Advanced Math

3. Exercise Consider a stock with price (S1)120. (i) Consider a bull spread at current time t = 0, consisting of a long call option with strike $10 and a short call option with strike $30, both with maturity T = 1. Compute its payoff and draw its graph. Show that it is non-negative for all values of St. (ii) Use monotonicity theorem to conclude that the value of the bull spread in (i) at current time t = 0 is strictly positive. Hence when entering into this bull spread, one needs to pay an up-front fee, which we may assume to be c = $5 for the following problems. (iii) Compute the profit of this spread at maturity and draw its graph. (iv) Suppose P(St = 5) = P(ST = 20) = P(ST = 40) = 1/3, that is, the stock price Sy at matu- rity can take three values $5, $20, and $40 with equal probabilities. What is the expec- tation and standard deviation of the profit of this bull spread?

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ENGR 301 – Engineering Economics and Project Management Homework #1 Deadline: 10/02/2020 01- A particular product can be manufactured by either of two machining sequences, SI or S2. Sequence Si consists of processing through five machines: M1, M2, M3, M4 and M5. For sequence S2, processing is by three machines: MA, MB and MC. The scrap rate for each of these machines is as follows: MI -3%, M2 -5%, M3 – 5%, M4 – 4%, M5 – 4%, MA = 5%, MB = 3% and MC = 3%. Assume a batch size of 100 units is to be processed through each sequence. The raw material cost is $1.00per unit. The total processing cost through sequence SI is $5500and through sequence S2 is $6200. Which sequence of processing results in the lowest unit cost of final product? (20 marks) Q2- Robert borrows $4,000 from Susan and agrees to return it by the end of the fourth year. What should be the size of the payments if : a- 8% compound interest is used? b- 8% not compound interest is used? (20 marks) Q3 How long does it take for money to double in value, if you earn (a) 2%, (b) 3%, (C) 4%, (d) 6%, (e) 8%, or (t) 12% annual compound interest? (20 marks) Q4- How much must you deposit, today, in order to accumulate $10,000 in 4 years, if you earn 5% compounded annually on your investment? (20 marks) Q5- Ali is an Engineer in Yanbu Refinery and the pump of the crude oil was broken and he will report this problem and the solution to his manager, Could you please help him by providing some recommendations to solve this problem? (Hint: use the Engineering Economy Principles). (20 marks)

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