Question

XYZ company presently pays a dividend of $ 1.50 per share on its common
stock. The company expects to increase the dividend at a 20% annual rate the
first four years and at the rate of 13% at the next four years then the growth on
the dividend at a 7% thereafter. This phased growth patterns is in keeping with
the expected life cycle of earnings. You are required a 16% return to invest in
this stock. What value should you place on a share of this Stock?

Answer 1

The value is computed as follows:

= Dividend in year 1 / (1 + required rate of return)¹ + Dividend in year 2 / (1 + required rate of return)² + Dividend in year 3 / (1 + required rate of return)³ + Dividend in year 4 / (1 + required rate of return)⁴ + Dividend in year 5 / (1 + required rate of return)⁵ + Dividend in year 6 / (1 + required rate of return)⁶ + Dividend in year 7 / (1 + required rate of return)⁷ + Dividend in year 8 / (1 + required rate of return)⁸ + 1 / (1 + required rate of return)⁸ [ ( Dividend in year 8 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 1.50 x 1.20) / 1.16¹ + ($ 1.50 x 1.20²) / 1.16² + ($ 1.50 x 1.20³) / 1.16³ + ($ 1.50 x 1.20⁴) / 1.16⁴ + ($ 1.50 x 1.20⁴ x 1.13) / 1.16⁵ + ($ 1.50 x 1.20⁴ x 1.13²) / 1.16⁶ + ($ 1.50 x 1.20⁴ x 1.13³) / 1.16⁷ + ($ 1.50 x 1.20⁴ x 1.13⁴ ) / 1.16⁸ + 1 / 1.16⁸ x [ ($ 1.50 x 1.20⁴ x 1.13⁴ x 1.07) / (0.16 - 0.07)

= $ 1.80 / 1.16 + $ 2.16 / 1.16² + $ 2.592 / 1.16³ + $ 3.1104 / 1.16⁴ + $ 3.514752 / 1.16⁵ + $ 3.97166976 / 1.16⁶ + $ 4.487986829 / 1.16⁷ + $ 5.071425117 / 1.16⁸ + 1 / 1.16⁸ x [ $ 5.426424875 / 0.09 ]

= $ 1.80 / 1.16 + $ 2.16 / 1.16² + $ 2.592 / 1.16³ + $ 3.1104 / 1.16⁴ + $ 3.514752 / 1.16⁵ + $ 3.97166976 / 1.16⁶ + $ 4.487986829 / 1.16⁷ + $ 5.071425117 / 1.16⁸ + $ 60.29360972 / 1.16⁸

= $ 1.80 / 1.16 + $ 2.16 / 1.16² + $ 2.592 / 1.16³ + $ 3.1104 / 1.16⁴ + $ 3.514752 / 1.16⁵ + $ 3.97166976 / 1.16⁶ + $ 4.487986829 / 1.16⁷ + $ 65.36503484 / 1.16⁸

= $ 31.36

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