Question

Question 1/ Firm A has just paid a dividend of $1.5 per share. The dividends are expected to grow during year 1 by 14.5% and during year 2 by 11.9% and during year 3 by 8.5% and during year 4 by 6.5%. Starting from year 4 the dividends are expected to grow constantly by 4.5% forever. The required rate of return on the stocks is 12%.

a/ Compute the intrinsic value of the stock now? (Show your steps)
b/ Compute the intrinsic value of the stock by the end of year 3? (Show your steps) c/ Compute the intrinsic value of the stock by the end of year 10? (Show your steps)

Question 2/ Firm B next dividend will be $2.5 per share. The dividends are expected to grow during year 1 by 21.5% and during year 2 by 18.5%. From year 2 to year 6 they are expected to grow by 12%. From year 6 to year 12 there is no growth of the dividends. From year 12 there will be a constant growth rate of 8% forever. The required rate of return on the stocks is 11.5%.

a/ Compute the intrinsic value of the stock now? (Show your steps)
b/ Compute the intrinsic value of the stock at the end of year 2? (Show your steps) c/ Compute the intrinsic value of the stock at the end of year 8? (Show your steps) d/ Compute the intrinsic value of the stock at the end of year 22? (Show your steps)

1

Investment/ homework 2/Spring 2020/Dr. Boukhris, CFA

Question 3/ Firm C is planning its first dividend in 4 years from now. Firm C retention ratio is 65%. Firm C current net income is $2millions with 500,000 shares outstanding. The net income is expected to grow by 1% during the next 4 years. The dividends are expected to grow during year 5 by 11.5% and during year 6 by 9.5%. From year 6 to year 14 they is no expected growth in dividends. However starting from year 15 there will be a constant dividend growth rate of 5% forever. The required rate of return on the stocks is 8%.

a/ Compute the intrinsic value of the stock now? (Show your steps)
b/ Compute the intrinsic value of the stock at the end of year 2? (Show your steps) c/ Compute the intrinsic value of the stock at the end of year 8? (Show your steps) d/ Compute the intrinsic value of the stock at the end of year 14? (Show your steps)

Question 4/ Firm D is planning its first dividend in 3 years from now. The dividend per share by the end of year 3 is $1.4. Firm C has an equity Beta of 1.2. The T-bill rate is 2.5% and the return on the equity market index is 7.5%. The dividends are expected to grow from year 3 to years 6 by 13.5% and during year 6 by 9.5%. From year 6 to year 11 they are expected to grow by 10%. However starting from year 11 there will be no growth of dividends forever.

a/ Compute the intrinsic value of the stock now? (Show your steps)
b/ Compute the intrinsic value of the stock at the end of year 2? (Show your steps) c/ Compute the intrinsic value of the stock at the end of year 8? (Show your steps) d/ Compute the intrinsic value of the stock at the end of year 50? (Show your steps)

Answer 1

Answer to Q1.

The intrinsic value of the stock is calculated by the Dividend Discount Model

Part a

The computation of the intricsic value of the share as on today is as given below. The assumption is that dividends will be paid at the end of the year. Since, the growth rate stabilises after the fourth year, we can apply the Gordon Growth Formula for ariving at the perpetuity value.

Year	Growth in dividend	Dividend	Perpetuity value	Present value factor	Present value
a	b	c	d	e	f
0		1.50		100.00%
1	14.50%	1.72		89.29%	1.53
2	11.90%	1.92		79.72%	1.53
3	8.50%	2.09		71.18%	1.48
4	6.50%	2.22	30.94	63.55%	21.08
5	4.50%	2.32		56.74%
				Value of the share	25.63

The various steps in the above computation are given below:

Dividend for the year = Previous year's dividend x (1 + growth in dividend)

Perpetuity value at the end of year 4 = Dividend in year 5 / (expected return - dividend growth rate after year 4)

Present value factor = 1 / (1+expected return) ^ Years

Present value = (Dividend for the year + Perpetuity value) x present value factor

Part b

Similarly, intrinsic value of the stock at the end of year 3 can be computed as below:

The onl change from the above computation would be in the present value computation which is considered assuming Year 4 to be the first year of discounting.

Year	Growth in dividend	Dividend	Terminal value	Present value factor at the end of Year 3	Present value
a	b	c	d	e	f
0		1.50
1	14.50%	1.72
2	11.90%	1.92
3	8.50%	2.09
4	6.50%	2.22	30.94	89.29%	29.61
5	4.50%	2.32
				Value of the share	29.61

Part c

The intrinsic value of the stock after 10 years can be computed as below:

Based on the above computation, the dividend in year 5 is 2.32

Considering a constant growth rate of 4.5% per annum, dividend in the year 10 would be 2.32 x (1+4.5%)^(10-5) = 2.89

To compute the value of the stock at the end of year 10, we can apply the Gordon Growth Formula as below:

Value of the stock = Dividend for Year 10 x (1+Growth rate) / (Expected Return - Growth) = 2.89 x (1 + 4.5%) / (12% - 4.5%) = 40.30