Question

Andrews Manufacturing offers three models for one of its products to its customers. You have been asked to analyze the choices from the customer’s perspective. Which model should a customer choose if each model has a life of 12 years? Doing nothing is an alternative.

Alternative

Deluxe Regular Economy

First cost $220,000 $125,000 $75,000

Annual benefit 79,000 43,000 28000

Maintenance and 38,000 13,000 8000

operating costs

Salvage value 16,000 6,900 . 3000

(a) Construct a choice table for interest rates from 0% to 100%.

(b) MARR = 15%. Using incremental rate of return analysis, which alternative, if any, should the customer choose?

Answer 1

A c. D E Particular Deluxe Year Particulars Deluxe Regular Economy 1 2 0 3 1 4 5 6 7 3 4 5 Incremental = Incremental = Regular Deluxe- Economy Regular ($50,000) ($95.000) $10.000 $11,000 $10,000 $11,000 $10,000 $11,000 $10,000 $11,000 $10,000 $11,000 $10,000 $11,000 $10.000 $11,000 $10,000 $11,000 $10,000 $11,000 $10.000 $11,000 ($75,000) $20.000 $20.000 $20.000 $20.000 $20,000 $20.000 $20.000 $20,000 $20,000 $20.000 6 7 8 9 8 First Cost (S220,000) ($125.000) Annual benefit - Operating Cost $41.000 $30,000 Annual benefit - Operating Cost $41,000 $30,000 Annual benefit - Operating Cost $41,000 $30,000 Annual benefit - Operating Cost $41,000 $30,000 Annual benefit - Operating Cost $41.000 $30,000 Annual benefit - Operating Cost $41,000 $30,000 Annual benefit - Operating Cost $41.000 $30,000 Annual benefit - Operating Cost $41,000 $30,000 Annual benefit - Operating Cost $41.000 $30,000 Annual benefit - Operating Cost $41,000 $30,000 Annual benefit - Operating Cost + Salvage $57,000 $36,900 Value Incremental rate of return NPV of incremental cash flows at 15% MARR 9 10 11 12 10 11 12 $23.000 $13,900 $20,100 13 14 15 16.52% S3,175.40 5.32% (S35,473.19) 16 17 18 19 20 21 22 23 24 25 26 Interest rate 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% NPV of Deluxe $247,000 $219,414 $194.129 $170,916 $149,573 $129,918 $111.790 $95.047 $79,560 $65,213 $51,905 $39,544 $28.045 $17,336 $7,348 (S1,979) ($10,699) NPV of Regular $211,900 $192,213 $174.155 $157,563 $142,296 $128,227 $115.241 $103,238 $92,128 $81,830 $72,270 $63,385 $55,115 $47,407 $40.215 $33,494 $27,208 NPV of Economy S148,000 $135,042 $123.150 $112.220 $102,158 $92,882 $84,318 $76,399 $69.066 S62,266 $55,953 $50,082 $44.616 $39,521 $34,765 $30,319 $26,159 27 28 29 30 31 32 33 34


35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% 31% 32% 33% 34% 35% 36% 37% 38% 39% 40% 41% 42% 43% 44% 45% 46% 47% 48% 49% 50% 51% 52% ($18,862) ($26,513) (533,692) ($40.437) (S46,781) ($52,753) (S58.383) ($63,695) ($68,713) (S73,458) ($77,948) (582,202) ($86,237) ($90,066) ($93,705) ($97.164) ($100,457) ($103,593) ($106,583) ($109,436) ($112.160) ($114,764) ($117.253) ($119,636) ($121,918) ($124,105) ($126,203) ($128.216) ($130,150) ($132,008) ($133,794) ($135,514) ($137,169) ($138,763) ($140,300) ($141,782) $21,319 $15,797 $10,613 $5,740 $1.155 ($3,164) ($7.237) ($11,082) ($14.715) ($18,152) (S21,406 (S24.491) (S27.417) ($30,195) (S32.835) (535,347) ($37,738) (S40,017) (S42.189) ($44,263) (546,244) (S48,137) ($49,948) (S51,682) (S53,343) (S54.935) ($56,462) (S57.928) (559,337) (S60,690) (561,992) (S63,245) (564,452) (S65,614) (566,734) (S67,815) $22.262 $18,606 $15.173 $11.945 $8.907 $6.045 $3,345 $795 ($1.614) (S3,894) ($6,053) ($8,100) ($10,042) ($11.886) ($13.639) ($15,307) ($16,895) ($18,408) ($19,852) ($21.230) ($22,546) ($23,804) ($25,008) ($26,161) ($27.265) ($28,324) ($29,339) ($30.314) ($31.251) ($32,152) ($33,018) ($33,851) ($34.654) ($35,428) ($36,173) ($36,893) 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

