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Networks Ltd is experiencing a period of rapid growth. Earnings and dividends are expected to grow at a rate of 18% during the next two years, 15% in the third, and then at a constant rate of 6 per cent thereafter. Networks’ last dividend, which has just been paid, was $0.115. If the required return on the shares is 12%, what is the price of the share today?

Question

Networks Ltd is experiencing a period of rapid growth. Earnings and dividends are expected to grow at a rate of 18% during the next two years, 15% in the third, and then at a constant rate of 6 per cent thereafter. Networks’ last dividend, which has just been paid, was $0.115. If the required return on the shares is 12%, what is the price of the share today?

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Solution

To calculate the price of the share today, we need to calculate the present value of the dividends for the next three years and the present value of the dividends from the fourth year onwards (which grow at a constant rate).

  1. Calculate the dividends for the next three years:

    • For the first year: D1 = D0 * (1 + g1) = 0.115∗(1+180.115 * (1 + 18%) = 0.1357
    • For the second year: D2 = D1 * (1 + g2) = 0.1357∗(1+180.1357 * (1 + 18%) = 0.160026
    • For the third year: D3 = D2 * (1 + g3) = 0.160026∗(1+150.160026 * (1 + 15%) = 0.18403

  2. Calculate the present value of these dividends:

    • PV(D1) = D1 / (1 + r) = 0.1357/(1+120.1357 / (1 + 12%) = 0.12116
    • PV(D2) = D2 / (1 + r)^2 = 0.160026/(1+120.160026 / (1 + 12%)^2 = 0.12757
    • PV(D3) = D3 / (1 + r)^3 = 0.18403/(1+120.18403 / (1 + 12%)^3 = 0.13096

  3. Calculate the dividends for the fourth year: D4 = D3 * (1 + g4) = 0.18403∗(1+60.18403 * (1 + 6%) = 0.19507

  4. Calculate the present value of all future dividends from the fourth year onwards. This is a perpetuity that grows at a constant rate, so we can use the Gordon growth model: PV(D4 onwards) = D4 / (r - g4) = 0.19507/(120.19507 / (12% - 6%) = 3.2512

  5. Calculate the present value of this perpetuity: PV(D4 onwards) = 3.2512/(1+r)3=3.2512 / (1 + r)^3 = 2.3065

  6. Add up all these present values to get the price of the share today: P0 = PV(D1) + PV(D2) + PV(D3) + PV(D4 onwards) = 0.12116+0.12116 + 0.12757 + 0.13096+0.13096 + 2.3065 = $2.68619

So, the price of the share today is approximately $2.69.

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