Math  /  Algebra

QuestionAccount Dashboard Courses Calendar Inbox History 10 Multiple Choice 3.5 points
A $30,000\$ 30,000 corporate bond is convertible to 120 shares of the corporation's common stock. What price per share must the corporation's stock be before bondholders would consider converting a bond to the company's common stock? \$50 \$250 \$300 \$30 Next Help

Studdy Solution

STEP 1

What is this asking? If I have a bond worth $30,000\$30,000 that I can swap for **120** shares of a company's stock, what does the price of each share need to be before I decide to make that swap? Watch out! Don't get tricked by extra information!
We just need to figure out the price per share that makes the stock worth the same as the bond.

STEP 2

1. Calculate the break-even price.

STEP 3

Alright, so we've got this **magical bond** worth $30,000\$30,000, and we can trade it in for **120 shares** of some cool company's stock.
The question is, when is it a good deal to make the trade?

STEP 4

Let's think about it.
We want to know the price *per share* that makes those **120 shares** worth the same as our **\$30,000** bond.
That's the *break-even price*!

STEP 5

So, we're going to **divide** the **total value of the bond** ($30,000\$30,000) by the **number of shares** we can get (**120**).
This will tell us how much each share needs to be worth to match the bond's value.

STEP 6

$30,000120 shares \frac{\$30,000}{120 \text{ shares}}

STEP 7

Let's do the math! $30,000\$30,000 divided by **120** gives us... $250\$250!

STEP 8

$30,000120=$250/share \frac{\$30,000}{120} = \$250/\text{share}

STEP 9

So, if the stock price is *less* than $250\$250, we're better off holding onto our **bond**.
But if the stock price goes *above* $250\$250, then swapping for stock becomes the better deal!

STEP 10

The stock price must be at least $250\$250 per share for bondholders to consider converting.

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