Question $5$

$[$Total: $\backslash (\backslash$mathbf$\{25\}\backslash )$ marks$]$

An entrepreneur has two start$-$up ideas that require the same investment of $\backslash (\backslash$$ $160\backslash )$ million at $\backslash (\backslash$mathrm$\{$t$\}=0\backslash ).$ The first idea is for a food delivery app that will generate at $\backslash (\backslash$mathrm$\{$t$\}=2\backslash )$ a cash$-$flow of $\backslash (\backslash$$ $220\backslash )$ million with a probability $0\mathrm{.}7$ or a cash$-$flow of $\backslash (\backslash$$ $80\backslash )$ million with a probability $0\mathrm{.}3.$ The second idea is for a ride$-$sharing app that will generate at $\backslash (\backslash$mathrm$\{$t$\}=2\backslash )$ a cash$-$flow of $\backslash (\backslash$$ $400\backslash )$ million with a probability $0\mathrm{.}3$ or a cash$-$flow of $\backslash (\backslash$$ $80\backslash )$ million with a probability $0\mathrm{.}7.$ The entrepreneur can only pursue one of the two ideas at a time, she has no money to invest in her ideas, and must raise the investment funds externally. The discount rate is $0$ and there are no taxes.

a$)$ Find the net present value of each of the two projects.

$[5$ marks$]$

b$)$ Assume that the entrepreneur approaches a bank to raise all the funds and that the bank believes that the entrepreneur will invest in the food delivery app. What is the face value of the debt? Which of the two ideas will be adopted by the entrepreneur? What is the expected payoff of the bank? Discuss your results.

$[10$ marks$]$

c$)$ Now assume that the bank anticipates the incentives of the entrepreneur and believes that once the funds have been raised, she will choose to develop the ridesharing app. What is the face value of the debt? Which of the two ideas will be adopted by the entrepreneur? What is the expected payoff of the bank? Discuss your results.

$[10$ marks$]$