Nu-Tings, a start-up company, will pay no dividends on its stock for the first 4 years.It will then pay a £0.45 per share dividend, which is expected to grow by 7% per year thereafter.If the required rate of return on the stock is 25%, what is the current value of one hundred shares of Nu-Tings?
Question
Nu-Tings, a start-up company, will pay no dividends on its stock for the first 4 years.It will then pay a £0.45 per share dividend, which is expected to grow by 7% per year thereafter.If the required rate of return on the stock is 25%, what is the current value of one hundred shares of Nu-Tings?
Solution
To calculate the current value of the shares, we need to use the Gordon Growth Model (also known as the Dividend Discount Model). This model is used to determine the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate.
Given: Dividend (D1) = £0.45 (This is the dividend expected to be received in the 5th year) Growth rate (g) = 7% or 0.07 Required rate of return (k) = 25% or 0.25
The formula for the Gordon Growth Model is:
P = D1 / (k - g)
First, we calculate the price of one share:
P = £0.45 / (0.25 - 0.07) = £2.5
However, this gives us the price of the stock in year 4. Since the dividend is received in the 5th year, we need to discount this price back to the present (year 0). We do this by dividing the price by (1 + k) raised to the power of the number of years we are discounting.
P0 = P / (1 + k)^n P0 = £2.5 / (1 + 0.25)^4 = £1.28
So, the price of one share today is £1.28.
Since we want to find the value of 100 shares, we multiply this price by 100:
Value of 100 shares = 100 * £1.28 = £128
So, the current value of one hundred shares of Nu-Tings is £128.
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