As a portfolio manager at WhiteStone Capital, you are considering a potential buy of the stock of

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Question:

As a portfolio manager at WhiteStone Capital, you are considering a potential buy of the stock of Tivamy Co, which is strongly recommended by your analyst Joe. His reason is pretty straightforward: the stock price is extremely low, compared with 1 years ago. Joe collected the following data about Tivamy Co. and the market from your company's database and risk system.

The market value of equity is $15.8569025861272 million; the company's only liability is a debt with face value $220 million to be paid in 9 months, no periodic interest payment; risk-free rate r = 5% per year in continuously compounding; volatility of the asset return σA = 30% per annum on average:

(a) [2 points] What is the estimated market value of asset, according to Merton's model?

(b)Based on the result of (a), you are pretty sure the company can still grow at µA = 10% per year on average, estimate the probability of default of the company. What do you think may be the reason for the low price of the stock? 19

(c) Continue with (b), based on your experience, when a company is at the risk of default, the uncertainty increases whether it could indeed repay the debt or not, especially when the maturity is arriving. That uncertainty will be priced in by the market, if the market is efficient enough. Therefore, the σA = 30% estimated from the historical data may not be applicable. You'd like to do the following scenario analysis: for σA = 40%, 50%, 60%, and 70%, what would be the corresponding probability of default, holding other parameters unchanged (D=220, T= 9 months, r = 5%, µA = 10%)?