Mock exam on inflation

FDU Mock Exam - Sol

Q1: B

Q2: B

Q3: A

Q4: C

Q5: adbeg

Q6:

1. Expansion option
2. Production option
3. Abandonment option
4. Timing option

Q7:

1. Decision tree: single decision node with three branches X, Y, Z leading to chance node with outcomes Up/Flat/Down and payoffs as table.
2. EMV calculations (in thousands):

• EMV(X) = 0.35·220 + 0.45·110 + 0.20·30 = 77 + 49.5 + 6 = 132.5
• EMV(Y) = 0.35·160 + 0.45·130 + 0.20·70 = 56 + 58.5 + 14 = 128.5
• EMV(Z) = 0.35·95 + 0.45·95 + 0.20·95 = 95

Recommendation: Choose X (highest EMV = 132.5k).

1. Opportunity loss table: for each state, determine best payoff and compute regrets.

State best payoff: Up → max(220,160,95)=220; Flat → max(110,130,95)=130; Down → max(30,70,95)=95.

Regret matrix (best − alternative):

• X: Up 0, Flat 20, Down 65 → weighted EOL(X)=0.35·0 + 0.45·20 + 0.20·65 = 0 + 9 + 13 = 22
• Y: Up 60, Flat 0, Down 25 → EOL(Y)=0.35·60 + 0.45·0 + 0.20·25 = 21 + 0 + 5 = 26
• Z: Up 125, Flat 35, Down 0 → EOL(Z)=0.35·125 + 0.45·35 + 0.20·0 = 43.75 + 15.75 + 0 = 59.5

1. EVPI = expected value with perfect information − best EMV. Expected value with perfect info = Σ_state p(state)·(best payoff in that state) = 0.35·220 + 0.45·130 + 0.20·95 = 77 + 58.5 + 19 = 154.5K; Best EMV (without info) = 132.5K; EVPI = 154.5 − 132.5 = 22K.

Q8:

We want P(Equity ↓ | Interest ↑) = count(Equity ↓ and Interest ↑) / count(Interest ↑) = 900 / 1000 = 0.90.

Q9:

Inputs: Immediate: cost 6.0 at t0; CF at t1: 13 (p0.35), 7 (p0.45), 3 (p0.20). Discount R=11%.

Immediate strategy NPV:

• Expected CF at t1 = 0.35·13 + 0.45·7 + 0.20·3 = 4.55 + 3.15 + 0.6 = 8.3M
• PV of expected CF = 8.3 / (1+0.11) ≈ 8.3 / 1.11 ≈ 7.48
• NPV_immediate = −6.0 + 7.48 = 1.48M

Wait strategy:

• Pay waiting cost 0.6 at t0 (so immediate outflow −0.6). After one year you observe signal: favorable p=0.65 --- if invest at t1 cost 6.0 and receive 12 at t2; unfavorable p=0.35 --- you may invest and get 5 at t2 or abandon (optimal: invest only if positive NPV at that time — compare PV of expected CF at t2 discounted to t1). Compute at t1 expected payoff conditional on favorable:
• Favorable: CF at t2 = 12; net at t1 if invest = −6 + (12 / (1+0.11)) = −6 + 10.81 = 4.81 (value at t1)
• Unfavorable: if invest: −6 + (5 / 1.11) = −6 + 4.5 = −1.5, it is negative, so optimal action is abandon (value 0). Therefore value at t1 = 0.65·4.81 + 0.35·0 = 3.13 (value expressed at t1). Discount that back to t0: PV = 3.13 / 1.11 ≈ 2.82 Subtract waiting cost 0.6 gives NPV_wait = −0.6 + 2.82 = 2.22M

Comparison: NPV_wait (2.22) > NPV_immediate (1.48), thus waiting is better. Real option type: option to delay; Option value = NPV_wait − NPV_immediate ≈ 0.74M.

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