Colgate-Palmolive Company has just paid an annual dividend of $0.85. Analysts are predicting a 10% per year growth rate in earnings over the next five years. After that, Colgate’s earnings are expected to grow at the current industry average of 4.7% per year. If Colgate’s equity cost of capital is 7% per year and its dividend payout ratio remains constant, for what price does the dividend-discount model predict Colgate stock should sell?
To calculate the price at which Colgate stock should sell using the dividend-discount model, follow these steps:
1. Determine the dividend in Year 1: The annual dividend payment is provided in the question, which is $0.85.
2. Estimate the dividends for the next five years: To do this, use the 10% per year earnings growth rate. Multiply the dividend in Year 1 by (1 + earnings growth rate) for each of the next five years. The calculated dividends for years 2 to 6 would be:
Year 2: $0.85 * (1 + 10%) = $0.935
Year 3: $0.935 * (1 + 10%) = $1.0285
Year 4: $1.0285 * (1 + 10%) = $1.13135
Year 5: $1.13135 * (1 + 10%) = $1.244485
Year 6: $1.244485 * (1 + 4.7%) = $1.303913795
3. Determine the dividends beyond year 6: For year 7 and beyond, the earnings are expected to grow at the current industry average of 4.7% per year. Multiply the dividend in year 6 by (1 + 4.7%) for each subsequent year. These dividends will be:
Year 7: $1.303913795 * (1 + 4.7%) = $1.363154629
Year 8: $1.363154629 * (1 + 4.7%) = $1.426974725
4. Calculate the present value of future dividends using the equity cost of capital: The equity cost of capital is given as 7% per year. Discount each dividend to its present value by dividing it by (1 + equity cost of capital) raised to the power of the corresponding year. Then sum up these present values. The formula used for this is:
Present Value = Dividend / (1 + Equity Cost of Capital) ^ Year
The present value of future dividends for years 1 to 6 is calculated as follows:
Year 1: $0.85 / (1 + 7%)^1 = $0.7933
Year 2: $0.935 / (1 + 7%)^2 = $0.8105
Year 3: $1.0285 / (1 + 7%)^3 = $0.8074
Year 4: $1.13135 / (1 + 7%)^4 = $0.8167
Year 5: $1.244485 / (1 + 7%)^5 = $0.8285
Year 6: $1.303913795 / (1 + 7%)^6 = $0.7857
The present value of future dividends for years 7 and beyond can be calculated similarly:
Year 7: $1.363154629 / (1 + 7%)^7 = $0.8424
Year 8: $1.426974725 / (1 + 7%)^8 = $0.8044
5. Calculate the sum of the present values: Add up the present values of all future dividends calculated in steps 4 and 5. The sum of the present values for all calculated years is:
$0.7933 + $0.8105 + $0.8074 + $0.8167 + $0.8285 + $0.7857 + $0.8424 + $0.8044 = $6.4899
6. Determine the stock price: The stock price is equal to the sum of the present values calculated in step 5. Therefore, the dividend-discount model predicts that Colgate stock should sell for approximately $6.4899.
Please note that this calculation assumes the dividend payout ratio remains constant, which implies that the dividend growth rate matches the earnings growth rate. Any change in the dividend payout ratio would require adjustments to the calculation.