QUIESTION 1
A three-phase synchronous generator is connected to an infinite bus. The infinite bus voltage and the generated voltage are o 1.0 pu ∠0 and o 1.0pu ∠42.84 , respectively. The synchronous reactance is 0.85 pu and resistances are neglected. a) Compute power angle (δ), armature current (Is), power factor (pf), real power (P), and reactive power (Q). Draw the phasor diagram. b) If the prime mover torque is kept constant at a value corresponding to P=0.8 pu, compute the required value of the generated voltage (E2) for the unity power factor condition (and constant power, P=0.8 pu). What is the new value of power angle (δ2)? Solution: δ= 42.84o , Is = 0.86pu ∠21.44o , pf=0.93, P=0.8 ph, Q= -0.314pu, δ2 = 34.2o , E2= 1.21pu

QUESTION 2
Two “three-phase Y-connected synchronous generators” have per phase generated voltages of o 1 E = 120 V∠10 and o 2 E = 120 V∠20 under no load, and resistance of X j5 Ω / phase 1 = and X j8 Ω / phase 2 = . They are connected in parallel to a load impedance of XL = 4 + j3 Ω / phase . Compute: a) Per phase terminal voltage Vt (both magnitude and phase angle). b) Armature currents for each generator ( a1 a2 I and I ). c) Power supplied by each generator (P1 and P2 ). d) The total output power (Pout ). Solution: Vt= 82 V ∠-5.94o , Ia1 = 9.36 A ∠-51.17o , Ia2 = 7.31 A ∠-32.06o , P1 = 1621 W, P2 = 1614.5 W, Pout = 3236 W.

Design and construct a computer program in one of the approved languages (C++) that will illustrate the use of a fourth-order explicit Runge-Kutta method of your own design. In other words, you will first have to solve the Runge-Kutta equations of condition for the coefficients of a fourth-order Runge-Kutta method. See the Mathematica notebook on solving the equations for 4th order RK method. That notebook can be found at rk4Solution.nb . PLEASE DO NOT USE a[1] = 1/2 or a[2] = 1/2. In general, you should pick a[1] and a[2] to be distinct values greater than zero and less than one. Then, you will use these coefficients in a computer program to solve the ordinary differential equation below. Be sure to follow the documentation and programming style policies of the Computer Science Department.

The initial value problem to be solved is the following: x'(t) = 3 x2 cos(5 t) subject to the initial condition: x(0) = 1.0 Obtain a numerical solution to this problem over the range from t=0.0 to t=2.0 for seven different values of the stepsize, h=0.1, 0.05 , 0.025 , 0.0125 , 0.00625 , 0.003125 , and 0.0015625 . In other words, make seven runs with 20, 40, 80, 160, 320, 640, and 1280 steps, respectively. For each run, print out the value of h, then a table of t and x, and then the error at t=2. You may use the following very precise value for your "true answer" in order to compute the error at t=2: 0.753913186469598763502963347. The true solution of this differential equation resembles the following plot of x(t) as a function of t.

Crude oil, products and merchandise inventories are carried at the lower of current market value or cost (generally determined under the last-in, first-out method – LIFO). Inventory costs include expenditures and other charges (including depreciation) directly and indirectly incurred in bringing the inventory to its existing condition and location.

In 2016, 2015 and 2014, net income included losses of $295 million and $186 million, and a gain of $187 million, respectively, attributable to the combined effects of LIFO inventory accumulations and drawdowns. The aggregate replacement cost of inventories was estimated to exceed their LIFO carrying values by $8.1 billion and $4.5 billion at December 31, 2016, and 2015, respectively.

Crude oil, products and merchandise as of year-end 2016 and 2015 consist of the following:

5.3 If ExxonMobil had used FIFO in 2016, what would be the value of the inventory?

ou plan to invest in the Kish Hedge Fund, which has total capital of $500 million invested in five stocks:

Optimal Capital Structure with Hamada

Beckman Engineering and Associates (BEA) is considering a change in its capital structure. BEA currently has $20 million in debt carrying a rate of 7%, and its stock price is $40 per share with 2 million shares outstanding. BEA is a zero growth firm and pays out all of its earnings as dividends. The firm's EBIT is $14.386 million, and it faces a 40% federal-plus-state tax rate. The market risk premium is 6%, and the risk-free rate is 4%. BEA is considering increasing its debt level to a capital structure with 30% debt, based on market values, and repurchasing shares with the extra money that it borrows. BEA will have to retire the old debt in order to issue new debt, and the rate on the new debt will be 8%. BEA has a beta of 1.0.

