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Both types of BCR with FW, growing income

Short answer

Future worth of benefits and costs are computed at MARR=15%. The conventional B/C ratio is 0.927 and the modified B/C is 0.911, both below 1, so the project should be rejected.

Calculate both types of BCR using FW formulation when:

  • Initial investment is Rs 50000;
  • Income is Rs 10000 at the end of first year and increasing by 10% per year;
  • Annual expenditure is Rs 2000 at the end of first year and increasing by Rs 200 per year;
  • Useful life is 6 years;
  • Salvage value is Rs 20000;
  • MARR = 15%.

Definitions used (Sullivan, FW form):

  • Conventional B/C = FW(benefits) / [FW(investment) + FW(O&M) − salvage value]
  • Modified B/C = [FW(benefits) − FW(O&M)] / [FW(investment) − salvage value]

Data: I = Rs 50,000; benefit B₁ = 10,000 growing 10% per year; O&M M₁ = 2,000 + 200 per year; n = 6; S = 20,000 (at year 6, so FW = 20,000); i = 15%.

 Benefit : 10,000 -> 11,000 -> 12,100 ... (x1.10 each year)
 O&M     :  2,000 ->  2,200 ->  2,400 ... (+200 each year)
 Year 6  : salvage +20,000
YrBenefitO&M(F/P,15%,6-t)FW benefitFW O&M
110,000.002,0002.011420,113.574,022.71
211,000.002,2001.749019,239.073,847.81
312,100.002,4001.520918,402.593,650.10
413,310.002,6001.322517,602.483,438.50
514,641.002,8001.150016,837.153,220.00
616,105.103,0001.000016,105.103,000.00
Total108,299.9521,179.13

Check by formulas: FW(B) = 10,000 [(1.15)^6 − (1.10)^6] / (0.15 − 0.10) = 108,299.95. FW(I) = 50,000 (1.15)^6 = 50,000 × 2.31306 = 115,653.04.

Conventional B/C = 108,300 / (115,653 + 21,179 − 20,000) = 108,300 / 116,832 = 0.927

Modified B/C = (108,300 − 21,179) / (115,653 − 20,000) = 87,121 / 95,653 = 0.911

Decision: both ratios are less than 1, so the benefits do not cover the costs at MARR = 15%. The project should be rejected.

✓ Answer checked by Claude Opus 5.5 (high effort)

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