73 五乃乃乃。 74 76 77 78 79 80 81 82 53 54% 55"o 600 5796 580p 599。 600。 61o 6206 63% 649 65o 6606 676 689。 699o 70's 71% 720 73% 83 84 85 86 87 88 的 ($143.212) ($144.593) ($145.926) ($147.215) ($148.462) ($149.667) ($150.834) ($151,964) ($153.059) ($154.120) ($155.148) ($156.146) ($157.114) ($158.054) ($158.966) ($159.853) (S160.715) ($161.553) ($162.368) ($163.161) ($163.932) ($164.684) ($165.415) ($166.128) ($166.823) ($167.500) ($168.161) ($168.805) (S169.433) ($170.047) ($170.646) (S171.231) ($171.802) ($172.360) ($172.905) ($173.439) ($173.960) ($68.858) ($69.866) ($70.839) ($71.779) (572.689) ($73.568) (S74.420) ($75.245) (S76.044) (576.819) (577.570) ($78.298) ($79.005) ($79.692) ($80.358) (S81.006) (581.6.36) ($82.248) (S82.843) ($83.423) (583.986) (S84.535) (585.070) (585.591) (586.099) (S86.594) (587.077) (587.548) ($88.007) (588.456) ($88.893) (589.321) ($89.739) (S90.147) ($90.545) ($90.935) (591317) ($37.587) ($38.258) ($38.905) ($39.531) ($40.137) ($40.723) ($41.290) ($41.839) ($42.371) ($42.887) (543.387) ($43.872) ($44.343) ($44.800) ($45.245) ($45.676) ($46.095) ($46,503) ($46.900) ($47.286) ($47.661) ($48.027) ($48.384) ($48.731) ($49.069) ($49.399) ($49.720) ($50.034) ($50.340) ($50.639) ($50.931) ($51.216) ($51.494) ($51.766) ($52.032) ($52.292) ($52.5461 90 91 92 740o 93 94 95 6 97 98 9 100 101 102 103 104 105 106 107 75%。 769。 770。 7896 7996 80% 810 8206 8309 8496 8500 869。 879 889o 899o

108 109 110 111 112 113 114 115 116 117 118 90% 91% 92% 93% 94% 95% 96% 97% 98% 99% 100% ($174.470) ($174.969) ($175,457) ($175,934) ($176,402) ($176,860) ($177,308) ($177,747) ($178,177) ($178,599) ($179,012) ($91,689) (592.054) (592.411) ($92,760) (593,102) (593.437) (593,765) ($94,086) (594,401) ($94.709) (595,011) (552,794) (S53,037) (553.275) ($53,508) (S53,736) (553,959) ($54.178) (S54,392) (554.601) (554,807) ($55,008) 119 120 121 122 123 124 Solution (a) Deluxe is profitable with positive NPV between Regular is profitable with positive NPV between Economy is profitable with positive NPV between 0% to 14% 0% to 21% 0% to 24% 125 5.32% 126 Solution (b) Incremental from regular to delux (Deluxe - Regular) is not profittable as incremental rate of return is less than 15% Incremental from Economy to Regular (Regular - Economy) is not profittable as incremental rate of return is more than 15% 16.52% 127

If MARR is 15% , the alternative to choose would be " Regular "as it has higher positive NPV than Delux & Economy alternatives as shown in the above table.

-NPV of Deluxe NPV of Regular NPV of Econor 30000000% 25000000% 20000000% 15000000% 10000000% 5000000% 0% -5000000% 0% -10000000% -15000000% -20000000% -25000000% 20 ROD 100%

