A a = 0.55 (m) × b = 0.3 (m) concrete box with Manning roughness coefficient of n = 0.016 is to be placed under a roadway. During the T = 100 years design storm, it is expected that water will pond behind the culvert to a height h = 0.2 (m) above the crown of the culvert. If the culvert entrance is to be rounded with the exit loss coefficient of Ke = 0.2 and discharge coefficient of Cd = 0.45. If the slope of the culvert is S% = 0.2 and the length of the culvert is L = 4 (m),

1. estimate the flow rate through the culvert.
2. If the flow rate drops down to 20% of the design storm, estimate the depth of water behind the culvert.

How far away is a star that has a parallax of 0.03 seconds of arc? 0.3 parsecs/333.3 parsecs/33.3 parsecs/3.3 parsecs

If you took a measuremnt for a stars position in March, using parallex when is the optimum month for the next measurement? Sept /Oct/ April/ any month

The nearest stars have been catalogued using parallax what is the range of the stars found in this catalogue? 4 to 100 parsecs/ 2 to 1000 parsecs/ 10 to 50 parsecs/ all stars out to 500 parsecs

Compared to close stars, the parallax angle is ________________ for more distant stars. Smaller/ larger/ the same as/ unrelated to distance of stars

Why are astronomers much more interested in the luminosity of a star than its apparent brightness? because the luminosity tells us how bright a star really is, while apparent brightness only tells us how bright it happens to look from Earth/because luminosity can be measured exactly, but apparent brightness can only be roughly estimated/because the luminosity also tells us what elements the star is made of, while apparent brightness cannot tell us a star's chemical make

Company X and Company Y have been offered the following rates per annum on a 10 million 5-year loan: Fixed Rate Floating Rate Company X 6.2% LIBOR + 0.3% Company Y 7.8% LIBOR + 1% Company X requires a floating rate loan; company Y requires a fixed rate loan. Design a swap that will net a bank acting as intermediary 0.3 percent per annum and which will be equally attractive to X and Y. You need to draw a diagram to indicate the interest rate flows.

Listed below is the number of movie tickets sold at the Library Cinema-Complex, in thousands, for the period from 2004 to 2016. Compute a five-year weighted moving average using weights of 0.1, 0.1, 0.2, 0.3, and 0.3, respectively. Describe the trend in yield. (Round your answers to 3 decimal places.)

The weighted moving averages are:

You are investigating two sensors to use in an experiment. Sensor A has area 600 ± 0.3 mm2 and the gap thickness is 0.3 ± 0.01 mm. Sensor B has area 400 ± 0.25 mm2 and the gap thickness is 0.2 ± 0.02 mm. Estimate the relative (hint: this is a %) and absolute uncertainties (hint: this has units of capacitance) in capacitance for both sensors. Your experiment requires that the capacitance is measured accurately within 5%. Which would you select for your experiment? Justify your response.

C = 8.85 × 10^?15 F/mm A/t

You have estimated how Stock A’s return will vary.

Economy                      Probability                         Return

Below average                0.3                                     -6%

Average                           0.4                                      12%

Above average               0.3                                      26%

What is the standard deviation of Stock A?

Stock B has an expected return of 15%, and a standard deviation of 20%. The returns of the two stocks are not perfectly correlated; the correlation coefficient is 0.7. You have put together a portfolio that consists of 50% Stock A and 50% Stock B. What is the expected return of your portfolio and what is the standard deviation of your portfolio?

You are trying to estimate the enterprise value of Firm X. Since this firm is private, you cannot directly estimate the firm’s cost of equity using its stock data. Fortunately, there is a similar firm, Firm Y, which is in the same industry with comparable operating risk characteristics. Assume that the CAPM holds. The risk-free rate is 2% and the market risk premium is 5%.

QUESTION 1

Firm Y has a debt-to-equity ratio of 3 and it plans to keep this ratio fixed. Firm Y’s equity beta is 6.6 and debt beta is 0.2. What is Firm Y’s unlevered equity beta?

QUESTION 2

What is Firm X’s unlevered equity beta?

QUESTION 3

Assume that Firm X’s cost of debt is 2.5%. What is Firm X’s debt beta?

The analytics department of a public transit service group is trying to forecast the future number of passengers using the University subway station during the Fall term. During the first 10 days of September, the team count the number of passengers entering and exiting the station between 8:00am to 10:00pm.
Day   # Passengers
1   2250
2   2100
3   2150
4   2450
5   2250
6   2500
7   2300
8   2650
9   2350
10   2600

a)   Compute manually (show your formulas) the forecast for days 1-4 using the exponential smoothing method with an alpha of 0.3.
b)   Now switch to Excel and compute the exponential smoothing forecasts for days 11 and 12 (again using an alpha of 0.3). (Show your Excel Formulas)
c)   Reforecast days 11 and 12 using an alpha of 0.7.
d)   Compare how well the model forecast for periods 8-10 for alpha = 0.3 vs alpha =0.7. Which one was better? Explain.