[Tural1988]

Hi. Dear all, I have a problem on corporate Finance. I could not solve that problem. The problem is: ‘ Lang Co. wishes to maintain a growth rate of 8 percent a year, a debt-equity ratio of .45, and a dividend payout ratio of 60 percent. The ratio of total assets to sales is constant at 1.60. What profit margin must the firm achieve?
I hope you will help me. I really need it. It is very important for me.Thanks previously

[ArcSine]

Let's call the growth rate g, and in your case we want g = 0.08. A company's growth rate is the result of multiplying two numbers:

1. The 'plowback rate'; let's call that one P;
2. The 'return on assets'; we'll call it R.

So, g = RP= RP, and you want an R and a P such that R P = 0.08.

OK, one at a time. The Plowback Rate P (aka 'reinvestment rate') is just 1, minus your dividend payout rate. You're given that Lang is paying out 60% of its earnings as dividends, which means it's reinvesting 40% of its earnings back into the biz. Thus, P = 0.40. Easy enough. Now let's go figure out R.

The return on assets R is just the ratio of net profit to Assets, or . Now, 'net profit' is Sales, times the 'profit margin'--and let's use M to denote profit margin. (Note that M--profit margin--is what your problem is asking for.) So by re-writing Net Profit as Sales M, we can re-write the formula for R this way...

R = . Hang in there... that last little manipulation is going to prove useful.

In the problem we're told that the Assets-to-Sales ratio is 1.60. We can flip that over by taking the reciprocal: . Looking back at our previous re-writing of R, we can now say that R = 0.625 R = 0.625 M M. Cool, huh?

We can finally revisit our target objective. The growth rate--8%, in this case--equals Return on Assets (R) times Plowback Rate (P). Using what we've discovered about R and P above, we can say...

0.08 = R P = 0.625 M 0.40. All that's left for you to do is solve for M, and you'll have the profit margin that will give Lang an 8% growth rate.

Best of luck in your studies!