Quiz Book Summer 2003 Prepared by: Eng. Ahmed Taha

Quiz 1 Considering the class policies, indicate whether each of the following statements is True (T) or False (F) by circling T or F next to each statement

Quiz 2 Depict the following transactions on a cash flow diagram: Depositing $4,000 today and withdrawing $2,000 after two years. The rest of the money is withdrawn after 4 years. If the interest rate is 10%, how much money will be available for the last withdrawal [-4000+2000(P/F,10%,2)](F/P,10,4) + F = 0  F = $3436.535 1 4 2 i = 10% F=? year $4000 $2000 How long would it take for $200 to double if the interest rate is 12%? 400 = 200(F/P,12%,n)  (F/P,12%,n) = 2 Using interpolation n = 6.11 years (almost 6 years & 1 month)

Quiz 3 Determine the annual installments of a loan of $5,000 to be paid in 5 equal end-of-year payments if the interest rate is 10%. 1 5 A=? i = 10% $5,000 year A = P (A/P,10%,5) A = 5000 (0.2638)  A = $1319 Find P in the graph to the right assuming that A = $1,000, and i = 10% -P + 1000 + 1000 (P/A,10%,7) = 0  P = 5868.4

Quiz 4 With i=10% find the present value of the series below 1 4 2 3 i = 10% year $2500 $2000 $1500 $1000 P = 2500 (P/A,10%,4)-500(P/G,10%,4) = 2500 (3.1699)-500(4.3781)  P = $5735.7 1 4 2 3 i = 10% year $500 $1500 $1000 2500 Find an equivalent payment A for the series above -solution 1: A = 5735.7 (A/P,10%,4) = $1809 -solution 2: PG = -500(4.3781) A2 = PG (A/P,10%,4) = $ 690.57 Af = 2500-690.57 = $1809.42

Quiz 5 What interest rate is being charged if a loan of $10,000 received today is to be repaid in 5 equal end-of-year payments of $2400 each? 1 5 A=2400 i = ?% $10,000 year P = A (P/A,i%,5) 10,000 = 2400 (P/A,i%,5)  (P/A,i%,5) = 4.167 using interpolation  i= 6.4% Which is better, to buy a computer by paying $2,000 immediately, or by paying 5 equal end-of-year payments of $2400 each, if you can invest your money at 8%? Why? Five equal payments would be slightly better. P = A(P/A,8%,5) P = 500 (P/A,8%,5)  P = $1996.35

Quiz 6 What lump sum would have to be deposited today into an account bearing interest of 10% per year to provide withdrawals of $1000 8,9,10,11 years from today? P = 1000(P/A,10%,4)(P/F,10%,7)  P = 1626.79 11 8 A=2400 i = 10% P=? year How many years will it take for a uniform annual deposit of size A to have the same value as a single deposit now that is 4 times the size of one annual deposit? Assume that i = 10%. n 1 A i = 10% P=4A year P = A(P/A,10%,n) 4A = A(P/A,10%,n)  (P/A,10%,n) = 4 Using extrapolation  n = 5.37 years

Quiz 7 A loan of $50,000 is to be repaid in 8 equal end-of-year payments at 10% Find the value of the installments After 3 years, how much of the loan would be paid? How much would it cost to buy down the interest to 9%? A= 50,000(A/P,10%,8) = $9,372.07 X =50,000(F/P,10%,3)–9,372.07 (F/A,10%,3)  X = $35,528.44 Paid amount = 50,000- X = $14,417.56 A1 = 50,000(A/P,10%,8) = $9,372.07 A2 = 50,000(A/P,9%,8) = $9,033.42  Cost = (A1- A2) (A/P,9%,8)= $1,874.41 8 A=? i = 10% year $50,000 1

Quiz 8 Consider the following mutually exclusive 5 A MARR = 10% year S 1 P Consider the following mutually exclusive investment alternatives (MARR=10%): Compare the three alternatives based on PW. Which is better? PWa = -200+22 (P/A,10%,5)+ 200 (P/F,10%,5) = $7.58 PWb = -4,000+600(P/A,10%,5)+ 2,500(P/F,10%,5) = -$173.27 PWb = -5,500+750(P/A,10%,5)+ 4,500(P/F,10%,5) = $137.15 Without performing any calculations, which of B&C have a higher ROR? C

Quiz 9 Consider the following mutually exclusive 5 A MARR = 10% year S 1 P Consider the following mutually exclusive investment alternatives (MARR=10%): Which alternatives are feasible based on their ROR 0 = -200+22 (P/A,i%,5)+200(P/F,i%,5) Using trial & Error  i=12.57% > MARR 0 = -4000+620 (P/A,i%,5)+2600(P/F,i%,5) i=9.74% < MARR (rejected) 0 = -5400+740 (P/A,i%,5)+4300(P/F,i%,5)  i=10.13% > MARR See next slide for the best alternative based on the ROR?

Quiz 9 continued 5 A MARR = 10% year S 1 P To determine which of A or C is better we must calculate the ROR based on the difference . i = 10.03% Based on this, we may say that C is better than A, or that the difference is too small and for all practical purposes we may consider them equivalent. In other words, doing A and investing the rest at 10% is almost the same as doing C.

Quiz 10 Which is better: a 5 PW = -1,000(P/A,10%,5)-2,000(P/F,10%,5) 4 end-of-year receipts of $1,000each, and a on time receipt of $3,000 at the end of the fifth year. $500 annually forever assuming that the prevalent interest rate is 10% 5 $1,000 i = 10% year $2,000 1 PW = -1,000(P/A,10%,5)-2,000(P/F,10%,5) = -1,000(3.7907)-2,000(0.6209) = $5032.62 PW = A/i = -500/0.1 = -$5,000  $500 i = 10% year 1 a II. Find the discounted payback period of the cash flow diagram to the right assuming P= $5,000, A=$1,400, and MARR = 10%. Draw the investment balance diagram. 5

Quiz 11 A bond with a face value of $5,000 pays interest of 10% per year will be redeemed at a par value at the end of its 10-year life. How much should be paid for this bond now in order to yield: 8% per year. 12% per year. 10 A= $500 year $5,000 1 P A = 5000(0.1)=500 i= 8%  P = 500(P/A,8%,10)+5000 (P/F,8%,10) = $5671 i= 12%  P = 500(P/A,12%,10)+5000 (P/F,12%,10) = $4434.97 In both cases above, if the bond had a life of 8 years, would it be better(higher PW) or worse? i= 8%  P = 500(P/A,8%,8)+5000 (P/F,8%,8) = $5574.66 (Worse) i= 12%  P = 500(P/A,12%,8)+5000 (P/F,12%,8) = $4503.23 (Better)

Quiz 12 What is the B/C ratio of an investment that requires an initial payment of $8,000 in return for equal end-of-year returns of $3,000 for 8 years, if the O&M expenses are $2,000? Assume i=10%. I = $8,000 B = $3,000 O&M = $2,000 B/C = B/(I+O&M) = 3000/(8000(A/P,10%,8) + 2000) = 0.85 Or B/C = (B- O&M)/I = (3000-2000)/(8000(A/P,10%,8)) = 0.66 How would your answer changes if a salvage value of $3,000 is expected B/C = B/(I-S+O&M) = 3000/ (8000(A/P,10%,8)- 3000(A/F,10%,8) +2000) = 0.92 Or B/C = (B-O&M)/(I-S) = (3000-2000)/ (8000(A/P,10%,8)- 3000(A/F,10%,8) = 0.8