Quiz Book Summer 2003 Prepared by Eng Ahmed

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 The rest of the money is withdrawn after 4 years.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 $2000 F=? i = 10% • How long would it take for $200 to double if the interest rate is 12%? 1 $4000 400 = 200(F/P, 12%, n) = 2 Using interpolation n = 6. 11 years (almost 6 years & 1 month) 2 4 year

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%. A = P (A/P, 10%, 5) A = 5000 (0. 2638) A = $1319 $5, 000 year i = 10% 0 1 • Find P in the graph to the right assuming that A = $1, 000, and i = 10% -P + 1000 (P/A, 10%, 7) = 0 P = 5868. 4 A=? 5

Quiz 4 • With i=10% find the present value of the series below $2500 P = 2500 (P/A, 10%, 4)-500(P/G, 10%, 4) = 2500 (3. 1699)-500(4. 3781) P = $5735. 7 0 • 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) A 2 = PG (A/P, 10%, 4) = $ 690. 57 Af = 2500 -690. 57 = $1809. 42 $2000 $1500 year 1 2 3 i = 10% 1 2 $500 4 year 2500 0 $1000 3 $1000 4 i = 10% $1500

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? $10, 000 P = A (P/A, i%, 5) year i = ? % 10, 000 = 2400 (P/A, i%, 5) = 4. 167 A=2400 0 1 5 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 P = A(P/A, 8%, 5) be slightly better. 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 0 year i = 10% 8 A=2400 11 P=? • 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%. year i = 10% P = A(P/A, 10%, n) 0 1 4 A = A(P/A, 10%, n) = 4 Using extrapolation n = 5. 37 years P=4 A A n

Quiz 7 A loan of $50, 000 is to be repaid in 8 equal end-of-year payments at 10% a. Find the value of the installments b. After 3 years, how much of the loan would be paid? c. How much would it cost to buy down the interest to 9%? a. A= 50, 000(A/P, 10%, 8) = $9, 372. 07 b. X =50, 000(F/P, 10%, 3)– 9, 372. 07 (F/A, 10%, 3) a. X = $35, 528. 44 $50, 000 b. Paid amount = 50, 000 - X = $14, 417. 56 0 1 c. A 1 = 50, 000(A/P, 10%, 8) = $9, 372. 07 a. A 2 = 50, 000(A/P, 9%, 8) = $9, 033. 42 Cost = (A 1 - A 2) (A/P, 9%, 8)= $1, 874. 41 year i = 10% A=? 8

Quiz 8 Consider the following mutually exclusive investment alternatives (MARR=10%): Compare three alternatives based on PW. Which is better? S A 0 1 MARR = 10% year 5 P 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 investment alternatives (MARR=10%): Which alternatives are feasible based on their ROR S A 0 1 MARR = 10% P 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? year 5

Quiz 9 continued To determine which of A or C is better we must calculate the ROR based on the difference. i = 10. 03% S A 0 1 MARR = 10% year 5 P 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 I. Which is better: I. II. 4 end-of-year receipts of $1, 000 each, 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 i = 10% year 10% a. PW = -1, 000(P/A, 10%, 5)-2, 000(P/F, 10%, 5) b. = -1, 000(3. 7907)2, 000(0. 6209) c. = $5032. 62 a d. PW = A/i = -500/0. 1 = -$5, 000 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 0 1 $1, 000 i = 10% 0 1 $500 5 $2, 000 year

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. $5, 000 A= $500 0 1 year 10 A = 5000(0. 1)=500 P 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