D. A company's retained earnings are mathematically defined as follows:                             

Prior Retained Earnings+Net Income-Dividends.  (Net Income=Revenues-Expenses)              

Hence, in this problem, Retained Earnings = Prior Retained Earnings+Revenues-Expenses-Dividends = 0+6M-5M-0 = $1M

 

E. Book Equity = Issued Shares*Sale Price + Retained Earnings = 2M*$12.50 + 1M*$17.50 + $1M = $43.5M

 

F. Market Equity = Outstanding Shares*Current Market Price = 3M*$17.50 = $52.5M

Heather

Why is the 1 million authorized stock(4-2-1=1) left excluded from the following book equity formula? 

"E) Book equity = $3M + $39.5M +($6M - $5M) = $43.5M"

To calculate the book equity on part E, it says to use "original cash + earning - expense", which I interpret as = original cash + retained earning. (please correct me if that's wrong) 

My question: what counts as "original cash?"

 -  Is it the sale of outstanding stock price throughtout the year? i.e. ($12.5*2M) + ($17.5*1M) ?

 -  also want to confirm that orig. cash does not include the $8M used to buy land, since that amount is being canceled out (expenditure out first but gain back in asset)

Your help is greatly appreciated!

For part E:
If the land adds value to the company, why doesn't the $8MM's worth of land add equity to the company. Even though $8MM was spent on the land, wouldn't the $8MM have added value to the company and therefore its equity?

[NEAS: See the previous postings. If the firm spends cash and acquires land, book equity doesn't change.]

Retained earnings do not include sale of stocks. That would be capital. Retained earnings would be accumulated income. In this case, eacrnings  = 6 mil. Expenses = 5 mil, Therefore, retained earnings = 1 mil.

part D) The definition of retained earnings is: earnings (from sale of stocks) that are not distributed as dividend. I do not see how this question make sense. If none of the cash is used in dividends, then retained earnings are 2 mill*12.50 + 1 mill*17.5 = $42.5 mill regardless of what it was used for as investment.

in e) 1 mill share is sold to get additional paid-in capital so I think we will make a mistake if we add it in book equity.

So my answer is:
cash in : 12.5x2 + 6 + 17.5
cash out: 5 +1
equity : 42.5

I believe the land asset counts towards the book equity with the same value that you purchased it at, so it cancels out. You lose $8m in cash, but gain $8m in land (which doesn't depreciate--that's the key part of the question).

By contrast, the renovation doesn't result in a physical "renovation" asset that the company can say it holds... Therefore the $5m cost for that is subtracted from book equity without being replaced by anything.

That's how I see it, anyway.

For part d, do you not have to take into consideration the $8M used to purchase the land?

Here is what I have:

c) 12.5(2mil)-1(1mil)+17.5(1mil)-1(1mil) = 39.5 mil

d) 6mil - 5 mil = 1mil

e) 3mil + 39.5 mil + 1 mil = 43.5 mil

f) I agree with you, 17.5(3mil) = 52.5mil