|
A company's dividend policy is based on its earnings per share (EPS). The earnings per share for the company is based on the state of the economy.
For a good economy, the conditional probabilities of EPS are as follows:
P(Increase in EPS| good economy) =0.60
P(No change in EPS| good economy) = 0.30
P(Decrease in EPS| good economy) = 0.10
For a bad economy, the conditional probabilities of EPS are as follows:
P(Increase in EPS| bad economy) = 0.10
P(No change in EPS| bad economy) = 0.20
P(Decrease in EPS| bad economy) = 0.70
The dividend payment is $1.00 per share if the EPS increases, $0.70 if there is no change in EPS and $0.20 if the EPS decreases. Compute the conditional expected value of the dividend payment for each statement of the economy. The probabilities of occurrence of a good economy and a bad economy are 0.60 and 0.40 respectively.
Solution:
The expected value of dividend payment when the state of the economy is good = E(X| good economy) = 0.60*$1.00 + 0.30*$0.70 + 0.10*$0.20 = $0.83
The expected value of dividend payment when the statement of the economy is bad = E(X| bad economy) = 0.10*$1.00 + 0.20*$0.70 + 0.70*$0.20 = $0.38
Once we get the conditional expected values, we can easily calculate the unconditional expected value.
Unconditional expected value of dividend payment = Conditional expected value for good economy*Probability of good economy + Conditional expected value for bad economy*Probability of bad economy = $0.83*0.60 + $0.38*0.40 = $0.65
|
