FINANCIAL STATEMENTS, CASH FLOW, AND TAXES
(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)
PART I New and Revised Carryover Problems and Questions
Multiple Choice: Problems Notes to Professors: A good bit of relatively simple arithme
1
.
Chapter 4 Ramala Corp's sales last year were $48,000, and its total assets were $25,500. What was its total assets turnover ratio (TATO)? a. 1.88 b. 1.99 c. 1.10 d. 1.21 e. 1.32 Ruby Corp's sales last year were $435,500, its operating costs were $350,
Manag Int Rev (2010) 50:347378
DOI 10.1007/s11575-010-0036-1
R e s e a r c h Art i c l e
Political Survival, Energy Policies,
and Multinational Corporations
A Historical Study for Standard Oil of New Jersey in
Colombia, Mexico, and Venezuela in the Twenti
is also practical, because the pivots can locate the
eigenvalues: A has positive pivots A2I has a negative
pivot A = 3 3 0 3 10 7 0 7 8 A2I = 1 3 0 3
8 7 0 7 6 . A has positive eigenvalues, by our test. But
we know that min is smaller than 2, because subt
can work with the nonsingular A+ I and AI, and at the
end let 0.) Proof. We want to borrow a trick from
topology. Suppose C is linked to an orthogonal matrix Q
by a continuous chain of nonsingular matrices C(t). At t =
0 and t = 1, C(0) = C and C(1) = Q.
space. Then A + has the explicit formula U T (U U T ) 1 (L
TL) 1L T . Why is A +b in the row space with U T at the
front? Why does A TAA+b = A Tb, so that x + = A +b
satisfies the normal equation as it should? 22. Explain
why AA+ and A +A are projection m
lower dimension. The major axis Of this cross section
cannot be longer than the major axis of the whole
ellipsoid: 1(B) 1(A). But the major axis of the cross
section is at least as long as the second axis of the
original ellipsoid: 1(B) 2(A). Similarly th
Singular Value Decomposition 371 that A must have
independent columns.) In the reverse order A = S 0Q, the
matrix S 0 is the symmetric positive definite square root
of AAT . 4. Least Squares For a rectangular system Ax = b.
the least-squares solution come
tet . The top equation is du1/dt = u1 + u2, and its
solution is 1 2 t 2 e t . When has multiplicity m with
only one eigenvector, the extra factor t appears m1
times. These powers and exponentials of J are a part of
the solutions uk and u(t). The other par
1AS = . Then the Jordan form coincides with the
diagonal . This is impossible for a defective
(nondiagonalizable) matrix. For every missing
eigenvector, the Jordan form will have a 1 just above its
main diagonal. The eigenvalues appear on the diagonal
bec
, but it is n by n. Remark 5. Here is the reason that Avj =
juj . Start with A TAvj = 2 j v j : Multiply by A AATAv j =
2 j Avj (2) This says that Avj is an eigenvector of AAT !
We just moved parentheses to (AAT )(Avj). The length of
this eigenvector Avj
combination acb 2 may be negative. This occurred in
both examples, when b dominated a and c. It also occurs
if a and c have opposite signs. Then two directions give
opposite resultsin one direction f increases, in the
other it decreases. It is useful to c
eigenvalues and eigenmatrices for A T = A. 16. (a) Find
an orthogonal Q so that Q 1AQ = if A = 1 1 1 1 1 1
1 1 1 and = 0 0 0 0 0 0 0 0 3 . 5.6
Similarity Transformations 337 Then find a second pair of
orthonormal eigenvectors x1, x2 for = 0. (b) Verify th
Example 2. In our original f the coefficient 2b = 4 was
positive. Does this ensure a minimum? Again the answer
is no; the sign of b is of no importance! Even though its
second derivatives are positive, 2x 2 +4xy+y 2 is not
positive definite. Neither F nor
that: P 1BP = " 0 1 1 0#"1 0 1 1#"0 1 1 0# = " 1 1 0 1# = J.
