For the loan that promises to pay off $25,000 (instead of providing it): In the tornado state, the creditor gets all $20,000. In the sunshine state, the creditor receives the promise of $25,000. Therefore, the creditor’s expected payoff is 20% . $20,000 + 80% . $25,000 = $24,000. To offer an expected rate of return of 10%, you can get $24,000/1.1 ≈ $21,818 from the creditor today.

(a) Repeating the table:

Event Prob Building Value Mortgage Value Levered Ownership Tornado 20% $20,000 $20,000 $0 Sunshine 80% $100,000 $25,000 $75,000 Expected Value at Time 1 $84,000 $24,000 $60,000 Present Value at Time 0 $76,364 $21,818 $54,546 From Time 0 to Time 1, E(˜r) 10% 10% 10%

(b) The loan pays $21,818 today.

(c) The promised rate of return is therefore $25,000/$21,818 − 1 ≈ 14.58%.

(d) The levered building ownership is riskier than the full building ownership.