Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.88 and growth in dividends for year 2, 3, and 4 is 23.8% and constant growth afterwards is 0.58%. The cost of equity is 6.91%. (Answer in 2 decimal places, 6.21 for $6.21).

Question

BlackTom AI · Accepted Answer

Dividend discount model with a short high-growth period applies: P0 = Σ_{t=1 to 4} Dt/(1+ke)^t + TV4/(1+ke)^4, where TV4 = D5/(ke − g∞).

1) Key concepts:
- Supernormal (multi-stage) DDM: explicitly discount dividends during the high-growth years, then use a perpetual-growth (Gordon) value at the end of the supernormal period.
- Here D1 = $1.88, years 2–4 grow at 23.8% (gH = 0.238), long-run growth g∞ = 0.0058, cost of equity ke = 0.0691.

2) Step-by-step calculation (showing intermediate steps):
- D2 = D1*(1+gH) = 1.88*(1.238) = 2.32744
- D3 = D2*(1+gH) = 2.32744*(1.238) = 2.88137072
- D4 = D3*(1+gH) = 2.88137072*(1.238) = 3.56713695136
- D5 = D4*(1+g∞) = 3.56713695136*(1.0058) = 3.58782634568

- Discount factors:
  (1+ke) = 1.0691
  (1+ke)^2 = 1.14297481
  (1+ke)^3 = 1.22195436937
  (1+ke)^4 = 1.30639141629

- Present values of explicit dividends:
  PV1 = 1.88 / 1.0691 = 1.75847
  PV2 = 2.32744 / 1.14297481 = 2.03670
  PV3 = 2.88137072 / 1.22195436937 = 2.35902
  PV4 = 3.56713695136 / 1.30639141629 = 2.72992

- Terminal value at t=4:
  TV4 = D5 / (ke − g∞) = 3.58782634568 / (0.0691 − 0.0058) = 3.58782634568 / 0.0633 = 56.678
  PV(TV4) = 56.678 / 1.30639141629 = 43.693 (discounted to time 0)

3) Sum all present values:
  P0 = PV1 + PV2 + PV3 + PV4 + PV(TV4)
     = 1.75847 + 2.03670 + 2.35902 + 2.72992 + 43.693
     ≈ 52.27

4) Why this is correct:
- The method correctly treats the first four dividends individually under the high growth rate and then captures all subsequent dividends via the Gordon growth formula using D5 and the long-run growth g∞. All cash flows are discounted at the cost of equity.

5) Common mistakes (why other answers would be wrong):
- Using g∞ = 0.58 (instead of 0.58%) or 58% by mistake dramatically overstates value.
- Using D4 rather than D5 in the Gordon formula (should use the first post-terminal dividend).
- Forgetting to discount the terminal value back to time 0.

Conclusion: The intrinsic value P0 computed by the multi-stage DDM is $52.27, matching the provided answer.

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