ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.3 : (a) In the M / M / 1 queue that happens with randomness, let State 0 = the queue and server are empty, State 1 = the server is in use and the queue is empty, State 2 = the server is in use and 1 is in the queue, State 3 = the server is in use and 2 in the queue. Let P (0) = probability of State 0, P (1) = probability of State 1, P (2) = probability of State 2, P (3) = probability of State 3 and so on. If c = constant, P (1) = c P (0), P (2) = c [ c P (0) ], P (3) = c { c [ c P (0) ] }, write an equation that involves P (N), P (N + 1) and c. (b) Let L = market price of risk, r = riskless rate, m = expected return, s = volatility. Given that L = (m - r) / s related to oil prices, expected return = 12 %, s = 20 %, riskless rate = 8 %, calculate the market price of risk.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.3 : (a) P (1) = c P (0), P (2) = c [ c P (0) ] = c P (1), P (3) = c { c [ c P (0) ] } = c P (2). Then P (N + 1) = c P (N). (b) Let m = 12 %, r = 8 %, s = 20 %, then L = (m - r) / s = (12 - 8) / 20 = 4 / 20 = 1 / 5. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 37 - Calculate the bubble temperature T at P = 85-kPa for a binary liquid with x(1) = 0.4. The liquid solution is ideal. The saturation pressures are Psat(1) = exp [ 14.3 - 2945 / (T + 224) ], Psat(2) = exp [ 14.2 - 2943 / (T + 209) ] where T is in degree Celsius. Please take note that x(1) + x(2) = 1. Please take note that y(1) + y(2) = 1, y(1) = [ x(1) * Psat(1) ] / P, y(2) = [ x(2) * Psat(2) ] / P, * is multiplication. P is in kPa.
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4 Answers BCPL, HPCL, NOCL, Reliance,
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.29 : An engineering company that produces small biochemical tools applies Installment Sales Method in its accounting. Let A = Installment Sales, B = Cost of Installment Sales, C = Gross Profit, D = Gross Profit Ratio. In year 20X8, let A = $400, B = $250, C = $150. In year 20X9, let A = $450, B = $315, C = $135. If the value of D = 37.5 % in year 20X8 : (a) find the value of D for year 20X9; (b) calculate the realized gross profit = ED / 100, for year 20X8 when the cash collected from sales is E = $100.
QUANTUM BIOLOGY - EXAMPLE 33.1 : In quantum biology, conditional entropy is given by H (S | O) = H (SO) - H (O). With reference to such equation, find another equation for H (SA).
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.7 : An engineering investor purchases a $1000 bond that matures in 25 years. The coupon rate is 8 %. The purchase price is at 95 or 95 % of the par bond value. (a) What is the purchase price of the bond? (b) How much discount is enjoyed by the investor on average each year? (c) Find the income generated from coupon rate each year. (d) Find the overall interet rate or Yield to Maturity (YTM) by using the formula : YTM = [ Answer in (c) + Answer in (b) ] x 200 / [ par bond value + Answer in (a) ].
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