The following are the data spreadsheet:-,

Economy Economy = A B D E Year Particulars Deluxe Regular Incremental Regular - Incremental Deluxe- 1 Economy Regular 2 0 First Cost -220000 -125000 - 75000 =D2-E2 =C2-D2 31 Annual benefit - Operating Cost =79000-38000 =43000-13000 1=28000-8000 =D3-E3 =C3-D3 4 3 Annual benefit - Operating Cost =79000-38000 - 43000-13000 1=28000-8000 D4-E4 -C4-D4 54 Annual benefit - Operating Cost - 79000-38000 -43000-13000 - 28000-8000 -DS-ES 1-C5-DS 65 Annual benefit - Operating Cost =79000-38000 -43000-13000 1=28000-8000 =D6-E6 =C6-D6 76 Annual benefit - Operating Cost =79000-38000 =43000-13000 =28000-8000 =D7-E7 8 7 Annual benefit - Operating Cost =79000-38000 =43000-13000 =28000-8000 =D8-E8 =C8-D8 98 Annual benefit - Operating Cost =79000-38000 =43000-13000 =28000-8000 =D9-E9 =C9-D9 10 9 Annual benefit - Operating Cost 79000-38000 43000-13000 -28000-8000 -D10-EIO C10-D10 11 10 Annual benefit - Operating Cost -79000-38000 - 43000-13000 - 28000-8000 -D11-E11 -C11-11 12 11 Annual benefit - Operating Cost =79000-38000 =43000-13000 =28000-8000 =D12-E12 =C12-D12 Annual benefit - Operating Cost + Salvage 13 12 Value =79000-38000+16000 =43000-13000+6900 28000-8000+3000 =D13-E13 =C13-D13 14 Incremental rate of return IRR(F2:F13) =IRR(G2:13) 15 NPV of incremental cash flows at 15% MARR =NPV(15%,F3:F13)+F2 =NPV(15%,G3:G13)+G2 16 17 Interest rate NPV of Deluxe NPV of Regular NPV of Economy 18 0 =NPV(A18.SCS3:SCS13)+$C$2 =NPV(A18,SD$3:$D$13)+SDS2 =NPV(A18, SE$3:SE$13)+$E$2 19 0.01 -NPV(A19.SCS3:SCS13)+SCS2 NPV(A19, SD$3:$D$13)+SDS2 -NPV(A19.SE$3:SES13)+SES2 20 0.02 NPV(A20,SC$3:SCS13)+$C$2 NPV(A20,SD$3:$D$13)+SDS2 NPV(A20, SE$3:SES13)+SES2 21 0.03 =NPV(A21,SC$3:$C$13)+$C$2 =NPV(A21,SD$3:$D$13)+SDS2 =NPV(A21,SE$3:SE$13)+$E$2 =NPV(A22.SCS3.SC$13)+$C$2 =NPV(A22,SD$3:$D$13)+SDS2 =NPV(A22.SES3:SES13)+SES2 23 0.05 =NPV(A23.SC3:SCS13)-$C$2 =NPV(A23,SD$3:$D$13)+SDS2 =NPV(A23, SE$3:SES13)+$E$2 24 0.06 ENPV(A24.SC$3:SC$13)+$C$2 =NPV(A24,SD$3:$D$13)+SDS2 =NPV(A24.SE$3.SES13)+$E$2 25 0.07 NPV(A25.SC$3:$C$13)+$C$2 -NPV(A25,SD$3:$D$13)+$D$2 NPV(A25,SE$3:$E$13)+$E$2 26 0.08 =NPV(A26,SCS3:SC$13)+SCS2 =NPV(A26,SD$3:$D$13)+SDS2 =NPV(A26,SES3:SES13)+SES2 27 0.09 =NPV(A27.SC3:SC$13)+$C$2=NPV(A27,SD$3:$D$13)+SDS2 =NPV(A27,SE$3:SE$13)+$E$2 28 0.1 =NPV(A28. SCS3 SCS13)+$CS2 =NPV(A28, SD$3:SD$13)+SDS2 =NPV(A28 SES3:SES13)+SES2 29 0.11 =NPV(A29.SCS3:SCS13)+$CS2 =NPV(A29,SDS3:$D$13)+SDS2 =NPV(A29.SES3.SE$13)+SES2 30 0.12 ENPV(A30,$C$3:SCS13)+$C$2=NPV(A30,SD$3:$D$13)+SDS2 NPV(A30,SE$3:$E$13)+$E$2 31 0.13 -NPV(A31.SC$3:$C$13)+$CS2 -NPV(A31,SD$3:$D$13)+SD$2 -NPV(A31.SE$3:$E$13)+$E$2 32 0.14 =NPV(A32.SCS3 SCS13)+SCS2 =NPV(A32 SDS3:$D$13)+SDS2 =NPV(A32.SES3 SES13)+SES2 33 0.15 =NPV(A33,SC$3:SCS13)+SCS2 =NPV(A33,SDS3:SDS13)+SDS2 =NPV(A33,SES3:SE$13)+SES2 34 0.16 =NPV(A34.SCS3.SCS13)+SCS2 =NPV(A34,SD$3:$D$13)+SDS2 =NPV(A34,SD$3:$D$13)+SDS2 =NPV(A34.SE$3.SES13)+SES2 35 0.17 =NPV(A35.SC$3:SCS13)+$CS2 =NPV(A35.SD$3:$D$13)+SDS2 =NPV(A35.SES3:SES13) SES2 22 0.04

Similarly upto 100%.

