Tony’s Gelati has the following capital structure: $100 Million in debt with a beta of 0; $40 Million of Preferred Stock with beta 0.2; and $200 Million of common stock with beta 1.2.

a) What is the firm’s asset beta?

b) How would the asset beta change if Tony issued an additional $140 Million of common stock and used the cash to repurchase all the debt and preferred stock?

c) Assuming CAPM, what discount rate should we use for investments that expand the scale of operations without changing the asset beta? Assume a risk premium of 8.6 and a treasury rate of 5.

Expected return

A stock's returns have the following distribution:

1. Calculate the stock's expected return. Round your answer to two decimal places.
   %

2. Calculate the stock's standard deviation. Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Calculate the stock's coefficient of variation. Round your answer to two decimal places.

Students have an average GPA of 2.78 with a standard deviation of 0.45.

You have been tasked by the university president to select a random sample of students, and to conduct in-depth interviews with them about how their academics were impacted by COVID-19. We would like the random students that you select to be representative of the entire student body, and therefore the GPA of your sample should be within 0.2 grade points of the population mean.

How many students should you randomly select for interviews if you want to be 99% sure that the mean GPA of your interviewees is between 2.58 and 2.98?

Assume that demand for a commodity is represented by the equation P = 20 – 0.6 Q d, and supply by the equation P = 10 + 0.2 Qs where Qd and Q s are quantity demanded and quantity supplied, respectively, and P is the Price. Use the equilibrium condition Qs = Qd

1: Solve the equations to determine equilibrium price.

2: Now determine equilibrium quantity.

3: Graph the two equations to substantiate your answers and label these two graphs as D1 and S1.

4: Furthermore; using demand and supply show what happen to equilibrium price and quantity if eating this product causes cardiac problem.

Solow Growth Model

a. Assume the production function is y = f(k) = 5 ∗ √?. That is for a given level of the capital-labor ratio, k, output, y, is five times the square-root of k. Assume n, the rate of population growth, is 0.02 and d, the rate of depreciation is 0.03. Assume the savings rate, s, is 0.10. Calculate the steady state levels of output, y*, and the capital-labor ratio, k* for the Solow Growth Model with no technological progress.

b. Assume the savings rate doubles to s= 0.2, but everything else from part a is the same. Find the new k* and y*.

You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution.

1. Expected Return for Stock X and Stock Y.
2. Standard Deviation for Stock X and Stock Y
3. Would you invest in Stock X or Stock Y? Explain.

Consider a Solow economy with the following production function

F(K,N) = zK^(1/3)N^(2/3)

and parameters d = 0.05, s = 0.2, N0 = 100 and z = 1.0. Suppose K = 300 in period 0 and the

unit period is one year. In contrast to the standard Solow model, we assume that the population

growth rate n is no longer exogenous but rather endogenous and determined by

(1 + n) = N’/N = g(C/N) = (C/N)^3 as it is the case in the Malthusian model.

1) Determine the dynamics for the per worker capital (k). This is the first question in the problem

At a grocery store eggs come in cartons that hold a dozen eggs. Experience indicated that 66.5% of the cartons have no broken eggs, 27.2% have one broken egg, 6.1& have 2 broken eggs, and 0.2% have 3 broken eggs, and the percentage of cartons with 4 or more broken eggs is negligible.

Using baye's rule or law of total probability:

1. an egg is selected at random from a carton. what is the probability that the egg is broken?

2. an egg selected at random from a carton is found to be broken, what is the probability that it came from a carton with to broken eggs?

The flywheel of an old steam engine is a solid homogeneous metal disk of mass M = 112 kg and radius R = 80 cm. The engine rotates the wheel at 520 rpm. In an emergency, to bring the engine to a stop, the flywheel is disengaged from the engine and a brake pad is applied at the edge to provide a radially inward force F = 125 N. If the coefficient of kinetic friction between the pad and the flywheel is μk = 0.2.

How many revolutions does the flywheel make before coming to rest?

How long does it take for the flywheel to come to rest?

Calculate the work done by the torque during this time.