Question

. Dividend discount model: Consider the following three stocks: a. Stock A is expected to provide a dividend of $15 a share forever. b. Stock B is expected to pay a dividend of $9 next year. Thereafter, dividend growth is expected to be 4% a year forever. c. Stock C is expected to pay a dividend of $9 next year. Thereafter, dividend growth is expected to be 30% a year for three years (i.e., years 2 through 4) and zero thereafter. If the market capitalization rate for each stock is 8%, which stock is the most valuable? What if the capitalization rate is 11%?

Answer 1

- stock A

1) at 8%

Present Value of Perpetuity = Perpetual Cash flow / market capitalization rate

= 15/.08

= $187.50

2) at 11%

Present Value of Perpetuity = Perpetual Cash flow / market capitalization rate

= 15/.11

= $136.36

- stock B

1) at 8%

Po = D1 / (Ke – g)

Where,

Po – Current share price = ?

D1 – Next year expected dividend = 9

Ke – Cost of equity = 8%

G – Growth rate in dividend = 4%

P0 = 9/(.08-.04)

= 9/.04

= $225.00

2) at 11%

P0 = 9/(.11-.04)

= 9/.07

= $128.57

- stock C

1) at 8%

Step 1: Computation of market price at the end of year 4 using Gordon Growth Mdel

P4 = D5 /market capitalization rate

= (9*1.3^3)/.08

= 19.773/.08

= $247.1625

Step 2: Computing current share price by discounting the cashflow at required return

Year	Dividend	PVF@8%	Present Value (Cashflow*PVF)
1	9.00	0.9259	8.33
2	11.70	0.8573	10.03
3	15.21	0.7938	12.07
4	266.94	0.7350	196.21

current share price = Cashflow*PVF

= 8.33+10.03+12.07+196.21

= $226.64

2) at 11%

Step 1: Computation of market price at the end of year 4 using Gordon Growth Mdel

P4 = D5 /market capitalization rate

= (9*1.3^3)/.11

= 19.773/.11

= $179.7545

Step 2: Computing current share price by discounting the cashflow at required return

Year	Dividend	PVF@11%	Present Value (Cashflow*PVF)
1	9.00	0.9009	8.11
2	11.70	0.8116	9.50
3	15.21	0.7312	11.12
4	266.94	0.6587	175.84

current share price = Cashflow*PVF

= 8.11+9.50+11.12+175.84

= $204.57

Stock C is more valuable under both the situations.