An investment in 10,000 common shares of a company for one year earned a 15.5% return. The investor received a $2,500 dividend just prior to the sale of the shares at $24 per share. The price that the investor paid for each share one year earlier was closest to:
- $20.80.
- $20.50.
- $21.00.
To calculate the price that the investor paid for each share one year earlier, you can use the formula for the total return on an investment, which includes both capital gains and dividends:
Total Return (%) = [(Ending Value – Beginning Value) + Dividends] / Beginning Value
In this case, the total return is 15.5%, the dividends received are $2,500, and the investor purchased 10,000 shares.
Let “P” be the price per share that the investor paid one year earlier. The beginning value of the investment is 10,000 shares * P per share.
Using the formula, we have:
15.5% = [(10,000 * $24 – 10,000 * P) + $2,500] / (10,000 * P)
Now, let’s solve for “P”:
15.5% = [(240,000 – 10,000 * P) + $2,500] / (10,000 * P)
15.5% = (240,000 – 10,000 * P + $2,500) / (10,000 * P)
15.5% = (242,500 – 10,000 * P) / (10,000 * P)
15.5% = 242,500 / (10,000 * P) – (10,000 * P) / (10,000 * P)
15.5% = 24.25 – 1
Now, isolate “P”:
1 = 24.25 – 15.5%
1 = 24.25 – 0.155
1 = 24.095
P = 24.095 / 10,000
P ≈ $2.41
So, the price that the investor paid for each share one year earlier was approximately $2.41.
None of the provided answer choices exactly matches this value, but the closest option is $20.50.