Maddox Pritchard has an entrepreneurial project called the Measuring Shovel, and he lacks capital for his business expansion. He is endowed with $A, which is greater than $0; and the expansion requires the capital investment of $150,000 in total. Thus, Maddox needs to raise $(150,000 A) from outside investors. The project generates either $200,000 with probability p {0.8,0.3} or $0 with probability 1 p. Maddox chooses to either work hard to set p = 0.8 at the expense of opportunity cost of $10,000, or shirk (i.e., p = 0.3). For simplicity, investors are willing to provide capital as long as they break even. For simplicity, assume zero required return. https://youtu.be/wvj0qxQZknI

**PLEASE SHOW ALL WORK WITH EXPLANATIONS THANK YOU a) Calculate the Net Present Value (NPV) of the project with p = 0.8.

b) Calculate the Net Present Value (NPV) of the project with p = 0.3.

c) Derive the minimum stake for Maddox in the success of the project (i.e., $200,000) for him to have an incentive to work, not shirk.

d) Derive the lowest value of A that induces outside investors to provide capital $(150,000 A) to Maddox (Hint: you need to assume that Maddox will take the minimum stake, as calculated in C)

e) Suppose that A = $50,000. Derive the optimal stake percentage for Maddox, given that investors provide capital as long as they break even.

f) If A = $0, can Maddox raise capital from investors? Why or why not?