Consider a 1550 nm laser diode with a rise time of 0.8 ns, spectral half-width of 6 nm, that launches 2 mW optical power into a 60 km long single-mode fiber with an attenuation of 0.3 dB/km. The intramodal dispersion is 3 ps/nm.km. An InGaAs APD with a -32 dBm sensitivity is used at 2.5 Gb/s (NRZ coding). A short optical jumper cable at each end of the cable with a loss of 3 dB is used to connect the fiber to the equipment rack. In addition, the connector loss at each joint between the jumper and fiber cable and jumper and equipment rack is 1 dB each. Determine the temporal response of the system components and calculate the maximum transmission rate. Discuss if the system is bandwidth limited.

The following information is given for a stock. Investors assume that the return of the stock is best explained by a two-factor model that includes the market factor and a second risk factor. Using a dividend discount model, what is the price for this stock?

Stock covariance with the market= 0.5

Market variance = 0.25

Stock covariance with a second risk factor= 0.6

Variance of the second factor= 0.3

Market Premium:3%

Second factor risk premium=1%

Risk free rate =2 %

Current earnings per share= $5,

The ROE is expected to shrink (decrease) at the rate 10% for first 5 years

The ROE is expected to grow at the rate 8% forever after the first 5 years

Payout for the first 5 years: 50%

Payout after 5 years: 50%

1. The following information is given for a stock. Investors assume that the return of the stock is best explained by a two-factor model that includes the market factor and a second risk factor. Using a dividend discount model, what is the price for this stock?

Stock covariance with the market= 0.5

Market variance = 0.25

Stock covariance with a second risk factor= 0.6

Variance of the second factor= 0.3

Market Premium:3%

Second factor risk premium=1%

Risk free rate =2 %

Current earnings per share= $5,

The ROE is expected to shrink (decrease) at the rate 10% for first 5 years

The ROE is expected to grow at the rate 8% forever after the first 5 years

Payout for the first 5 years: 50%

Payout after 5 years: 50%

1. The output of an economy is characterized by a Cobb-Douglas production function with constant return to scale and an output elasticity with respect to capital equal to 0.3. Also given are the following parameters: 30% saving rate, 5% depreciation rate, 2% population growth rate, and the technology factor is 2.

a). Find the capital-labour ratio, and also the output, consumption and investment on a per capita basis in the steady state equilibrium.

b). Is a government policy that raises the saving rate to 40% socially desirable? Explain your answer with reference to a comparison of this new steady state equilibrium and the initial steady state equilibrium in a) above.

c). If the initial capital-labour ratio is 30, is the economy operating efficiently in the sense that welfare cannot be improved? Explain concisely. What if the initial capital-labour ratio is 15? Again explain concisely.

The following information is given for a stock. Investors assume that the return of the stock is best explained by a two-factor model that includes the market factor and a second risk factor. Using a dividend discount model, what is the price for this stock?

Stock covariance with the market= 0.5

Market variance = 0.25

Stock covariance with a second risk factor= 0.6

Variance of the second factor= 0.3

Market Premium:3%

Second factor risk premium=1%

Risk free rate =2 %

Current earnings per share= $5,

The ROE is expected to shrink (decrease) at the rate 10% for first 5 years

The ROE is expected to grow at the rate 8% forever after the first 5 years

Payout for the first 5 years: 50%

Payout after 5 years: 50%

Jessica has a margin account in which she deposits $300,000 (Equity). Assume that the initial margin requirement is 50% and that the margin maintenance is 15%. Jessica is planning to invest (long) in Ford stock which is currently selling at $40/share. a) Show that Jessica could purchase 15,000 shares, using the maximum allowable margin. b) Assume that the broker charges 5% annual interest rate, assume that the broker's fees are 0.3% of the total amount paid for the purchase and received upon the sale. A year later Jessica receives $1 per share dividend and sells the stock for $45/share. What is the rate of return on her investment? c) Will Jessica receive a margin call if the price of the Ford stock falls during the year to 19$/share? Justify

The Oko-Cocoa Corporation's equity has a beta of 1.4. Its debt has a beta of 0.2. Its debt/equity (D/E) ratio is 0.3. The Johnson Corporation's equity has a beta of 2. The company has zero beta debt, and its debt/equity ratio is 0.5. The risk free rate is 8%, and the expected return on the market portfolio is 19%. There are no taxes.

(a) The Johnson Corporation is thinking of investing in the same line of business that OkaCocoa is engaged in. What discount rate should it use?

(b) Now suppose the Johnson Corporation has decided to invest in projects of this type. These projects now constitute 10% of the overall value of the Johnson Corporation. Given that its debt/equity ratio and the beta of its debt remain unchanged, what will the beta of Johnson's equity be now?

Probability

Let A, B and C be Boolean variables denoting three independent events with P(A=1) = 0.7, P(B=1) = 0.3, and P(C=1) = 0.1. Let D be the event that at least one of A and B occurs, i.e., D = A OR B. Let E be the event that at least one of B and C occurs, i.e., E = B OR C. Let F be the event that exactly one of A and B occurs, i.e., F = A XOR B.

(a) (4 pts) Express F as a set of clauses (i.e., as a conjunction of disjunctions) involving A and B.

(b) (9 pts) Suppose that A and E are true. What is the probability that B is true? Show your work.

(c) (9 pts) Suppose that D and E are true. What is the probability that A is true? Show your work.