ABC Corporation has requested a $2.1 million loan. The corporation has a $2 million in retained earnings held as cash, and an existing debt obligation that calls for a repayment of $4 million one period hence, which has seniority over any new bank loan. The firm has assets that will be worth $6 million with probability 0.7 and nothing with probability 0.3 one period hence in addition to the retained earnings. These are the assets in place if the firm does not make any investment at present. The firm also has the choice of investing in one of two mutually exclusive projects (A or B). Project A will yield $4 million with probability 0.7 and $2 million with probability 0.3 one period hence. Its cash flows are uncorrelated with (and in addition to) those from the assets in place. Project B will yield $13 million with probability 0.2 and nothing with probability 0.8. Its cash flows are also uncorrelated with those from the assets in place. Assume that everybody is risk neutral and that there is no discounting (the bank's cost of funds is zero).

i) If the bank assumes that project A will be undertaken, show that it will competatively price the loan at 14.29%. Confirm that the bank's assumption that project A will be undertaken is correct.

*Notice there is a difference between the way how XH(a/b) are computed. How come project A uses the upper tree "(0.49+0.21)(XHA) + lower tree 0.21(2) = 2.1"whereas project B summed all 3 probability "(0.14+0.56+0.06)(XHB) = 2.1" to compute?why that so?