QuestionJuly 17, 2025

West Side Co expects the following dividends to be paid over the next 6 years: 10, 9, 8 7, 6 and 5 Afterward, the company pledges to maintain a constant growth rate of 3% forever. If the required rate of return is 10% calculate the current share price. (Round to 2 decimals)

West Side Co expects the following dividends to be paid over the next 6 years: 10, 9, 8 7, 6 and 5 Afterward, the company pledges to maintain a constant growth rate of 3% forever. If the required rate of return is 10% calculate the current share price. (Round to 2 decimals)
West Side Co expects the following dividends to be paid over the next 6 years: 10, 9, 8
 7, 6 and 5 Afterward, the company pledges to maintain a constant growth rate of 3% 
forever. If the required rate of return is 10%  calculate the current share price. (Round to 2
decimals)

Solution
4.4(241 votes)

Answer

75.56 Explanation 1. Calculate Present Value of Dividends Use the formula for present value: PV = \frac{D}{(1 + r)^t} for each dividend. Calculate for D_1 = 10, D_2 = 9, D_3 = 8, D_4 = 7, D_5 = 6, D_6 = 5 with r = 0.10. - PV_1 = \frac{10}{(1 + 0.10)^1} = 9.09 - PV_2 = \frac{9}{(1 + 0.10)^2} = 7.44 - PV_3 = \frac{8}{(1 + 0.10)^3} = 6.01 - PV_4 = \frac{7}{(1 + 0.10)^4} = 4.79 - PV_5 = \frac{6}{(1 + 0.10)^5} = 3.73 - PV_6 = \frac{5}{(1 + 0.10)^6} = 3.11 2. Calculate Terminal Value Use the Gordon Growth Model for dividends after year 6: TV = \frac{D_7}{r - g} where D_7 = 5 \times (1 + 0.03), r = 0.10, g = 0.03. - D_7 = 5 \times 1.03 = 5.15 - TV = \frac{5.15}{0.10 - 0.03} = 73.57 3. Calculate Present Value of Terminal Value Discount the terminal value back to present value: PV_{TV} = \frac{TV}{(1 + r)^6}. - PV_{TV} = \frac{73.57}{(1 + 0.10)^6} = 41.39 4. Sum Present Values Add all present values calculated: PV_{Total} = PV_1 + PV_2 + PV_3 + PV_4 + PV_5 + PV_6 + PV_{TV}. - PV_{Total} = 9.09 + 7.44 + 6.01 + 4.79 + 3.73 + 3.11 + 41.39 = 75.56

Explanation

1. Calculate Present Value of Dividends<br /> Use the formula for present value: $PV = \frac{D}{(1 + r)^t}$ for each dividend. Calculate for $D_1 = 10$, $D_2 = 9$, $D_3 = 8$, $D_4 = 7$, $D_5 = 6$, $D_6 = 5$ with $r = 0.10$.<br />- $PV_1 = \frac{10}{(1 + 0.10)^1} = 9.09$<br />- $PV_2 = \frac{9}{(1 + 0.10)^2} = 7.44$<br />- $PV_3 = \frac{8}{(1 + 0.10)^3} = 6.01$<br />- $PV_4 = \frac{7}{(1 + 0.10)^4} = 4.79$<br />- $PV_5 = \frac{6}{(1 + 0.10)^5} = 3.73$<br />- $PV_6 = \frac{5}{(1 + 0.10)^6} = 3.11$<br /><br />2. Calculate Terminal Value<br /> Use the Gordon Growth Model for dividends after year 6: $TV = \frac{D_7}{r - g}$ where $D_7 = 5 \times (1 + 0.03)$, $r = 0.10$, $g = 0.03$.<br />- $D_7 = 5 \times 1.03 = 5.15$<br />- $TV = \frac{5.15}{0.10 - 0.03} = 73.57$<br /><br />3. Calculate Present Value of Terminal Value<br /> Discount the terminal value back to present value: $PV_{TV} = \frac{TV}{(1 + r)^6}$.<br />- $PV_{TV} = \frac{73.57}{(1 + 0.10)^6} = 41.39$<br /><br />4. Sum Present Values<br /> Add all present values calculated: $PV_{Total} = PV_1 + PV_2 + PV_3 + PV_4 + PV_5 + PV_6 + PV_{TV}$.<br />- $PV_{Total} = 9.09 + 7.44 + 6.01 + 4.79 + 3.73 + 3.11 + 41.39 = 75.56$
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