Yang Corp. is growing quickly. Dividends are expected to grow at a rate of 31 pe
ID: 2628903 • Letter: Y
Question
Yang Corp. is growing quickly. Dividends are expected to grow at a rate of 31 percent for the next three years, with the growth rate falling off to a constant 6.6 percent thereafter.
If the required return is 12 percent and the company just paid a $2.65 dividend, what is the current share price? (Hint: Calculate the first four dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
Required:If the required return is 12 percent and the company just paid a $2.65 dividend, what is the current share price? (Hint: Calculate the first four dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
Explanation / Answer
Concept : COMPLETE EXPLANATION
Calc each dividend, then the terminal value at the constant growth rate, and discount back by 12%.
Dn = Div,number
g = initial growth rate (31%, or 0.31)
D0 = 2.65
D1 = D0*(1+g)..=2.65* 1.31 = 3.47150 (you can round to penny here, or wait, - you'll get a different answer if you wait and keep the decimals after the penny, or round now)
D2 = D0*(1+g)^2..=2.65*1.31^2 = 4.54767
D3 = D0*(1+g)^3...= 2.65*1.31^3 = 5.95744
D4 is the constant dividend..D3*(1+constant g) = 5.95744*1.06 = 6.31489
value of stock at the end of year 3 = D4/(k-g), where k is the discount rate...
value at end year 3 = 6.31489/ (0.12 - 0.06) = 6.31489/0.06 = $105.24813, or $105.25
Next, discount each cash flow by 1.12^n, where n corresponds to the time from today. In year #3 you will receive D3 PLUS the value (price) at end year 3, so both of these will be discounted 3 years. Don't make the common mistake of discounting the terminal price (end year 3) by 4 years!!
Next, discount the cash flows: (My calculator would "remember" numbers after 5 decimals, so I will just "plug" the 5 decimal place numbers. Remember, if you round each Dividend, the following dividend will change, so don't just round my numbers above. Example: if D1 is rounded to $3.47, then D2 will be 3.47 * 1.31 = 4.5457, rounded to 4.55, and D3 will be based off of 4.55, not 4.5457, etc. - rounding will also affect the terminal price)
Price at time 0 (today)=
the PV of the cash flows = 3.47150 /1.12^1 + 4.54767/1.12^2 + 5.95744/1.12^3 + 105.25/1.12^3
= $85.88019, rounded to $85.88
FYI - if I round at each step:
the cash flows are: CF#1: 3.47, CF#2: 4.55, CF#3: (5.96 + 105.29see note below), and PV0 (price today) = $85.91
note: D4 = 5.96*1.06 = 6.3176 rounded to $6.32, so terminal value is 6.32/0.06 = 105.29<price 3 years from now
Hope this helps...price today is simply a summation of discounted dividends + discounted terminal value, where the terminal value uses the Gordon growth model: the "next" dividend / (k-g)
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