Question

Branson, Inc. has made a commitment to pay the following dividends over the next four years: $7, $13, $18, and $3.25. At the end of this four year period, the firn has further commited to grow the dividend indefinitiely at a constant 5 percent growth rate. If you require a return on this stock of 8.4 percent, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

STOCK VALUATION USING DIVIDEND DISCOUNT MODEL: -

Dividend discount valuation model calculates stock price by discounting future cashflows with the desired earning rate of return. Example dividend in case of stock valuation.

Formula for constant dividend growth rate is: -

Price = D / ( r - g)

where

D is dividend

r is expected rate of return

g is dividend growth rate

Here

r is 8.4%,

g is 5%

D needs to be calculated as Dividend at the end of fourth year x ( 1 + Rate of dividend growth)

i.e.

Here we will take dividend at the end of fourth year and calculate stock price as on year end 5.

D5 = D4 x ( 1 + g)

D5 = $3.25 x (1 + 0.05)

D5 = $3.4125

Therefore, P5 (Price at year 5 = D5 (r - g)

=> P5 = 3.4125 / (8.40% - 5.00%)

=> P5 = 3.4125 / (3.40%)

=> P5 = 100.3676

Now let us quickly discount all dividends at year 1, 2, 3, 4 and price of share at year 5 with requred rate of return i.e. 8.4%

Sr. No,	Cashflows(Dividend 1to 4 year and Price as on 5th year	Present Value discounted at 8.4%
1	7	6.45756
2	13	11.06330
3	18	14.13138
4	3.25	2.35378
5	100.3676 (calculated above)	67.05746
Sum of discounted values	101.06352

Therefore, Present Stock Value is $ 101.06