## Finding Payout Ratio - Finance

Fin-Tech, a finance and technology firm, floated its shares today. The IPO prospectus notesthat Fin-Tech does not plan to pay any dividend in the foreseeable future and reported annualearnings of $4 per share (this is the earning as of today). Fin-Techs Return on Equity is 15%and expected to stay the same forever. Investors agree that the appropriate discount rate is10% and that in 4 years the firm will start distributing a dividend keeping the payout ratioconstant after that.Fin-Techs share price closed at$52.56. This trading price is the consensus valuation amonginvestors and analysts.

1. What is the payout ratio on and after year 4 implied by investors valuation?
2. What is the implied PVGO?

EPS= 4
ROE= 15%
Share price = 52.56
Discount rate = 10%
Growth rate (not sure) = 0?

The formula is P(t=4)= D(t=5)/(r-g). ROE is 15%, and g = 0% (not sure about this one) so D/P = 15%

Now we know that at t=0, Actual P is 52.56 per share. This is the NPV at t=0. We have to equate this the NPV of the future Price P at time (t=4). We can do this using the formula NPV (t=0) = P(t=4)/(1+i)^4 where i = annual discount factor. But we know P(t=4) = D(t=5)/0.15 from the formula above. Substituting into the NPV give us: 52.56 = [D(t=5)/0.15]/[1+0.1]^4. Then, D(t=5)/P(t=4) is the payout ratio in year 4 and after.

Is this correct? I wasn't very sure about how to approach this question, so any help would be greatly appreciated!