The intrinsic value of company's share is $89.90
The share price is expected to rise in the incoming years
The intrinsic value of share remains the same when payout ratio reduces to 20%
What is the firm growth rate in each of the future years?
The growth rate of the company, which is also the growth rate for earnings per share in each of the first 5 years
Growth rate in the first 5 years=ROE*reinvestment rate
ROE=20%
reinvestment rate=100%(all earnings would be reinvested)
Growth rate in the first 5 years=100%*20%
Growth rate in the first 5 years=20%
Earnings in 5 years=current EPS*(1+growth rate)^5
Earnings in 5 years=$10*(1+20%)^5
Earnings in 5 years=$24.8832
Growth rate for year 6 and beyond=15%*(1-40%)
Growth rate for year 6 and beyond=9.00%
Earnings in year 6=$24.8832*(1+9%)
earnings in year 6=$27.122688
Out of the EPS, 40% would be paid as dividends
dividends in year 6=$27.122688*40%
dividends in year 6=$10.8490752
We can compute the share price at the end of year using the present value formula of perpetuity
share price in year 5=$10.8490752/(15%-9%)
share price in year 5=$180.81792
share price now=$180.81792/(1+15%)^5
share price now=$89.90
The fact that share price and the intrinsic value are the same implies that share price would increase over the next year and the year after because the dividends would continue to growth at a constant rate of 9%
Out of the EPS, 20% would be paid as dividends
dividends in year 6=$27.122688*20%
dividends in year 6=$5.4245376
growth rate=15%*(1-20%)=12.00%
We can compute the share price at the end of year using the present value formula of perpetuity
share price in year 5=$5.4245376/(15%-12%)
share price in year 5=$180.81792
share price now=$180.81792/(1+15%)^5
share price now=$89.90
The share price in payout ratio from 40% to 20% has no effect on the intrinsic value since the share prices are the same under the two scenarios
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