You are calculating the intrinsic value of a company that paid a dividend of $2.17 last year. Analysts believe that dividends will grow 14.6% this year, 4.6% next year, and 0.9% thereafter and the cost of equity is 8.7%. What is the current price of the stock? (Answer in $, so $16.21 is 16.21).

Question

BlackTom AI · Accepted Answer

Use the two-stage dividend-discount model: dividends grow at 14.6% for one year, 4.6% the next year, then perpetually at 0.9%. Discount future dividends at the cost of equity 8.7%.

1) Relevant knowledge points
- Dividend Discount Model (DDM): value = present value of expected future dividends.
- For multi-stage growth: value = PV(D1) + PV(D2 + Terminal value at t=2).
- Terminal value at t=2 = D3 / (r - g_infty), where D3 is dividend in year 3 and g_infty is perpetual growth.

2) Step-by-step reasoning and calculations
- Given D0 = 2.17, g1 = 14.6%, g2 = 4.6%, g_infty = 0.9%, r = 8.7%.

Compute year-by-year dividends:
- D1 = D0*(1 + g1) = 2.17 * 1.146 = 2.48682
- D2 = D1*(1 + g2) = 2.48682 * 1.046 = 2.60121372
- D3 = D2*(1 + g_infty) = 2.60121372 * 1.009 = 2.6246246435

Compute terminal value at t=2:
- P2 = D3 / (r - g_infty) = 2.6246246435 / (0.087 - 0.009) = 2.6246246435 / 0.078 = 33.649 (rounded)

Discount factors:
- (1 + r) = 1.087
- (1 + r)^2 = 1.087^2 = 1.181569

Present values:
- PV(D1) = 2.48682 / 1.087 = 2.2870 (rounded)
- PV(D2 + P2) = (2.60121372 + 33.649) / 1.181569 = 36.25021372 / 1.181569 = 30.6830 (rounded)

3) Sum of PVs (the current stock price):
- Price = PV(D1) + PV(D2 + P2) = 2.2870 + 30.6830 = 32.970 ≈ 32.97

4) Why the correct answer is correct
- The calculation correctly applies the two-stage DDM: explicitly grows dividends for the two high/medium growth years, forms a Gordon-growth terminal value using year-3 dividend and perpetual growth, and discounts all cash flows at the required return.

5) Why other approaches would be incorrect
- Common mistakes: using D1 directly in the Gordon formula (would double-count growth), using the wrong discount periods, or using r - g with incorrect g (e.g., using 4.6% instead of 0.9%) which materially changes terminal value.

6) Conclusion
- The computed intrinsic value is 32.97, which matches the provided correct answer 32.97.

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