You are going to hold a stock for 3 years. It is estimated to pay dividends of $2.50, $2.60 and $2.80. The estimated sale price at the end of the holding period is
$68. Using the dividend discount model, calculate the value of the stock if your required rate of return is 14%.
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A. B. C. D.A
Calculation = $2.50/(1+.14) + 2.60/(1+.14)^2 + 2.80/(1+.14)^3 + 68.00/(1+.14)^3 = $51.98.
To calculate the value of the stock using the dividend discount model (DDM), we need to discount the future dividends and the estimated sale price at the end of the holding period to their present values. The DDM assumes that the value of a stock is equal to the present value of all future dividends it is expected to pay, plus the present value of the expected sale price at the end of the holding period.
Given data: Dividend in Year 1 (D1) = $2.50 Dividend in Year 2 (D2) = $2.60 Dividend in Year 3 (D3) = $2.80 Estimated sale price at the end of Year 3 (P3) = $68 Required rate of return (r) = 14%
Step 1: Calculate the present value of future dividends. To calculate the present value of each dividend, we need to discount it by the required rate of return for each respective year.
Present Value of Dividend in Year 1 (PV1) = D1 / (1 + r)^1 = $2.50 / (1 + 0.14)^1 = $2.50 / 1.14 ≈ $2.19
Present Value of Dividend in Year 2 (PV2) = D2 / (1 + r)^2 = $2.60 / (1 + 0.14)^2 = $2.60 / 1.2996 ≈ $2.00
Present Value of Dividend in Year 3 (PV3) = D3 / (1 + r)^3 = $2.80 / (1 + 0.14)^3 = $2.80 / 1.4859 ≈ $1.88
Step 2: Calculate the present value of the estimated sale price. To calculate the present value of the sale price at the end of Year 3, we need to discount it by the required rate of return for three years.
Present Value of Sale Price in Year 3 (PV3) = P3 / (1 + r)^3 = $68 / (1 + 0.14)^3 = $68 / 1.4859 ≈ $45.77
Step 3: Calculate the value of the stock. The value of the stock is the sum of the present values of the dividends and the present value of the sale price.
Value of Stock = PV1 + PV2 + PV3 + PV3 = $2.19 + $2.00 + $1.88 + $45.77 ≈ $51.84
The value of the stock, rounded to two decimal places, is approximately $51.84.
Comparing this with the provided answer choices, the closest option is: A. $51.98
Therefore, option A. $51.98 is the most accurate answer based on the calculations.