Market value of debt = V – E

问题如下：

A fixed-income portfolio analyst is applying the Merton model to derive the market value of debt for a non-dividend paying chemical manufacturing company whose assets have a current market value of CAD 85 million. The face value of the company’s only debt, a zero-coupon bond maturing in 2 years, is CAD 55 million. The analyst uses the following additional information to complete the calculation:

•N(d1): 0.9495

•N(d2): 0.8983

•Annual risk-free interest rate: 5%

•Annual volatility of the company’s assets: 26%

What is the correct estimate of the market value of the company’s debt using the Merton model?

选项：

A.

CAD 48.996 million

B.

CAD 49.764 million

C.

CAD 53.699 million

D.

CAD 54.056 million

解释：

A is correct. Applying the Merton model, first calculate the value of equity (S), expressed as follows:

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^(-0.05*2) = 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

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.