you sit down with management and figure out a price that it can sell at. you bel
ID: 2725790 • Letter: Y
Question
you sit down with management and figure out a price that it can sell at. you believe that the company will pay its first dividend in 8 years.a t that point it will pay a dividend of 1.80, which it will then increase at 6.5% each year. you think that the appropriate discount rate for the company is 9.5%
a) based on your analysis , what is the predicted price of the company today?
b)you suggest a price of 24 for company. Given this price, what is the project return on the first day of trading,assuming that market participants share your views and price the stock equal the predicted price from a?
c)what do you expect the stock price to be n seven years (one year before the first dividend payment)? in fact, the stock price equals to 45, at what rate r would this be the correct price (assuming nothing else has changed, so that the first dividend is still expected to be 1.80)?
d) now you think that the dividend growth rate was too optimistic. at what level g would the price in seven years be correct assuming the original level of k ( and a first dividend payment of 1.8)?
Explanation / Answer
a) Predicted price of the company as of today is the PV of the expected cash flows from the stock.
The expected cash flows are a dividend of $1.8 in the eighth year and then a stream of dividends that grow perpetually at the rate of 6.5%. The PV of these divdend cash flows would be
1.8/1.095^8 + [(1.8*1.065)/(0.095 - 0.065)]/1.095^8 = 0.87 + 30.92 = $31.79
b) Projected return = 31.79 - 24 = $7.79 or
(31.79/24) - 1 =0.3246 = 32.46%
c) The stock price seven years after (one year before the first dividend payment) would be:
1.8/1.095 + [(1.8*1.065)/(0.095 - 0.065)]/1.095 = 1.64 + 58.36 = $60
If the stock price equals 45, then r, the discount factor has to be found out from the following equation:
1.8/(1+r) + [(1.8*1.065)/(r - 0.065)]/(1+r) = $45
By trial and error the 'r' will be equal to 10%.
c) g has to be found out from the following equation
1.8/(1.095) + [(1.8*(1+g)/(0.095 -g)]/(1.095) = $45
By trial and error it is found to be 5.5% ie: g should be 5.5% for the price to be $ 45 at the end of the seventh year, the discount rate being 9.5%.
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