You purchase 100 shares of stock for $40 a share. the stock pays a $2 per share dividend at year-end. a. what is the rate of return on your investment if the end-of-year stock price is (i) $38; (ii) $40; (iii) $46? b. what is your real (inflation-adjusted) rate of return if the inflation rate is 3%?

A. (i) 0% (ii) 5% (iii) 20%

B. (i) -2.91% (ii) 1.94% (iii) 16.50%

Explanation:

A. The total rate of return of a stock is the net gain (loss) on the investments and it includes both capital gain (loss) and dividend income.

Formula: (Capital Gain (Loss) + Dividend)/Initial Investment

or

(Year End Value + Dividend)/initial investment - 1

Solution:

(i) (38 + 2)/40 - 1 = 0%

(ii) (40 + 2)/40 - 1 = 5%

(iii) (46 + 2)/40 - 1 = 20%

B. Inflation adjusted return is the return on investment after accounting for inflation, it reveals the true earning potential of an investment.

The following formula is used to calculate inflation adjusted return:

Inflation adjusted return = (1 + rate of return) / (1 + inflation rate) - 1

Since, we have already calculated rate of return in Part A we just need to adjust it for inflation

Solution:

(i) (1 + 0%) / (1 + 3%) - 1 = -2.91%

(ii)  (1 + 5%) / (1 + 3%) - 1 = 1.94%

(iii) (1 + 20%) / (1 + 3%) - 1 = 16.50%

*The inflation adjusted return is rounded off to two decimal points*

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