Suppose your calculation shows that the PV of depreciation tax shield (including terminal value) is 100,000, and the PV of non-depreciation FCF (including terminal value) is 900,000. Assuming that Apple currently has 10 million shares outstanding (or 10,000 thousand shares), which range of share price would be the maximum level that you are willing to pay to acquire the firm?

Question

Suppose your calculation shows that the PV of depreciation tax shield (including terminal value) is 100,000, and the PV of non-depreciation FCF (including terminal value) is 900,000.  Assuming that Apple currently has 10 million shares outstanding (or 10,000 thousand shares), which range of share price would be the maximum level that you are willing to pay to acquire the firm?

BlackTom AI · Accepted Answer

Restating the problem: You have PV of depreciation tax shield (including terminal value) = 100,000 and PV of non-depreciation FCF (including terminal value) = 900,000. The firm has 10 million shares outstanding (10,000 thousand shares). The question asks for the range of share price that represents the maximum amount you would be willing to pay to acquire the firm.

First, compute the total value implied by the two PV components combined: 100,000 + 900,000 = 1,000,000. This can be interpreted as the total enterprise value (or equity value, depending on the framing) available to shareholders under the given projections.

Next, translate the total value into a per-share value by dividing by the number of shares: 1,000,000 / 10,000 thousand shares = 1,000,000 / 10,000,000 = 0.10? Wait, careful with units. The problem states 10 million shares outstanding (or 10,000 thousand shares). If the total value 1,000,000 refers to the same currency units as the per-share denominators, you would divide 1,000,000 by 10,000 thousand to get per-share value in the same currency units as the inputs.

To avoid unit confusion, interpret the arithmetic as: total value = 1,000,000 (in the same currency units as the per-share pricing). Number of shares = 10,000 thousand = 10,000,000 shares. Per-share value = 1,000,000 / 10,000,000 = 0.10. However, this outcome (0.10 per share) seems inconsistent with the scale of the inputs, suggesting that the problem intends the 1,000,000 to be in thousands of dollars if the share count is in thousands, or that the total is meant to be allocated across 10,000 thousand shares. If we instead treat 1,000,000 as thousand dollars and 10,000 thousand shares, per-share value = 1,000,000,000 / 10,000,000 = 100. This yields a per-share value of $100.

Given typical financial conventions in such questions, the intended result is that the total PV (1,000,000) corresponds to an equity value of $1,000,000,000 spread over 10,000,000 shares, giving $100 per share. If any additional adjustments (debt, cash, or minority interests) were specified, the per-share price could change, but none are provided in the prompt.

Now evaluate each answer choice:

- Option "$48-$52": This range is far below the trailing per-share value of about $100 derived from dividing the total PV by 10 million shares. Since the maximum price you’d be willing to pay would be at least the per-share value implied by the PV figures, this range is inconsistent with the calculation and would be too low.
- Option "$60-$64": Similar to the previous, this range remains well under the $100 per-share figure implied by 1,000,000 total value divided by 10,000,000 shares. It misstates the maximum affordable price given the PVs provided.
- Option "$44-48": This range also sits below the calculated $100 per share, and thus misrepresents the maximum value derived from the PV figures.
- Option "None of the above": Since all the listed ranges ($48-$52, $60-$64, $44-48) fail to match the per-share value implied by the PV totals, this option accommodates the discrepancy and aligns with the expectation that a value around $100 per share (given the numbers) would be possible, not any of the specified sub-$60 ranges.
- Option "$52-$60": This range is also lower than the implied $100 per share from the PV totals and would therefore not reflect the maximum price suggested by the provided figures.

In summary, each of the numeric ranges falls short of the per-share value implied by combining the PV figures and allocating across 10 million shares. Only the "None of the above" option remains consistent with the calculation outcome given the data provided, since none of the specified ranges matches the $100 per share implication.

FA25-BL-BUS-F305-1130 Final Exam

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