George Clooney has been offered $14 million (to be paid in 1 year from now) for starring in Batman 4, Batman 5, and Batman 6. If Clooney accepts this offer, he will have to forego acting in Ocean’s 14, Ocean’s 15, and Ocean’s 16 that would have paid him $5 million each (in 2, 3, and 4 years from now). Clooney assumes his personal cost of capital is 10%. Based on this information, the NPV today of Clooney’s decision to accept Batman films is:

Question

BlackTom AI · Accepted Answer

Compare the present value of the $14.0 million Batman payment with the present value of the three forgone $5.0 million Ocean’s payments, using a 10% discount rate.

Relevant concepts:
- Net present value (NPV) = PV of benefits − PV of costs (here, forgone earnings are an opportunity cost).
- Present value of a single future payment: PV = FV / (1 + r)^t.

Step-by-step calculation:
1. PV of Batman payment (received in 1 year):
   PV_Batman = 14 / (1.10)^1 = 14 / 1.10 = 12.7272727 million ≈ 12.7273M.

2. PVs of forgone Ocean’s payments:
   - Year 2: PV_O2 = 5 / (1.10)^2 = 5 / 1.21 = 4.1322314M ≈ 4.1322M.
   - Year 3: PV_O3 = 5 / (1.10)^3 = 5 / 1.331 = 3.7578810M ≈ 3.7579M.
   - Year 4: PV_O4 = 5 / (1.10)^4 = 5 / 1.4641 = 3.4149660M ≈ 3.4150M.

3. Sum PV of forgone earnings:
   PV_forgone = 4.1322 + 3.7579 + 3.4150 = 11.3051M (rounded).

4. NPV today of accepting Batman films:
   NPV = PV_Batman − PV_forgone = 12.7273 − 11.3051 = 1.4222M ≈ 1.42 million.

Why this answer is correct:
The decision’s value today must reflect discounted values of the future cash inflow and the opportunity costs. Discounting each payment correctly at 10% and subtracting the total PV of forgone earnings yields approximately $1.42 million, which is the positive NPV of accepting the Batman offer.

Why the other options are incorrect:
- $1.56M: inconsistent with precise discounting and summation above; likely the result of rounding errors or mis-discounting one payment.
- $12.72M: equals only the PV of the $14M Batman payment (14/1.1) and ignores the PV of forgone Ocean’s payments.
- $14.00M: is the nominal (undiscounted) future receipt and ignores time value of money and opportunity costs.

Conclusion: The correct NPV today of accepting the Batman films is $1.42 million, matching the provided answer.

类似问题

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