95 0.77 96 0.78 97 0.79 98 0.8 99 0.81 100 0.82 101 0.83 102 0.84 103 0.85 104 0.86 105 0.87 106 0.88 107 0.89 108 0.9 109 0.91 110 0.92 111 0.93 112 0.94 113 0.95 114 0.96 115 0.97 116 0.98 117 0.99 1181 119 4 120 121 122 123 =NPV(A95.SCS3 SC$13)+SCS2 =NPV(A95.SD$3:SD$13)+SDS2 =NPV(A95.SES3:SES13)+SES2 =NPV(A96,SCS3 SC$13)+$C$2 =NPV(A96,SD$3:SD$13)+SDS2 =NPV(A96, SES3:SE$13)+SES2 NPV(A97,$C$3:$C$13)+$C$2 NPV(A97,SD$3:SD$13)+SDS2 NPV(A97,SES3:SES13) SES2 =NPV(A98,$C$3:$C$13)+$C$2 =NPV(A98.SD$3:SD$13)+SDS2 =NPV(A98.SES3:SES13)+SES2 =NPV(A99,$C$3:$C$13)+$C$2=NPV(A99,SD$3:SD$13)+SDS2 =NPV(A99,SE$3:SE$13)+$E$2 -NPV(A100,$C$3:$C$13)+$C$2 NPV(A100,SD$3:SD$13)+SDS2 -NPV(A100,SE$3:SE$13)+$E$2 =NPV(A101,$C$3:$C$13)+SCS2 =NPV(A101,SD$3:SD$13)+SDS2 =NPV(A101.SES3:SES13)+$E$2 =NPV(A102,$C$3:$C$13)+$C$2 =NPV(A102.SD$3:SD$13)+SDS2 =NPV(A102,SES3:SE$13)+$E$2 =NPV(A103,$C$3:SC$13)+$C$2 NPV(A103.SD$3:SD$13)+SDS2 -NPV(A103.SES3.SES13)+SES2 NPV(A104,$C$3:SC$13)+SCS2 ENPV(A104,SD$3:SD$13)+SDS2 NPV(A104,SES3:SES13)+SES2 =NPV(A105,$C$3:$C$13)+$C$2 =NPV(A105,SD$3:SD$13)+SDS2 =NPV(A105.SE$3:SE$13)+$E$2 =NPV(A106,C$3.SC$13)+$C$2 =NPV(A106.SD$3.SD$13)+SDS2 =NPV(A106,SES3:SES13)+SES2 NPV(A107,$C3:SC$13)+$C$2 NPV(A107.SD$3:SD$13)+SDS2 NPV(A107,SES3 SES13)+SES2 =NPV(A108,$C$3:$C$13)+$C$2 =NPV(A108 SD$3:SD$13)+SDS2 =NPV(A108 SE$3:SE$13)+$E$2 =NPV(A109,$C$3.SC$13)+SCS2 =NPV(A109.SDS3 SD$13)+SDS2 =NPV(A109, SES3.SES13)+SES2 =NPV(A110,$C$3:SC$13)+SCS2 =NPV(A110.SD$3:SDS13)+SDS2 =NPV(A110, SES3:SES13)+SES2 =NPV(A111,$C$3:SC$13)+$C$2 =NPV(A111.SD$3:SD$13)+$D$2 =NPV(A111.SE$3:$E$13)+$E$2 =NPV(A112,SCS3 SC$13)+$CS2 =NPV(A112.SD$3:SD$13)+SDS2 =NPV(A112,SES3:SES13)+SES2 =NPV(A113,$C$3:SC$13)+SCS2 =NPV(A113.SD$3:SDS13)+SDS2 =NPV(A113.SES3:SES13)+$E$2 =NPV(A114,$C$3:$C$13)+$C$2 =NPV(A114,SD$3:SD$13)+SDS2 =NPV(A114,SES3-SES13)+SES2 =NPV(A115,$C$3:$C$13)+$C$2 =NPV(A115,SD$3:SD$13)+SDS2 =NPV(A115,SES3:SE$13)+SES2 =NPV(A116,$C$3:SC$13)+SCS2 =NPV(A116.SD$3:SD$13)+SDS2 ENPV(A116.SES3:SES13)+SES2 NPV(A117,$C$3:SC$13)+$C$2 NPV(A117,SD$3:SD$13)+SDS2 NPV(A117, SES3:SE$13)+SES2 =NPV(A118.$C$3:$C$13)+$CS2 -NPV(A118,SD$3:SD$13)+SDS2 =NPV(A118,SES3:SES13)+$E$2 Solution (a) Deluxe is profitable with positive NPV between Regular is profitable with positive NPV between Economy is profitable with positive NPV between 0% to 14% 0% to 21% 0% to 24% 124 125 Solution (b) Incremental from regular to delux (Deluxe - Regular) is not profittable as incremental rate of retum is less than 15% 126 =G14 Incremental from Economy to Regular (Regular - Economy) is not profittable as incremental rate of return is more than 127 15% =F14