct answer. The explanation has been slightly adapted to reflect the correct option letter based on the provided text.)
Applying the Merton model, first calculate the value of equity (E), expressed as follows:
E = V*N(d₁) − De⁻ʳᵀN(d₂)
where:
V = CAD 85 million = market value of assets
N(d₁) = 0.9495
N(d₂) = 0.8983
D = CAD 55 million = face value of the zero-coupon bond
e⁻ʳᵀ = e⁻⁰·⁰⁵ײ = 0.9048
Thus,
E = (85,000,000)(0.9495) − (0.9048)(55,000,000)*(0.8983)
= 80,707,500 − 44,703,001
= CAD 36,004,499.
Therefore,
Market value of debt = V − E = 85,000,000 − 36,004,499 = CAD 48,995,501 (which rounds to CAD 48.996 million).
A is correct.
B is incorrect. CAD 49,764,000 is the face value of debt discounted over 2 years.
C is incorrect. CAD 53,699,000 is the result obtained if the discount factor (e⁻ʳᵀ) in the formula for equity value is not applied.
D is incorrect. CAD 54,056,000 is the result obtained if N(d₂) in the formula for equity value is not applied.
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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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