Larry Rile is evaluating the investment merits of Bing Corp., a successful motorcycle manufacturer. Rile is forecasting a dividend in year I of $1.50 per share, a dividend in year 2 of $3.00 per share, and a dividend in year 3 of 4.50 per share. After year 3, Rile expects dividends to grow at the rate of 6% per year. Rile calculated a beta of 1.3 for Bing Corp. Rile expects the S&P 500 index to return 8%. The U.S. Treasury bill is yielding 2%. Using the multistage dividend discount model, what is Bing Corp.'s intrinsic value to the nearest dollar?
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A. B. C.B
To calculate Bing Corp.'s intrinsic value using the multistage dividend discount model, we need to discount the future dividends to their present value and sum them up. Here's the step-by-step explanation:
PV = D / (1 + r)^n
where PV is the present value, D is the dividend, r is the required rate of return, and n is the number of years.
Given dividends: Year 1 dividend (D1) = $1.50 per share Year 2 dividend (D2) = $3.00 per share Year 3 dividend (D3) = $4.50 per share
Required rate of return (discount rate): Risk-free rate (U.S. Treasury bill) = 2% Expected market return (S&P 500 index) = 8% Beta (β) = 1.3
To calculate the required rate of return for Bing Corp., we'll use the Capital Asset Pricing Model (CAPM):
Required rate of return (r) = Risk-free rate + Beta * (Expected market return - Risk-free rate) r = 2% + 1.3 * (8% - 2%) r = 2% + 1.3 * 6% r = 2% + 7.8% r = 9.8%
Now we can calculate the present value of the dividends:
PV1 = $1.50 / (1 + 9.8%)^1 PV2 = $3.00 / (1 + 9.8%)^2 PV3 = $4.50 / (1 + 9.8%)^3
PVn = Dn * (1 + g) / (r - g)
where PVn is the present value at year n, Dn is the dividend at year n, r is the required rate of return, and g is the growth rate.
For year 4 and beyond, the dividends are expected to grow at a constant rate of 6%. Therefore, the present value of dividends from year 4 onwards can be calculated as:
PV4 = D4 * (1 + g) / (r - g) PV5 = D5 * (1 + g) / (r - g) ...
Since we're asked to calculate the intrinsic value to the nearest dollar, we'll sum up the present values of the dividends and round the final result to the nearest dollar.
In this case, we have dividends for the first three years, so we'll calculate the present value of dividends from years 4 and beyond using the Gordon Growth Model. However, the problem statement doesn't provide the dividend for year 4 and onwards. Without that information, we cannot complete the calculation accurately.
Please note that the information provided in the problem statement is incomplete, as we don't have the dividend for year 4 and onwards. To calculate Bing Corp.'s intrinsic value, we would need the complete dividend projections.