1 SIE/ENGR 265 – HW 4 Solution 1. The annual equivalent amount of the bi-annual payment is $11,000 (A/F, 3%, 2) = $11,000 (0.4926) = $5,418.60 The capitalized worth is CW = A = $5,418 60 = $180,620 i 0 03 So, $180,620 must be deposited now into an account earning 3% per year such that $11,000 can be paid out every two years indefinitely (starting two years from now). 2. The PW of the incremental investment is: (8%) = $400 + ( 15,000 19 15,000 24 ) ( $3.50 ) (/, 8%, 10) = $400 + (164.5 gal/yr) ($3.50/gal) (6.7101) = $3,463 This is a very attractive investment in the Ford truck ($3,463 > 0). 3. The bond pays (0.05)($5,000) = $250 once per year. The yield, or effective annual interest rate, can be found as follows: 0 = $5,500 + $250 (P/A, i’%, 10) + $5,000 (P/F, i’%, 10) i’% = RATE(NPER,PMT,PV,FV) = RATE(10,250,-5500,5000) = 3.78% $5,000 A = $250 / year Buyer’s Viewpoint: 0 1 2 3 4 5 6 7 8 9 10 End of year 2 4. P = $150 (P/A, 2%/qtr., 60 qtr.) + $10,000 (P/F, 2%/qtr., 60 qtr.) P = $150(34.7609) + $10,000(0.3048) P = $5,214 + $3,048 P = $8,262 5. FW(15%) = $10,000 (F/P,15%,5) + ($8,000 $4000)(F/A,15%,5) $1,000 = $10,000 (2.0114) + $4000(6.7424) $1,000 = $5,855.60 Since FW(15%) ≥ 0, the project is acceptable. 6. Let X = annual savings required. AW(20%) = 0 = X – [$3,000,000(A/P, 20%, 7) $300,000(A/F, 20%, 7)] X = $808,980 / year Net savings per pallet = ($808,980/year) / (1,000,000 pallets/year) = $0.81 per pallet $255 7. $3,000 $3,000 = $255 (P/A, i′, 15) i′ = RATE(NPER,PMT,PV) = RATE(15,255,-3000) = 3.2% per month r = 12 × 3.2% = 38.4% compounded monthly (APR) ieff = (1 + ) 1 = (1 + 0.384 12 ) 12 – 1 = 0.459 or 45.9% per year 0 1 2 3 14 15 3 $375 8. $350 The CFD is from the lender’s viewpoint. The net cash flow will have a $350 outflow at end of month 0, uniform series of inflows of $25 from at end of months 1-11, and finally a $375 outflow at end of month 12. Using IRR function, we can then find the interest rate as shown in the table below: EOM Net Cash Flow 0 ($350) 1 $25 2 $25 3 $25 4 $25 5 $25 6 $25 7 $25 8 $25 9 $25 10 $25 11 $25 12 $375 IRR 7.14% The monthly interest rate (rmonthly) = 7.14%; The nominal annual rate (r) = 12 × 7.14% = 85.68%; The effective annual interest rate is ieff = (1 + ) 1 = (1 + 0.8568 12 ) 12 – 1 = (1.0714)12 – 1 = 1.288 (128.8%). Jess’s wife is correct in her worry. 0 1 2 3 11 12
