Question

You own 100 shares in the firm Alfa. The current share price is £10 and the earnings per share is £0.70. Assume there are no capital market imperfections and that Alfa’s annual earnings will remain constant in future. Alfa pays out all of its earnings each year as dividends. You prefer to invest your money in the firm, so you reinvest each year’s dividend in the firm by buying more of its shares. Your investment horizon is 10 years.

i. What is the value of your investment after 10 years? What would the value of your investment have been, if Alfa’s policy was a zero dividend payout over the same period?

Assume now that there are personal taxes but no other market imperfections. The tax rate on both dividends and capital gains is 30%.

2. Assume again that Alfa pays out all its earnings as dividends. You reinvest all your dividends back in the firm but decide to sell your shares at your 10 year investment horizon, immediately after the last dividend was paid. What is the value of your wealth?

What would be your answer in (ii), assuming now that Alfa’s policy was a zero dividend payout over the 10 years? Is it different? Why/why not?

Answer 1

Given,

Current price= £10, Number of shares= 100, EPS (constant)= £0.70 and investment horizon= 10 years.

Dividend payout = 100%,

Therefore, current value of investment = £10*100 = £1,000

Part (i): No taxes.

Value of investment in 10 years is the Future value (FV) calculated using the following formula:

FV= I(1+r)^n

Where I= Amount of investment, r= rate of return and n= number of years in investment horizon.

Amount of dividend paid and reinvested every year= £0.70*100 = £70

Therefore, rate of return ( r) = (70/1000)*100 = 7%

Value of investment after 10 years = 1000*(1+7%)^10 = £ 1,967.15

Part (ii): Tax rate on dividend and capital gains (T): 30%.

Given, dividend is paid (payout ratio 100%) and reinvested.

Therefore, dividend paid and reinvested per share every year= EPS*(1-T) = 0.70*(1-0.30) = £0.49

Rate of return= (0.49/10)*100 = 4.9%

Value of investment after 10 years before capital gain tax= 1000*(1+4.9%)^10 = £1,613.45

Value of investment after 10 years after capital gain tax= £1,613.45 * (1-30%) = £1,129.41

Part (iii): Zero dividend payout.

Earnings reinvested per share every year= £0.70

Value of investment after 10 years before capital gain tax= 1000*(1+7%)^10 = £ 1,967.15

Value of investment after 10 years after capital gain tax= £1,967.15 * (1-30%) = £1,377.01

The value of investment in 10 years is higher by 1377.01-1129.41= £247.60. The difference is because there is no dividend payout each year. Hence the entire EPS is reinvested every year, without deduction of tax.