Question

Suppose a video conferencing provider, Soom, is planning to pay its next dividend in one year. The dividend will be $1 per share, and Soom expects dividends to grow at 10% per year over the next three years. After that, they expect dividends to grow at 2% per year indefinitely (that is, forever). Suppose that investors have the alternative of buying corporate bonds that will earn 5% per year. Assume the company will next pay a dividend of $1 per share in one year’s time.

1. (a) What price would they pay for stock in this company? Explain your answer.

2. (b) What price would the same investor pay in one year’s time, immediately before the dividend is paid out?

3. (c) What price would the investor pay immediately after the dividend is paid out in one year’s time?

4. (d) If interest rates fall to 4%, what will happen to stock prices and to the user cost of capital for Soom? What will happen to investment at the company?

Answer 1

The value of the stock price will be calculated by the dividend discount model.

The present value of all the future dividends is the value of stock price. This will be calculated at a rate of interest of 5% as corporate bonds will earn 5% return per annum. r = 5%

Dividend is $1 in first year and dividends are expected to grow at a rate of 10 % for next 3 years. This stage is called the high growth stage of the company.

Post that the dividends will grow at 2% indefinately. We will find the terminal value for the same. g = 2%

Year	Expected Dividends	Present Value Factor formula	Present Value
1	1	0.952380952	0.952380952
2	1.1	0.907029478	0.997732426
3	1.21	0.863837599	1.045243494
4	1.331	0.822702475	1.095016994
		Present Value	4.090373867

Expected dividends are as per the data given to us till year 4.

Present Value factor formula is calculated by (P/A, 5%, year) for years 1 to 4.

Present value is then calculated by multipling the expected dividends with the factor fomula.

Hence, present value of the company in high growth phase = $ 4.0903

Now, lets calculate the terminal value for indefinite growth at 2%.

Expected dividend in year 5 = Expected dividend in year 4 * 1.02 = 1.35762

Terminal Value = Expected dividend in year 5 / (r - g)

= 1.35762 / 5% - 2%

= 1.35762 / 3%

Terminal value = $ 45.254 (at the end of year 4)

a)

Present Value of terminal value = Terminal value / 1.05^4

= 45.254 / 1.05^4

Present Value of Terminal Value = $ 37.2306

Price of Stock = Present value of the company in high growth phase + Present Value of Terminal Value

= 4.0903 + 37.2306

Price of Stock = $ 41.3209

b)

Price immediately before the first dividend will be calculated by discounting the dividends at one year ahead just before the dividend.

Hence, we can directly find the future value of the stock one year ahead with a rate of interest of 5%.

Price one year ahead = Price of stock now * 1.05

= 41.3209 * 1.05

Price one year ahead = $ 43.387 ( this is the price just before the dividend)

c)

Price investor would pay after the first dividend is paid out = Price one year ahead just beofre the dividend - Dividend Paid

= $ 43.387 - $ 1

Price investor would pay after the first dividend is paid out = $ 42.387

This is because the dividend is already paid, hence the investor will discount the value of dividend paid.

d)

When interest rates falls to 4%, the rate of interest will change to r = 4%

Lets re-calculate the present value in the high growth phase with r = 4%.

Year	Expected Dividends	Present Value Factor formula	Present Value
1	1	0.961538462	0.961538462
2	1.1	0.924556213	1.017011834
3	1.21	0.888996359	1.075685594
4	1.331	0.854804191	1.137744378
		Present Value	4.191980268

Terminal Value = Expected dividend in year 5 / (r - g)

= 1.35762 / 4% - 2%

= 1.35762 / 2%

Terminal value = $ 67.881 (at the end of year 4)

Present Value of terminal value = Terminal value / 1.04^4

= 67.881 / 1.04^4

Present Value of Terminal Value = $ 58.02496

Price of Stock = Present value of the company in high growth phase + Present Value of Terminal Value

= 4.1919 + 58.02496

Price of Stock = $ 62.21694

We obsere that the stock prices rises with fall in interest rates. This is because the cost of of capital for Soom has reduced with fall in interest rates. Thus, there would be less interest cost and more profit on the books which will raise the stock price.

Company would be able to plan new investment ventures at a lower cost of capital.