For the dynamite/dud project:

(a) The expected payoff is E(P) = 20% . $20,000 + 70% . $40,000 + 10% . $80,000 = $40,000.

(b) The present value of the expected payoff is $40,000/1.08 ≈ $37,037.

(c) The three rate of return outcomes are $20,000/$37,037 − 1≈ −46%, $40,000/$37,037 − 1≈ +8%,

$80,000/$37,037 − 1≈ +116%.

(d) The expected rate of return is 20% . (−46%) + 70% . (+8%) + 10% . (+116%) = −9.2% + 5.6% +
11.6% = 8%.