Robert Bosch GmbH is a privately held firm. As an analyst trying to determine the value of Robert Bosch GmbH's ordinary equity and bonds, you have estimated that the market value of the firm's assets is €50 million. The standard deviation of the asset return is estimated to be 0.2. The debt of Robert Bosch GmbH, which consists of zero-coupon bank loans, will come due 2 years from now and its face value is €40 million. Assume the risk-free rate is 3% p.a. (annually compounded). Determine the market value of debt using the binomial model. Use one binomial period. Interpret risky debt as a portfolio of risk-free debt and a short put on the assets of a firm, with a strike price equal to the face value of debt.

a) Calculate u and d. Note that the volatility is annual but the binomial period lasts for two years.

b) Calculate the risk-neutral probabilities. Note that the interest rate is quoted per annum but the binomial period lasts for two years.

c) Calculate the value of the short put option.

d) Calculate the market value of debt as the difference between the (discounted) debt face value and the value of the short put.