In: Finance
1. Dividend discount model: Company X is expected to pay an end-of-year dividend of $8 a share. After the dividend, its stock is expected to sell at $105. If the market capitalization rate is 10%, what is the current stock price? 2. Dividend discount model: Consider the following three stocks: a) Stock A is expected to provide a dividend of $10 a share forever. b) Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4% a year forever. c) Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i.e., years 2 through 6) and zero thereafter. If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 6%?
1 | ||||||
Market Capitalization Rate=10% | 0.1 | |||||
D1 | Dividend in yer 1 | $8 | ||||
P1 | Market Value of share in year 1 | $105 | ||||
D1/(1+0.1) | Present value of Dividend | $7.27 | ||||
P1/(1+0.1) | Present value of market value in year1 | $95.45 | ||||
P0 | Current Stock Price=7.27+95.45= | $102.73 | ||||
Current Stock Price | $102.73 | |||||
2 | ||||||
R | Market Capitalization Rate=10% | 0.1 | ||||
D | a)Amount of dividend forever | $10 | ||||
P0=D/R | Current Stock Price of tockA | $100 | ||||
b) | ||||||
D1 | Dividend Next year | $5 | ||||
g | Dividend growth rate=4% | 0.04 | ||||
P0=D1/(R-g) | Current Stock Price of StockB | $83.33 | ||||
c) | N | A | PV=A/((1+R)^N) | |||
Year | Cash Flow | Present Value of Cash Flow | ||||
Dividend in year1 | D1 | 1 | $5 | $4.55 | ||
Dividend in year2 | D2=D1*1.2 | 2 | $6.0 | $4.96 | ||
Dividend in year3 | D3=D2*1.2 | 3 | $7.2 | $5.41 | ||
Dividend in year4 | D4=D3*1.2 | 4 | $8.6 | $5.90 | ||
Dividend in year5 | D5=D4*1.2 | 5 | $10.4 | $6.44 | ||
Dividend in year6 | D6=D5*1.2 | 6 | $12.4 | $7.02 | ||
Price at Year 6 | P6=D7/0.1 | 6 | $124.0 | $69.99 | ||
SUM | $104.27 | |||||
Dividend in year7 | D7 | 7 | $12.4 | |||
P0 | Current Price =Sum of PV of cash flows= | $104.27 | ||||
Current Price of StockC | $104.27 | |||||
Stock C has the highest stock price | ||||||
Market Capitalization Rate=6% | ||||||
R | Market Capitalization Rate=6% | 0.06 | ||||
D | a)Amount of dividend forever | $10 | ||||
P0=D/R | Current Stock Price of A | $167 | ||||
b) | ||||||
D1 | Dividend Next year | $5 | ||||
g | Dividend growth rate=4% | 0.04 | ||||
P0=D1/(R-g) | Current Stock Price of stockB | $250.00 | ||||
c) | N | A | PV=A/((1+R)^N) | |||
Year | Cash Flow | Present Value of Cash Flow | ||||
Dividend in year1 | D1 | 1 | $5 | $4.72 | ||
Dividend in year2 | D2=D1*1.2 | 2 | $6.0 | $5.34 | ||
Dividend in year3 | D3=D2*1.2 | 3 | $7.2 | $6.05 | ||
Dividend in year4 | D4=D3*1.2 | 4 | $8.6 | $6.84 | ||
Dividend in year5 | D5=D4*1.2 | 5 | $10.4 | $7.75 | ||
Dividend in year6 | D6=D5*1.2 | 6 | $12.4 | $8.77 | ||
Price at Year 6 | P6=D7/0.1 | 6 | $206.7 | $145.69 | ||
SUM | $185.16 | |||||
Dividend in year7 | D7 | 7 | $12.4 | |||
P0 | Current Price =Sum of PV of cash flows= | $185.16 | ||||
Current Price of Stock C | $185.16 | |||||
Stock B has the highest stock price | ||||||