(A) From A to J, we go first to T as in equation (4). Then
change 2 to 1: U 1AU = " 1 2 0 1# = T and then M1T M
= " 1 1 0 1# = J. Example 5. A = 0 1 2 0 0 1 0 0 0
and B = 0 0 1 0 0 0 0 0 0 . Ze
There are no higher-order terms or lower-order terms
only second-order. The function is zero at x = (0,.,0), and
its first derivatives are zero. The tangent is flat; this is a
stationary point. We have to decide if x = 0 is a minimum
or a maximum or a sad
has a spectral decomposition into A = 1P1+kPk ,
where Pi is the projection onto the eigenspace for i .
Since there is a full set of eigenvectors, the projections
add up to the identity. And since the eigenspace are
orthogonal, two projections produce zero
diagonal) is between 1 and n. You can see this in Figure
6.6, where the horizontal distance to the ellipse (where
a11x 2 = 1) is between the shortest distance and the
longest distance: 1 n 1 a11 1 1 which is 1
a11 n. The diagonal entries of any symmetric
Manag Int Rev (2012) 52:847877
DOI 10.1007/s11575-012-0141-4
R e s e a r c h Art i c l e
Political Institutional Change, Obsolescing
Legitimacy, and Multinational Corporations
The Case of the Central American Banana Industry
Marcelo Bucheli Min-Young Kim
Business History
Vol. 50, No. 4, July 2008, 433454
Multinational corporations, totalitarian regimes and economic nationalism:
United Fruit Company in Central America, 18991975
Marcelo Bucheli*
Department of Business Administration and Department of Histor
Book Reviews
I
219
cases of conditional lending, where London debt even determined Mexico's commercial policy. The decision to resume debt service could be
political, as Mexico strongly needed Britain's support in its war against
Texas. On the other side
Book Reviews / 576
The Birth of Big Business in the United States, 18601914. By David O.
Whitten and Bessie E. Whitten. Westport, Conn.: Praeger, 2006. Index,
notes, bibliography, tables. Cloth, $89.95. ISBN: 0-313-32395-X.
Reviewed by Marcelo Bucheli
The
Book Reviews / 878
The Ecology of Oil: Environment, Labor, and the Mexican Revolution,
19001938. By Myrna I. Santiago. New York: Cambridge University
Press, 2006. xiv + 411 pp. Figures, bibliography, notes, index. Cloth,
$85.00. ISBN: 978-0-521-86324-7.
R
300
Book reviews
This book is a meticulously-researched, carefully-argued and well-written
dissection of a signicant corporate scandal. But a more historicised approach
would have contributed much to the assessment of Enrons broader signicance.
While such
Book Reviews / 192
The Enduring Legacy: Oil, Culture, and Society in Venezuela. By Miguel
Tinker Salas. Durham: Duke University Press, 2009. xvi + 325 pp. Bibliography, notes, index. Cloth, $84.95; paper, $23.95. ISBN: cloth, 9780-822-34400-1; paper, 978-
Book Reviews
Hernndez-Daz, Arleen (2006) Labor-Management Relations in Puerto Rico During
the Twentieth Century, University Press of Florida (Florida), 288 pp. 45.49 hbk.
Labour relations have occupied a privileged place in modern Latin American historiog
1. What financing proportions of debt (long-term bonds), preferred stock, and common equity should Shelly use i
calculation (WACC)?
2. What is Happy Marts cost of debt on a before and after tax basis?
3.
What
the cost of Happy
Marts preferred stock?
Case
determinant of A is the product of the eigenvalues. And if
condition I holds, we already know that these
eigenvalues are positive. But we also have to deal with
every upper left submatrix Ak . The trick is to look at all
nonzero vectors whose last nk comp
TAx > 0 all > 0 orthogonal Similar matrix: B = M1AM
(B) = (A) x(B) = M1 x(A) Projection: P = P 2 = P T = 1;0
column space; nullspace Reflection: I 2uuT = 1;1,.,1
u;u Rank-1 matrix: uvT = v Tu;0,.,0 u; v Inverse: A
1 1/(A) eigenvectors of A Shift: A+cI (A)