Question

you expect a share of stock to pay dividends of $1.00, $1.25, and $1.50 in each of the next 3 years. you believe the stock will sell for $20 at the end of the third year. what is the stock price if the discount rate for the stock is 10%? note: do not round intermediate calculations. round your answer to 2 decimal places. what is the dividend yield for year 1? note: do not round intermediate calculations. enter your answer as a percent rounded to 2 decimal places. what will be the dividend yield at the start of year 2? note: do not round intermediate calculations. enter your answer as a percent rounded to 2 decimal places.

Answer 1

An investor would pay approximately $256,500 for a share of Babble, Inc., by calculating the present discounted value of the future dividends at a 15% interest rate and dividing that by the number of shares.

Step-by-step explanation:

To determine what an investor would pay for a share of Babble, Inc. in this scenario, we need to calculate the present discounted value (PDV) of the expected future dividends. Since profits are distributed as dividends and given the provided interest rate of 15%, we will discount each year's expected profits back to their present value. We do this for profits of $15 million in the present, $20 million one year from now, and $25 million two years from now, and then combine these values to find the total PDV. Finally, we divide this total PDV by the number of shares to find the price per share.

Using the given data and a 15% discount rate, we calculate the PDV for each year and then sum them up. Afterward, dividing by 200 shares gives us the price per share, which should be approximately $256,500 per share. This price reflects the value today of the future profits that an investor expects to receive from owning the stock.

Answer 2

a. The stock price is approximately $18.47.

b. The dividend yield for year 1 is approximately 5.41%.

C. The dividend yield at the start of year 2 is approximately 6.77%.

How did we get the values?

Calculating the stock price using the dividend discount model (DDM), use the following formula:

`\[ \text{Stock Price} = \frac{\text{Dividend at Year 1}}{(1 + \text{Discount Rate})^1} + \frac{\text{Dividend at Year 2}}{(1 + \text{Discount Rate})^2} + \frac{\text{Dividend at Year 3} + \text{Stock Price at Year 3}}{(1 + \text{Discount Rate})^3} \]`

Let's substitute the values into the formula:

`\[ \text{Stock Price} = (1.00)/((1 + 0.10)^1) + (1.25)/((1 + 0.10)^2) + (1.50 + 20)/((1 + 0.10)^3) \]`

Calculating the numerator for each term:

`\[ \text{Stock Price} = (1.00)/(1.10) + (1.25)/(1.10^2) + (21.50)/(1.10^3) \]`

Calculate each term:

`\[ \text{Stock Price} = 0.9091 + 1.0331 + 16.5263 \]`

Add them up:

`\[ \text{Stock Price} = 18.4685 \]`

Now, round the stock price to two decimal places:

`\[ \text{Stock Price} \approx 18.47 \]`

The stock price is approximately $18.47 into two decimal places.

To calculate the dividend yield for year 1, you can use the following formula:

`\[ \text{Dividend Yield} = \frac{\text{Dividend at Year 1}}{\text{Stock Price at Year 0}} * 100 \]`

Substitute the values:

`\[ \text{Dividend Yield} = (1.00)/(18.47) * 100 \]`

Calculate:

`\[ \text{Dividend Yield} \approx 5.41\% \]`

The dividend yield for year 1 is approximately 5.41%.

Calculating the dividend yield at the start of year 2, use the stock price at the end of year 1. Since the stock is expected to sell for $20 at the end of year 3, the stock price at the end of year 1 is $18.36. Employ the same formula:

`\[ \text{Dividend Yield at Year 2} = \frac{\text{Dividend at Year 2}}{\text{Stock Price at Year 1}} * 100 \]`

Substitute the values:

`\[ \text{Dividend Yield at Year 2} = (1.25)/(18.47) * 100 \]`

Calculate:

`\[ \text{Dividend Yield at Year 2} \approx 6.77\% \]`

The dividend yield at the start of year 2 is approximately 6.77%.