F11-MidtermMSci261Solution - MIDTERM EXAM SOLUTION MSci 261...

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1 MIDTERM EXAM SOLUTION MSci 261 Engineering Economics Fall 2011 Department of Management Sciences, Faculty of Engineering Problem 1. For each multiple choice question below, select the one correct response by circling the letter. 1.1 [2 marks] A present amount P is equivalent to an annuity series of N payments each of size A (with the first payment one period after P ), and both are equivalent to a future amount F at the same time as the N th payment in the annuity series. The interest rate is i , and i >0. (a) F = N N N i i i A ) 1 ( 1 ) 1 ( lim . (b) F < NA . (c) A = P/N + iP . (d) P > NA . (e) none of the above. 1.2 [2 marks] A company has two mutually exclusive proposed investments, labelled A and B. Proposal A has the larger first cost. Each proposal has a present worth greater than zero. Proposal B has a greater present worth. Internal rates of return have been calculated for each proposal, and for the incremental investment in A compared to B. (a) The present worth of the incremental investment in A over B is positive. (b) The IRR of the incremental investment in A over B is less than the MARR of the company. (c) The annual worth of A is greater than the annual worth of B. (d) The IRR of A is less than the MARR. (e) none of the above 1.3 [2 marks] Three proposed investments, labeled A, B, C are independent except that A and B cannot both be done, and C can be done only if B is also done. Doing nothing is possible. How many mutually exclusive, feasible alternatives are there? (a) 8 (b) 6 (c) 5 (d) 4 (e) 3 . 1.4 [2 marks] A company uses a MARR estimated as the weighted cost of capital, i.e., MARR=w d i d +w e i e . Joe mistakenly calculates three present worths for a proposed investment, using the three interest rates MARR, i d and i e , denoted PW(MARR), PW(i d ) and PW(i e ). The proposed investment has a large first cost, followed by several years of positive net revenues. (a) PW(MARR) < PW(i d ) < PW(i e ) .
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2 (b) PW(i d ) < PW(MARR) < PW(i e ) . (c) PW(i e ) < PW(MARR) < PW(i d ) . (d) PW(i d ) < PW(i e ) < PW(MARR) . (e) none of the above. Problem 2. a) [4 marks] Bank A offers interest on savings accounts of 3% per year, compounded daily, and Bank B offers 3.1%, compounded monthly. If you want to deposit $1000 now in a bank account, to earn interest for one year, which bank has the better interest rate for you? Show relevant calculations. i A = (1+3%/365) 365 -1 = 3.045% 1 mark i B = (1+3.1%/12) 12 -1 = 3.144% 1 mark Therefore, bank B is preferable with greater interest rate. 2 marks b) [4 marks] Joe is saving to buy a car in 2.5 years (30 months). He needs to have $18,000 in 2.5 years. He plans to deposit $500 per month into a savings account, for the next 2.5 years. The interest on the savings account is at 12% per year, compounded monthly. He will either have too little money, or too much money saved to buy the car. Calculate either how much more money he will need in 2.5 years, or how much extra money he will have
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F11-MidtermMSci261Solution - MIDTERM EXAM SOLUTION MSci 261...

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