Acme Industries is a new firm that has raised $100 million by selling
shares of stock. Management plans to earn a 25 percent rate of return
on equity, which is more than the 15 percent rate of return available
on comparable-risk investments. Half of all earnings will be
reinvested in the firm.
a. What will be Acme's ratio of market value to book value?
b. How would that ratio change if the firm can earn only a 10 percent
rate of return on its investments?
c. Why do investments in financial markets almost always have zero
NPVs whereas firms can almost always find many investments in their
new product markets with positive NPVs?

Hi!!


a. What will be Acme's ratio of market value to book value?

The Book value is a company's common stock equity as it appears on a
balance sheet. This is the net worth of a company, the amount by which
assets exceed liabilities. It's also known as "shareholder's equity".
It is the total value of the company's assets that shareholders would
theoretically receive if a company were liquidated.

Book value = $100 million

We know that:
ROE = Earnings / Book Value

then:
Earnings = Book value * ROE =
         = $100 million * 0.25 = 
         = $25 million


We have that:
Plowback Ratio = 0.5

and:
Payout Ratio + Plowback Ratio = 1

then:
Payout Ratio = 1 - Plowback Ratio 

On the other hand:
Payout Ratio = Dividends / Earnings     (= DPS/EPS)

Then:
Dividends = Earnings * Payout Ratio =
          = Earnings * (1 ? plowback ratio) =
          = $25 million * (1 ? 0.5) =
          = $12.5 million

Growth rate = g = ROE * plowback ratio = 
                = 0.25 * 0.5 =
                = 0.125 or 12.5%

Market value = Dividends / (r - g) =    (r is the market rate of return)
             = $12.5 million / (0.15 - 0.125) =
             = $12.5 million / 0.025 =
             = $500 million

Market value to Book value ratio = $500 million / $100 million =
                                 = 5

Acme's ratio of market value to book value is 5.

              ---------------------

b. How would that ratio change if the firm can earn only a 10 percent
rate of return on its investments?

Growth rate falls to (0.10 x 0.50) = 0.05 or 5%, 

Earnings decline to ($100 million * 0.10) = $10 million, 

and Dividends decline to ($10 million * 0.5) = $5 million,

then:
Market value = Dividends / (r - g) =    
             = $5 million / (0.15 - 0.05) =
             = $5 million / 0.10 =
             = $50 million

Market value to Book value ratio = $50 million / $100 million =
                                 = 0.5

Acme's new ratio of market value to book value will be 0.5 .

The above result makes sense:
Now the firm earns less than the required rate of return on its
investments, so the project is worth less than it costs.

             -------------------

c. Why do investments in financial markets almost always have zero
NPVs whereas firms can almost always find many investments in their
new product markets with positive NPVs?

"Investments in financial markets (stocks or bonds) are available to
all participants in the marketplace. As a result, the prices of these
investments are bid up to "fair" levels, that is, prices which reflect
the present value of expected cash flows. If the investment weren't
zero-NPV, investors would buy or sell the asset and thereby put
pressure on its price until the investment was a zero-NPV prospect.
In contrast, investments in product markets are made by firms with
various forms of protection from full competition. Such protection
comes from specialized knowledge, name recognition and customer
loyalty, and patent protection. In these cases, a project may be
positive NPV for one firm with the know-how to make it work, but not
positive NPV for other firms. Or a project may be positive NPV, but
only available to one firm because it owns a name brand or patent. In
these cases, competitors are kept out of the market, and the cost of
the firm's investment opportunities are not bid to levels at which NPV
is reduced to zero."
From the "Department of Accounting & Finance of the University of
Strathclyde" site:
http://accfinweb.account.strath.ac.uk/40103/bmm_ch06.doc


For additional references see:
"Firm valuation":
http://ocw.mit.edu/NR/rdonlyres/Sloan-School-of-Management/15-414Financial-ManagementSummer2003/A43369BA-DD8E-4A92-8F2D-A115DDA65EF5/0/lec6_firm_valuation1.pdf

"Price-Book Value Ratio: Definition":
http://pages.stern.nyu.edu/~adamodar/pdfiles/pbv.pdf


I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards.
livioflores-ga

AWESOME!!!