Income tax. A corporation has a taxable income of $7,650,000 . At this income level, the federal income tax rate is 50 % the state lax rate is 20 % , and the local tax rate is 10 % . If each tax rate is applied to the total taxable income, the resulting tax liability for the corporation would be 80 % of taxable income. However, it is customary to deduct taxes paid to one agency before computing taxes for the other agencies. Assume that the federal taxes are based on the income that remains after the state and local taxes are deducted, and that state and local taxes are computed in a similar manner. What is the tax liability of the corporation (as a percentage of taxable income) if these deductions are taken into consideration?
Income tax. A corporation has a taxable income of $7,650,000 . At this income level, the federal income tax rate is 50 % the state lax rate is 20 % , and the local tax rate is 10 % . If each tax rate is applied to the total taxable income, the resulting tax liability for the corporation would be 80 % of taxable income. However, it is customary to deduct taxes paid to one agency before computing taxes for the other agencies. Assume that the federal taxes are based on the income that remains after the state and local taxes are deducted, and that state and local taxes are computed in a similar manner. What is the tax liability of the corporation (as a percentage of taxable income) if these deductions are taken into consideration?
Solution Summary: The author calculates the corporation's tax liability as a percentage of taxable income when the deductions of taxes were applicable.
Income tax. A corporation has a taxable income of
$7,650,000
. At this income level, the federal income tax rate is
50
%
the state lax rate is
20
%
, and the local tax rate is
10
%
. If each tax rate is applied to the total taxable income, the resulting tax liability for the corporation would be
80
%
of taxable income. However, it is customary to deduct taxes paid to one agency before computing taxes for the other agencies. Assume that the federal taxes are based on the income that remains after the state and local taxes are deducted, and that state and local taxes are computed in a similar manner. What is the tax liability of the corporation (as a percentage of taxable income) if these deductions are taken into consideration?
Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
AR and MA orders of this representation.
(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.
Module Code: MATH380202
1. (a) Define the terms "strongly stationary" and "weakly stationary".
Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is
weakly stationary, define the autocorrelation function (acf) Pk, for lag k.
What conditions must a process {X+) satisfy for it to be white noise?
(b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of
the following processes {X+} are weakly stationary for t> 0? Briefly justify your
answers.
i. Xt for all > 0.
ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0.
(c) Provide an expression for estimating the autocovariance function for a sample
X1,..., X believed to be from a weakly stationary process. How is the autocor-
relation function Pk then estimated, and a correlogram (or acf plot) constructed?
(d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where
{E} is a white noise process with variance 1. Compute the population autocorre-
lation function Pk for all k = 0, 1, ....
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