Question

You are an analyst with a big Wall Street firm in charge of valuing high-tech firms. You are currently analyzing a firm called Dalvi.com that specializes in pretending to make money. Dalvi.com is not currently profitable, but they have convinced you that they will eventually make money. Your projections, therefore, are that the firm will pay no dividends for the next 10 years. Eleven years from now, you expect its first dividend of $2.5 per share. Further, you expect dividends to increase at a rate of 20% per year for 3 years after that. At that point, you will then expect dividends to grow at 9% per year thereafter. If the stock is presently trading at $15 and you believe that a required rate return for this type of company is 14%, based on your estimated price and the current price, should you buy the stock?

Answer 1

To decide whether to buy Dalvi.com's stock, calculate the present value of expected future dividends using the dividend discount model and the Gordon Growth Model for the terminal value of the dividends. Sum the present values to estimate the intrinsic value per share; if it's above the current price of $15, it may be a good buy. Investing decisions should consider the estimations' uncertainty and market conditions.

Step-by-step explanation:

To determine whether to buy the stock of Dalvi.com, we need to calculate the present value of the expected dividends and compare it with the current trading price. Given the expected first dividend of $2.5 in eleven years and an anticipated growth rate of 20% for the following three years, followed by a 9% growth rate indefinitely, we use the dividend discount model to estimate the stock's intrinsic value.

For the initial 10 years without dividends, no value is added to the present value calculation. At year 11, the present value (PV) of that $2.5 dividend would be $2.5 / (1 + 0.14)^11. For years 12 to 14, we calculate the present value of each dividend similarly, considering the 20% growth. After year 14, we utilize the Gordon Growth Model to calculate the terminal value of the perpetuity, which is the last dividend, $2.5 * (1 + 0.20)^3, growing at 9% and discounted back to the present value with the formula:

PV = D / (k - g)

Where D is the expected dividend at year 15, k is the required rate of return (14%), and g is the long-term growth rate (9%). Once we have all present values, we sum them up to get the final estimated price per share and then compare it to the current market price of $15 to make a buy or sell decision. If the estimated price exceeds $15, it suggests that the stock may be undervalued, and buying could be a good decision.

It's important to remember that in the real world, these profits are estimations, and the required rate of return is subject to personal risk tolerance and market conditions. Therefore actual investment decisions should also consider these factors.

Answer 2

To assess the investment in Dalvi.com, we evaluate the present value of expected future dividends based on projected growth rates and compare it to the current stock price. Using the present value of a growing perpetuity and single cash flow formulas, we calculate if the stock is undervalued or overvalued relative to the investor's required rate of return.

Step-by-step explanation:

To determine whether Dalvi.com is a good investment at its current price of $15 per share, we need to calculate the present value of future dividends based on the expected growth rates and the required rate of return of 14%. We will calculate the present value of the dividends for each year starting from year 11 to year 14, when the dividend growth rate is 20%, and then calculate the present value of the dividends from year 15 onwards, assuming a constant growth rate of 9%.

The formula for the present value of a growing perpetuity (Gordon Growth Model) can be used to find the present value at year 14 (the last year of 20% growth) of all dividends from year 15 onwards:

PV = D1 / (r - g)

where D1 is the dividend in year 15, r is the required rate of return (14%), and g is the growth rate (9%). This model gives us the value of all dividends from year 15 to infinity, discounted back to year 14.

For the dividends from year 11 to year 14, we discount each of them back to the present using the present value formula for a single cash flow:

PV = D / (1 + r)^n

where D is the dividend, r is the required rate of return, and n is the number of years until the dividend is received.

Once we have the present values for each of these periods, we sum them together to estimate the present value of the entire stream of future dividends. If this present value is higher than the current trading price of $15 per share, the stock may be a good investment.