Estimate a venture’s terminal value based on the following information: current year’s net income = $20,000; next year’s expected cash flow = $26,000; constant future growth rate = 7%; and venture investors’ required rate of return = 20%.

Question

Estimate a venture’s terminal value based on the following information:  current year’s net income = $20,000; next year’s expected cash flow = $26,000; constant future growth rate = 7%; and venture investors’ required rate of return = 20%.

BlackTom AI · Accepted Answer

The Gordon (perpetuity growth) model is appropriate: terminal value = next period’s cash flow / (required return − growth rate). This model assumes cash flows grow at a constant rate g forever and that the required return r exceeds g.

Step-by-step reasoning and calculations:
1. Identify the inputs:
   - Next year’s expected cash flow, CF1 = $26,000 (use the given expected cash flow, not current net income).
   - Required rate of return, r = 20% = 0.20.
   - Constant growth rate, g = 7% = 0.07.
2. Verify applicability: r (0.20) > g (0.07), so the Gordon growth formula is valid.
3. Apply the formula:
   Terminal value (TV) = CF1 / (r − g).
4. Compute the denominator:
   r − g = 0.20 − 0.07 = 0.13.
5. Divide:
   TV = 26,000 / 0.13.
   26,000 ÷ 0.13 = 200,000.
6. Units: TV = $200,000.

Why this is correct:
- The model uses next year’s cash flow (CF1) because the perpetuity formula requires the cash flow at the start of the perpetual period. Using the current year’s net income ($20,000) instead would understate the terminal value because it ignores the expected increase to $26,000.
- The subtraction r − g accounts for the spread between required return and growth; dividing by r alone (or by g) would be mathematically and conceptually incorrect.

Common mistakes (explaining why other potential answers would be wrong):
- Using current net income ($20,000) as CF1 would give 20,000/0.13 = $153,846 — incorrect because CF1 is given as $26,000.
- Using r instead of (r − g) would give 26,000/0.20 = $130,000 — incorrect application of the perpetuity growth formula.

Conclusion: Using the Gordon growth model with CF1 = $26,000, r = 20%, and g = 7% yields a terminal value of $200,000, which matches the provided answer (200000).

Estimate a venture’s terminal value based on the following information: current year’s net income = $20,000; next year’s expected cash flow = $26,000; constant future growth rate = 7%; and venture investors’ required rate of return = 20%.数值题

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