An investor purchased a stock for $200 and sold it for $300, 6 years later. Each stock paid a dividend of $7.50 per year...

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Question

An investor purchased a stock for $200 and sold it for $300, 6 years later. Each stock paid a dividend of $7.50 per year...

An investor purchased a stock for $200 and sold it for $300, 6 years later. Each stock paid a dividend of $7.50 per year.

• What is the rate of return of this investment ignoring inflation?

• What is the rate of return of this investment, given an annual inflation of 2.7%?

Please explain in detail and show the formulas used. Thanks!

business economics

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Answer 1

Answer #1

i) In this we need to find a rate of interest in which the PV value of the dividends is equal to the PV of the future dividends and the price at which the stock is sold after 6 years.

Let the interest rate be i. v = 1/(1+i)

The present value of the future cashflows =

7.5v + 7.5v² + 7.5v³ + 7.5v⁴ + 7.5v⁵ + 7.5v⁶ + 300 v⁶

= 7.5a₆ + 300 v⁶

So the equation should be,

200= 7.5a₆ + 300v⁶

Expanding this we get,

200 = 7.5*((1-(1+i)^-⁶)/i) + 300* ((1/(1+i))⁶)

Solving this we get, i = 0.10198 = 10.198% = 10.2% (rounding to nearest 1 decimal place)

ii) Now we need to consider annual inflation rate of 2.7% So, the new rate of return after taking into consideration the inflation rate will be =

(1.10198 / 1.027) - 1

= 0.0806 = 8.06% = 8.1%(rounding to nearest 1 decimal place)

We can see that the rate of return has decreased and this was expected because a positive inflation rate will decrease the actual rate of return.

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Answer 2

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Add Answer to: An investor purchased a stock for $200 and sold it for $300, 6 years later. Each stock paid a dividend of $7.50 per year...

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