Let \( f(t) = -\frac{1}{3}t^2 + 1 \) (mm/hour) be the rate at which rain falls on a given day in Provo at time \( t \) (hours). The initial amount of rainfall at time \( t = 0 \) is 0.5 millimeters. What is the total amount of rainfall in Provo after \( t = 3 \) hours of rain? Be sure to include units in your answer.

What is the \( x \)-coordinate(s) of the local maximum of the function \

Let \( xy^3 – 5y^2 + 3 = 4x – 20 \). Find \( \frac{dy}{dx} \) when \( x = 6 \) and \( y = 1 \).

Find the derivative of \( f(x) = (\ln 4x)^3 \).

Use Figure A to answer the following question: What is the Terminal Value in 2018 (using Gordon Growth):

List the two main Approaches to valuation that we discussed/covered:

Use Figure A to answer the following question: Is Taylor Swift OVER or UNDER valued?  (answer either “Over” or “Under”)

Please use this figure (Figure B) to answer the following questions: Figure B   Target   Buyer   Pro-Forma New Buyer   Book Value Mkt Value   Book Value Mkt Value    Book Value   12/31/2002 12/31/2002   12/31/2002 12/31/2002   12/31/2002 Current Assets        100,000         100,000           600,000         500,000                     PP&E     2,000,000      2,100,000        8,000,000    10,000,000                     Goodwill                     –                    –                      –                    –      G                  Other Assets        200,000         200,000           800,000         900,000                     Total Assets     2,300,000      2,400,000        9,400,000    11,400,000                        –                   Accts Payable          75,000           75,000           100,000         100,000                     L-T Debt     1,000,000      1,000,000        4,000,000      4,000,000    D                  Equity     1,225,000      1,325,000        5,300,000      7,300,000    E                 2003E EPS                1.00                  3.00                     Shares Outst.             50,000             100,000                     Price/Share               44.00                 60.00       Assume Buyer is acquiring Target, financed with 70% debt and 30% stock.  The stock prices shown above are the prices involved (i.e., the buyer’s stock at time of deal is $60 and they are paying $44 for the Target). The deal is closing on 12/31/02. Shares outstanding and 2003 Estimated EPS for standalone companies are shown above.   The pre-tax interest rate on debt financing is 5.0%.  The effective tax rate for the combined entity (to use in calculations) is 39.0%. Calculate the 2003E EPS of the combined entity.  Assume zero synergies.

Use Figure B to answer the following question: How much of the “New Company” (i.e., Pro Forma New Buyer) does the Buyer Control after the acquisition?

An “Asset Sale” generates cash for the Firm and is typically Tax Free.