An unlevered firm has existing assets with a value of $100 and can invest in a project that costs $400 at t=0 and pays $800 with a probability of 50% and $200 with a probability of 50% at t=1. The firm needs to take on new debt with a face value of $400 to finance the project. Assume all market participants are risk neutral and have the same information about the cost and possible payoff of the project. The risk-free rate is 0. a. What is the amount that the lenders require at t=1 to be willing to provide the $400 investment costs? Calculate the PV of existing equity in this case. b. What share of the company do the existing equity holders need to sell if they want to fund the project by issuing new equity? Calculate the PV of existing equity in this case. c. Do the existing equity holders choose to fund the project by issuing debt or equity?

Assume for questions d. - f. that the existing equity holders know that the investment project will pay $800 for sure. External investors do not have this information. They still assess the project according to the information given above at the beginning of the exercise.

d. What is the amount that the lenders require at t=1 to be willing to provide the $400 investment costs? Calculate the PV of existing equity in this case. e. What share of the company do the existing equity holders need to sell if they want to fund the project by issuing new equity? Calculate the PV of existing equity in this case. f. Do the existing equity holders choose to fund the project by issuing debt or equity?