Chen Inc. announced today that it will begin paying annual dividends. The first dividend will be paid next year in the amount of $.75 a share. The following dividends will be $1.00, $1.10, and $1.20 a share annually for the following three years, respectively. After that, dividends are projected to increase by 3% per year. How much are you willing to pay to buy one share of this stock if your desired rate of return is 6%?
Please show all work.
As per dividend discount model, current share price is the present value of future dividends. | ||||||||||
Step-1:Present value of dividends of next 4 years | ||||||||||
Year | Dividend | Discount factor | Present value | |||||||
a | b | c=1.06^-a | d=b*c | |||||||
1 | $ 0.75 | 0.943396 | $ 0.71 | |||||||
2 | $ 1.00 | 0.889996 | $ 0.89 | |||||||
3 | $ 1.10 | 0.839619 | $ 0.92 | |||||||
4 | $ 1.20 | 0.792094 | $ 0.95 | |||||||
Total | $ 3.47 | |||||||||
Step-2:Present value of dividends after year 4 | ||||||||||
Present value | = | D4*(1+g)/(Ke-g)*DF4 | Where, | |||||||
= | $ 32.63 | D4 | = | Dividend of Year 4 | = | $ 1.20 | ||||
g | = | Growth rate | = | 3% | ||||||
Ke | = | Requied return | = | 6% | ||||||
DF4 | = | Discount factor of Year 4 | = | 0.792094 | ||||||
Step-3:Sum of present value of future dividends | ||||||||||
Sum | = | $ 3.47 | + | $ 32.63 | ||||||
= | $ 36.11 | |||||||||
So, | ||||||||||
Price of stock is $ 36.11 | ||||||||||
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