33.7
7. Your company has 1 million shares outstanding. You pay an
annual dividend of $5 per share and the next dividend is due today.
The required rate of return on your equity (stock) is 10% per
year. If you are expected to pay the $5 dividend forever, what is
the current value of the company? (2)
OK. A lot of people told me that this one was "out of the blue." or "nothing like anything we’ve done." Well, I’ll take a lot of criticism (especially about the midterm), but I’ve got to defend this one. This problem is the "FOR NEXT TIME" from Topic 10 VERBATIM. I didn’t even change the numbers. It’s in the notes and I did the problem in class.
$5M + ($5M/0.10) = $55 million
a. What is the value of one share of stock? (2)
Total value of the company is $55M and there are 1 million shares outstanding. Thus, each share is worth $55.
b. What will the value of each share of stock be immediately after the dividend is paid? (2)
After the dividend is paid, you will have $5 in cash (from the dividend) and your share will represent a claim on next year's and every future year's dividends. Thus your share will be worth $50 = ($5/.10).
c. This year, you unexpectedly generated an extra $2 million in cash flow. You are trying to decide whether to distribute the cash to your stockholders today, along with your scheduled dividend, or reinvest it. What is the new value of each share of stock with the news of the extra $2 million? (2)
The total value of the company is worth $55 M + $2M = $57M, so each share is worth $57.
d. What will the value of each share be immediately after you pay out the $5 dividend and the extra $2 dividend? (2)
You will be back down to just $50. (But you will have $7 in your pocket as well).
You are looking at an investment opportunity that would require you to reinvest the extra $2 million instead of distributing it to stockholders. This opportunity has the same risk level as your current business and would have the same discount rate.
Consider two scenarios: (a) your investment opportunity is expected to produce $2.3 million next year, which you will distribute as an extra dividend at that time, and (b) your investment opportunity is expected to produce $2.1 million next year, which you will distribute as an extra dividend at that time.
e.Show that under scenario (a), the project has a positive NPV and the value of the stock (based on expected dividends) is higher than if you had distributed the $2 million immediately. Then show that under scenario (b), the project has a negative NPV and the value of the stock (based on expected dividends) is lower than if you had distributed the $2 million immediately. (6)
NPV(a) = -2M + (2.3M/1.10) = +0.0909M
If the money is reinvested in scenario (a), the shareholders won't get an extra $2 dividend today, but they will get an extra $2.30 dividend next year. Thus, today, rather than having $7 in their pockets and a share worth $50, they'll have $5 in their pockets and a share worth $50 + ($2.30/1.1) = $52.09. The total value of their package of cash and shares is worth $57.09 instead of $57.
NPV(b) = -2M + (2.1M/1.10) = -0.0909M
If the money is reinvested in scenario (b), the shareholders won't get an extra $2 dividend today, but they will get an extra $2.10 dividend next year. Thus, today, rather than having $7 in their pockets and a share worth $50, they'll have $5 in their pockets and a share worth $50 + ($2.10/1.10) =$51.91. The total value of their package of cash and shares is worth $56.91 instead of $57.00.
f. Given the results of this question, when does it make sense for a financial manager to retain earnings and reinvest them in the company? (2)
It only makes sense to reinvest in the company when you are reinvesting in a positive NPV project. Otherwise, the shareholders would be better off if you returned the money to them so they can invest it elsewhere.