What is the total value of the firm with 30% debt? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to three decimal places.
$   million

1. What is BEA's unlevered beta? Use market value D/S (which is the same as w_d/w_s) when unlevering. Do not round intermediate calculations. Round your answer to two decimal places.
2. What are BEA's new beta and cost of equity if it has 30% debt? Do not round intermediate calculations. Round your answers to two decimal places.
   Beta:  
   Cost of equity:   %
3. What are BEA’s WACC and total value of the firm with 30% debt? Do not round intermediate calculations. Round your answer to two decimal places.
     %

A petroleum refinery can handle the processing of two grades of
crude oils, #1 and #2, to produce four kinds of products gasoline, kerosene, fuel oil and
residual.
The total costs include raw material costs and processing costs. The raw material costs for the
crude oils are $24/bbl for #1, and $15/bbl for #2. The processing costs are $0.5/bbl for #1, and
$1.0/bbl for #2.
The sales prices of the products are $36/bbl for gasoline, $24/bbl for kerosene, $21/bbl for fuel
oil and $10/bbl for residual.
The following is the information for the product yield (volume percent of raw material) and
maximum allowable production of each product (bbl/day):
One bbl crude oil #1 can produce 0.80 bbl gasoline, 0.05 bbl kerosene, 0.10 bbl fuel oil, and
0.05 bbl residual. One bbl crude oil #2 can produce 0.44 bbl gasoline, 0.10 bbl kerosene, 0.36
bbl fuel oil, and 0.10 bbl residual. The maximum allowable production for gasoline is 24,000
bbl/day, for kerosene is 2,000 bbl/day, and for fuel oil is 6,000 bbl/day, and no maximum
allowable production limitation for residual.
(1) Based on the data above, derive a mathematical formulation for this linear programming
problem and determine: The optimum feed schedule (bbl/day) of the two crude oils for the
maximum profit, using method of simultaneous equations. How much is the maximum profit
($/day)?
(2) Comment on how variation of raw material costs and sales prices will affect the feed
schedule and profitability on this kind of project in industry.

The management team of Accent Group Limited have received a proposal from the manager of Hype DC. This proposal concerns a major upgrade to Hype DC's stores to improve the customer experience. Key details relating to this proposal include:

• The initial cost will be $22 million. This cost will be depreciated using the straight line method over the 5 year life of the upgrade.
• During year 1, the firm will increase marketing costs by $2.0 million to promote the store upgrades.
• Over the five year life of the project, it is expected that the upgrade will increase the firm's sales by $18 million per year. On average, cost of sales is 45% of revenue.
• The firm will need to higher additional staff over the life of the project to help to deal with the increased sale volume. In year 1, the firm's staffing costs will increase by $1.0 million. These costs will increase by 3.5% p.a.
• The upgrade is expected to increase the firm's energy costs by $500,000 in year 1. This increase will be ongoing across the life of the project and will increase by 6% p.a.
• Upgraded stores will include an old shoe recycling drop off zone. This recylcing program will cost $75,000 in year 1. These costs will increase by 2% p.a.
• At the end of year 3, the firm will spend $1.5 million on a minor refurbishment to the stores.

The firm’s tax rate is 30%. The firm requires a 16% required rate of return on all potential investments.

1. Provide an overview of the key environmental and social factors that the firm should consider in evaluating the proposal
2. Discuss how sensitive your recommendations are to changes in assumptions in regards to the financial impact of the new capital investment. In your discussion, include examples which illustrate how changes to at least two assumptions impact the financial analysis .

The management team of Accent Group Limited have received a proposal from the manager of Hype DC. This proposal concerns a major upgrade to Hype DC's stores to improve the customer experience. Key details relating to this proposal include:

• The initial cost will be $22 million. This cost will be depreciated using the straight line method over the 5 year life of the upgrade.
• During year 1, the firm will increase marketing costs by $2.0 million to promote the store upgrades.
• Over the five year life of the project, it is expected that the upgrade will increase the firm's sales by $18 million per year. On average, cost of sales is 45% of revenue.
• The firm will need to higher additional staff over the life of the project to help to deal with the increased sale volume. In year 1, the firm's staffing costs will increase by $1.0 million. These costs will increase by 3.5% p.a.
• The upgrade is expected to increase the firm's energy costs by $500,000 in year 1. This increase will be ongoing across the life of the project and will increase by 6% p.a.
• Upgraded stores will include an old shoe recycling drop off zone. This recylcing program will cost $75,000 in year 1. These costs will increase by 2% p.a.
• At the end of year 3, the firm will spend $1.5 million on a minor refurbishment to the stores.

The firm’s tax rate is 30%. The firm requires a 16% required rate of return on all potential investments.

1. Provide an overview of the key environmental and social factors that the firm should consider in evaluating the proposal
2. Discuss how sensitive your recommendations are to changes in assumptions in regards to the financial impact of the new capital investment. In your discussion, include examples which illustrate how changes to at least two assumptions impact the financial analysis .