Question

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

1. Computation of required rate of return

T-bill rate (Risk Free rate) = 2.5%

Return on equity market index = 7.50%

Equity beta = 1.2

Required rate of return can be calculated by using CAPM (Capital Asset Pricing Model) formula.

Required rate of return under CAPM = Risk free rate + (Equity Beta (Return on equity market - Risk free rate)

= 2.5%+(1.2(7.5%-2.5%)) = 8.5%

This rate will be used to discount the future dividends to arrive at the present value.

2. Computation of Dividend per share

Year	Dividend per share	Growth	Working
3	1.40000
4	1.58900	13.50%	(1.4*(100%+13.5%)
5	1.80352	13.50%	(1.58900*(100%+13.5%)
6	1.97485	9.50%	(1.80352*(100%+9.5%)
7	2.17233	10%	(1.97485*(100%+10%)
8	2.38957	10%	(2.17233*(100%+10%)
9	2.62852	10%	(2.38957*(100%+10%)
10	2.89138	10%	(2.62852*(100%+10%)
11	3.18051	10%	(2.89138*(100%+10%)
All future period	3.18051	0%	Same as year 11

Terminal value (all future period value) = 3.18051/8.5% = 37.418

3. Computation of Intrinsic value of the stock

Intrinsic value of the stock equals the present value of all divident earned in future.

a. Intrinsic value of stock now

Year	n	Dividend per share	Discount factor at 8.5% (1/(1.085^n))	Present Value of Dividend Per share (Dividend per share * Discount factor)
1	1	-	0.922	-
2	2	-	0.849	-
3	3	1.400	0.783	1.096
4	4	1.589	0.722	1.147
5	5	1.804	0.665	1.199
6	6	1.975	0.613	1.210
7	7	2.172	0.565	1.227
8	8	2.390	0.521	1.244
9	9	2.629	0.480	1.261
10	10	2.891	0.442	1.279
11	11	3.181	0.408	1.296
Future years (terminal value)	11	37.418	0.408	15.253
Intrinsic value of stock now (sum of all present value)	26.213

b.Intrinsic value of stock at the end of year 2:

Year	n	Dividend per share	Discount factor at 8.5% (1/(1.085^n))	Present Value of Dividend Per share (Dividend per share * Discounting factor)
3	1	1.400	0.922	1.290
4	2	1.589	0.849	1.350
5	3	1.804	0.783	1.412
6	4	1.975	0.722	1.425
7	5	2.172	0.665	1.445
8	6	2.390	0.613	1.465
9	7	2.629	0.565	1.485
10	8	2.891	0.521	1.505
11	9	3.181	0.480	1.526
Future years (terminal value)	9	37.418	0.480	17.956
Intrinsic value of stock at the end of year 2 (sum of all present value)	30.859

Since the intrinsice value is to be estimated at the year 2, 'n' (no. of years) will have year 3 as 1, year 4 as 2 and so on.

c.Intrinsic value of stock at the end of year 8:

Year	n	Dividend per share	Discount factor at 8.5% (1/(1.085^n))	Present Value of Dividend Per share (Dividend per share * Discounting factor)
9	1	2.629	0.922	2.423
10	2	2.891	0.849	2.456
11	3	3.181	0.783	2.490
Future years (terminal value)	3	37.418	0.783	29.295
Intrinsic value of stock at the end of year 8 (sum of all present value)	36.663

Since the intrinsice value is to be estimated at the year 2, 'n' (no. of years) will have year 9 as 1, year 10 as 2 and so on.

d. Intrinsic value of the stock at the end of year 50

Intrinsic value of the stock at the end of year 50 = no growth and it represents the perpetual annuity. Thus, intrinsic value of a perpetuity = annual cash-flow / required rate of return = 3.18051/8.5% = 37.418 (same as terminal value used in all tables above)