Use the risk-neutral valuation method to directly show that the risk-neutral discounted value of the existing debt of Unitron is $636,000 higher if the project in Example 13.17 is adopted.
Example 13.17
Valuing Cash Flow to Equity Holders with Real Options In a two-date binomial model, assume that Unitron, from Example 13.16, has existing projects that generate a firm worth $110 million at date 1 if the up state occurs and $71.5 million if the down state occurs. Assuming no taxes, a risk-free rate of 10 percent, and riskneutral probabilities of 1⁄2 attached to each of the two states, Unitron's date 0 value is $82.5 million ( = [.5($110 million) + .5($71.5 million)]/1.1). Unitron currently has debt maturing at date 1 with a face value of $77 million and a date 0 market value of $67.5 million ( = [.5($77 million) + .5($71.5 million)]/1.1) and equity with a date 0 market value of $15 million ( = [.5($110 million $77 million) = .5($0)]/1.1). Anna Kramer identifies a riskless project that will cost Unitron $28.23 million and will produce a cash flow of $31.62 million at date 1, providing a 12 percent return. The project will be entirely financed with debt that is equal in seniority to Unitron's existing debt. Compute the effect of the adoption of this project on the value of Unitron's existing debt and on the value of its equity.