.Solve the following questions with clear explanations.
3.8.1 White Noise Observed through Matched Filters 3.8.7 Example. Consider a matched filter h(t) for a real signal S(t) at time T. The impulse response of that filter is h(t) = S(T -t). Let & denote the energy of S(t). Assume that the input to the matched filter is a zero mean white Gaussian noise W(t) with power spectral density of No/2. This system is shown in Fig. 3.8.1. Let Z denote the output of the filter at time WH ) h(t= S(T-t) t= T Figure 3.8.1: Matched filter with white noise input. T. Using the convolution integral, OO Z = W ( T )h ( T - T) dT - 0o roo (3.8.8) = W (T ) S(t) dT. -CO1. For which violation of the classical linear regression assumption does Durbin-Watson test is used for detection? And outline the procedure for the test merely formulating the hypotheses and stating the decision rule using the measure of autocorrelation, p, and the Durbin-Watson statistics, d-statistics. 2. The economic theory of investment states that investment expenditure at a given point in time (I) is negatively affected by interest rate at a given point in time (r). Suppose that the functional relationship in the stated economic theory is linear and estimated values of the intercept and slope are 82 and 0.6 respectively. Based on the stated economic theory and the associated information, derive the estimated econometric model and predicate the value of the dependent variable provided that 50 is given as value of the independent variable. 3. The following estimated equation was obtained by OLS regression using quarterly data for 1978 to 1996 inclusive. Y, = 2.20+0.104X, (3.4) (0.005) Standard errors are in parentheses, the explained sum of squares and the residual sum of squares were 109.6 and 18.48 respectively. Thus, a) Test a 5% level of significance for the statistical significance of the parameter estimates using t-test technique b) Test the overall test of significance ant 1% c) Calculate the coefficient of determination 4. Consider the following estimated regression model of monthly earnings of 25 employees selected at random from the pool of employees in a given organization. Assuming the monthly earning (ME) is affected by two explanatory variables-SEX and AGE of employees, the regression output is given as ME = -1.65+ 0.33SEX +0.4 AGE (-0.60) (0.18) (0.03) R' = 0.825 Given the standard errors of each estimate in brackets answer the following questions A. Test the statistical significance of the intercept using standard error test B. Test the statistical significance of SEX at 5% level of significance C. Test the overall significance of the model at 1% level of significance D. Interpret R21. An entrepreneur is thinking of starting a rm. The rm will pay Tk. 320,000 in wages/salary, Tk. 150,000 on raw materials, Tk. 100,000 for rent per month. If the entrepreneur worked as a manager for somebody else, he would earn 'I'k. 50,000 per month. The rm's total revenue per month is Tk. 600,000. a) Calculate the accounting prot of this rm. 13) Do you think the entrepreneur should start this rm, explain your answer. 2. List the characteristics of the four different types of market structures discussed in class and give an example of each. 3. Suppose you start a business of manufacturing computer software. Assume that this computer software company is a perfectly competitive rm. Your xed cost per month is Tk. 60,000 and total cost is Tk. 140,000. If you sell 1000 software per month and the average revenue is TR. 90, what should be your short-run decision regarding shut down and long run decision regarding exit? 4. On it and y axes, draw ATC, AVC and MC curves and four alternative demand curves that the Perfectly Competitive Firm might face. a) Draw D] such that the rm makes a prot. b) Draw D2 such that the firm breaks even (prot=0). c) Draw D3 such that the rm is at its shut down point. (:1) Draw D4 such that the rm would shut down rather than produce. Suppose a firm has an expected net profit (EBIT) of $1200. The entrepreneur wants to sell the firm and asks an investment bank for financial advice on how to sell the firm so that he can get a maximum price. All agents are risk neutral. The interest rate is 12%. (a) What is the value of the firm if 100% equity is issued? [2p] (b ) What is the value of the firm if debt with face value of $600 is issued and the rest is sold as equity? [3p] Now suppose the firm has to pay corporate taxes. The tax rate is 30%. (c) Compare the value of the firm in (a) and (b) when there is taxation. [4p] (d) Suppose a tax specialist can help the entrepreneur reduce the tax rate to 10%. What is the maximum the entrepreneur is willing to pay for that advice when the firm has $600 face value of debt outstanding? [3p] In subsequent questions, assume there are costs associated with bankruptcy and the probability of bankruptcy is given by D prob(bankruptcy) = 1200 and the costs of bankruptcy are $40. (e) The tax rate is 10%. What capital structure should the investment bank optimally suggest? What is the value of the firm? [6p] Given the tax avoidance strategies of firms, the government changes the tax code. Suppose under the new tax code, the optimal capital structure of the firm has debt with face value of $700. (f) What is the new tax rate? [4p]Suppose a firm has an expected net profit (EBIT) of $1200. The entrepreneur wants to sell the firm and asks an investment bank for financial advice on how to sell the firm so that he can get a maximum price. All agents are risk neutral. The interest rate is 12%. (a) What is the value of the firm if 100% equity is issued? [2p] (b ) What is the value of the firm if debt with face value of $600 is issued and the rest is sold as equity? [3p] Now suppose the firm has to pay corporate taxes. The tax rate is 30%. (c) Compare the value of the firm in (a) and (b) when there is taxation. [4p] (d) Suppose a tax specialist can help the entrepreneur reduce the tax rate to 10%. What is the maximum the entrepreneur is willing to pay for that advice when the firm has $600 face value of debt outstanding? [3p] In subsequent questions, assume there are costs associated with bankruptcy and the probability of bankruptcy is given by D prob(bankruptcy) = 1200 and the costs of bankruptcy are $40. (e) The tax rate is 10%. What capital structure should the investment bank optimally suggest? What is the value of the firm? [6p] Given the tax avoidance strategies of firms, the government changes the tax code. Suppose under the new tax code, the optimal capital structure of the firm has debt with face value of $700. (f) What is the new tax rate? [4p]
