Question

1. Suppose that a person bought 100 shares of company X for 100 euros per share on 01.01.2018. The commission fee charged on this transaction was 25 euros. This person kept these stocks for 2 years and sold his portfolio of company X stocks on 01.01.2020 for 121.55 euros per share. The commission fee charged on this transaction was 30 euros. During the holding period the investor received dividends 3.3 euros per share on 01.01.2019 and dividends 2.42 euros per share on 01.01.2020. Suppose that the realized capital gains are taxed at 20% and the dividends are tax exempt in the country of residence of this person. Suppose also that the annual rate of inflation in the country of residence of this person was 2% in 2018 and 2% also in 2019.

a) Find the nominal after-tax holding period rate of return for this person from the investment described.

b) Find the real after-tax holding period rate of return for this person from the investment described.

Answer 1

Original investment = 100 * 100 = 10000

Commission at the time of buying = 25

Current value of the investment = 121.55 * 100 = 12155

Commission at the time of selling = 30

Dividend in 2019 = 3.3

Dividend in 2020 = 2.42

Capital gain tax = 20 %

Dividends are tax exempt

Inflation rate is 2 % for 2018 and 2019

a) Find the nominal after-tax holding period rate of return for this person from the investment described.

The nominal rate of an investment is the amount of money generated by an investment before considering expenses such as inflation, investment fees and taxes

Nominal after-tax return = nominal return * (1 - capital tax rate)

Nominal return = (present market value – original investment value) / original investment value

                         = (12155 – 10000) / 10000

                       = 0.2155

                    = 21.55 %

Nominal after-tax return = 0.2155 * (1 – 20%)

                                        = 0.1724

   = 17.24 %

b) Find the real after-tax holding period rate of return for this person from the investment described.

The after-tax real rate of return is the amount generated from an investment after deducting inflation

real rate of return after tax = (1 + after tax nominal return) / (1 + inflation rate) - 1

= (1 + 0.1724) / (1 + 0.04) – 1

=   0.1273

= 12.73 %