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Investment analysis question 3.35
35. Investment Timing. You can purchase an optical scanner today for $400. The scanner pr vides benefits worth S60 a year. The expected life of the scanner is 10 years. Scanners a expected to decrease in price by 20 percent per year. Suppose the discount rate is 10 percer Should you purchase the scanner today or wait to purchase? When is the best purchase tim
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Answer #1

The investment analysis is done in spreadsheet as below:

F17 Q fx D17+E17 Purchase cost at end of vear 0- Annual Benefit- 400 60 Life of equipment (n)10 years 20% 10% 6.1446 Decrease in price per year 6 Discount rate- (P/A,l,n):| Future Value (FV) of Benefits368.67 10 End of Year (t) FV of Cost(P/F,i,t)PV of Cost PV of BenefitsNPV 12 13 14 15 16 17 18 19 20 400.00 320.00 256.00 204.80 163.84 131.07 104.86 83.89 67.11 53.69 42.95 1.0000 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 400.00 290.91 211.57 153.87 111.90 81.39 59.19 43.05 31.31 22.77 16.56 368.67 335.16 304.69 276.99 251.81 228.92 208.11 189.19 171.99 156.35 142.14 31.33 44.25 93.12 123.12 139.90 147.53 148.92 146.14 140.68 133.59 125.58 6 urchase now 10 25

EXCEL FORMULAS:

Purchase cost at end of year0 400 Annual Benefit- 60 Life of equipment (n) 10 Decrease in price per year-0.2 Discount rate 0.1 years (P/A,i,n)(1+D6)AD4-1)/D6/(1+D6)AD4 Future Value (FV) of Benefits D7 D 10 End of Year (t 11 0 12 A11+1 13 A12+1 4 A13+1 15 A14+1 16A15+1 17 A16+1 18 A17+1 19 FA18+1 0 A19+1 21 A20+1 FV of Cost P/F,i,t PV of Cost PV of Benefits SD$8 SD$8 C12D12+E12 IF(F12-MAX(SF$11:$F$21), purchase now, SD$8 C13 SDS8 C14D14+E14IF(F14-MAX(SFS11:SF$21),purchase now) SDS8 C15 NPV -SD$2*1-SD$5)MA11 1/(1+SD$6) A11 -SD$2*(1-SDS5)MA12 -1/(1+SD$6) A12 C11D11+E11 F(F11-MAXISF$11:SF$21), purchase now,) D13+E13 -IF(F13-MAX(SF$11:$F$21), purchase now, ) D15+E15-IF(F15-MAX(SFS11:SF$21), purchase now, ) -811 C11 -B12 C12 -B13 C13 -B14 C14 815 C15 -816 C16 -B17 C17 -B18 C18 -B19 C19 B20 C20 -821 C21 $D$2 (1-$D$5)AA15 1/(1+SD$6) A15 -SD$2*(1-SD$5)MA16 1/(1+SD$6) A16 -SD$2*(1-SDS5)MA17 -1/(1+SD$6) A17 SD$2*(1-SDS5) A181/(1+SD$6)MA18 C16D16+E16IF(F16-MAX(SFS11-SF$21),purchase now ) -SD$8 C17 D17+E17 IF(F17-MAX(SF$11:$F$21), purchase now,) SD$8 C18 SD$8 C19D19+E19 IFF19-MAX(SFS11:ŚF$21),purchase now) SDS8 C20D20+E20IFF20-MAXISF$11:FS21), purchase now.) SDS8 C21 D21+E21IF(F21-MAX(SF$11SF$21), purchase now,) -D18+E18-IF(F18-MAX($FS11:SF$21),purchase now,) SD$2*(1-$D$5)AA21 1/(1+SD$6) A21

NPV is the negative for purchase today. So I would not purchase the scanner today.

The NPV is maximum when the scanner is purchased at the end of year 6.

Therefore, I would purchase the scanner at the end of year 6, when its price has depreciated to $ 104.86 . It will be used for 10 years and give annual beenfits of $ 60. This investment strategy has a Net Present Value of $ 148.92

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