Question

You purchased Butterfly Wing Corporation stock exactly one year ago at a price of $79.11 per share. Over the past year, the stock paid dividends of $3.22 per share. Today, you sold your stock and earned a total return of 16.39 percent. What was the price at which you sold the stock?


Multiple Choice

$92.08


$94.38


$96.68


$98.21


$88.86

Answer 1

To calculate the selling price of the stock, we first need to understand the components of total return. The total return consists of capital gains (the difference between the selling price and the purchase price) plus dividends received.

Given:
- Purchase price per share = $79.11
- Dividends paid = $3.22 per share
- Total return = 16.39%

The formula for total return is:

\[
\text{Total Return} = \frac{(\text{Selling Price} - \text{Purchase Price}) + \text{Dividends}}{\text{Purchase Price}}
\]

Plugging in the known values:

\[
0.1639 = \frac{(\text{Selling Price} - 79.11) + 3.22}{79.11}
\]

First, let's compute the total returns in terms of the selling price:

\[
0.1639 \times 79.11 = (\text{Selling Price} - 79.11) + 3.22
\]

Calculating \(0.1639 \times 79.11\):

\[
0.1639 \times 79.11 \approx 12.95
\]

So we now have:

\[
12.95 = (\text{Selling Price} - 79.11) + 3.22
\]

Now, simplify this equation:

\[
12.95 = \text{Selling Price} - 79.11 + 3.22
\]

Thus:

\[
12.95 = \text{Selling Price} - 75.89
\]

Next, add \(75.89\) to both sides to find the selling price:

\[
\text{Selling Price} = 12.95 + 75.89 \approx 88.84
\]

Checking for the correct selling price:

\[
\text{Selling Price} = 88.84
\]

This value should match one of our options, but let's double-check our calculations based on the percent return.

We can also rearrange the earlier formula and compute directly:

\[
\text{Selling Price} = \text{Purchase Price} + (0.1639 \times \text{Purchase Price}) - \text{Dividends}
\]

Calculating that gives:

\[
\text{Selling Price} = 79.11 + (0.1639 \times 79.11) + 3.22
\]

But that suggests a mistake: we neglected the dividends.

Instead, rewriting it:

\[
\text{Selling Price} = \text{Purchase Price} + \text{Total Return in $} = 79.11 + (12.95 - 3.22)
\]

Calculating again confirms the oversight yield:

\[
\text{Selling Price} = 88.84
\]

After reassessing and checking:

Calculating actual selling price would yield closest approximation should roughly verify one option provided – as discrepancies in round-offs might transpire.

In conclusion iterating suitable figures, choice must finalize and adhere to rounded option where expected around.

Presenting rechecked lead confirms, hence our option selections are carried.

So, the correct answer among given choices would be closest valid:

\[
\text{Selling Price} \approx 88.86 \text{ (matching an option)}
\]

So, the answer is:

**$88.86**