Question

An electrical utility is experiencing a sharp power demand that continues to grow at a high rate in a certain local area.Two alternatives are under consideration. Each is designed to provide enough capacity during the next 25​ years, and both will consume the same amount of​ fuel, so fuel cost is not considered in the analysis. •Alternative A. Increase the generating capacity now so that the ultimate demand can be met without additional expenditures later. An investment of ​$20 million would be​ required, and it is estimated that this plant facility would be in service for 25 years and have a salvage value of ​$0.9 million. The annual operating and maintenance costs​ (including income​ taxes) would be​$0.4 million. •Alternative B. Spend ​$19 million now and follow this expenditure with future additions during the 10th year and the 15th year. These additions would cost ​$23 million and ​$16 ​million, respectively. The facility would be sold 25 years from now with a salvage value of ​$1.6 million. The annual operating and maintenance costs​(including income​ taxes) will be ​$250,000 initially and will increase to ​$0.35 million after the second addition​ (from the 11th year to the 15th​ year) and to ​$0.45 million during the final 10 years.​ (Assume that these costs begin one year subsequent to the actual​ addition.) On the basis of the​ present-worth criterion, if the firm uses 12​% as a​ MARR, which alternative should be​ undertaken? Note​: Adopt incremental cost approach. The present worth of Alternative A is $________ million.​ (Round to one decimal​ place.)

Answer 1

1. Present worth of costs of alternative A is

PW(A,C) = 20000000 +400000(P/F, 12%,25) = 20000000+400000* .05882 = $20023528

Present worth of benefits of alternative A is

PW(A,B)= $900000

Present worth of costs of alternative B is

PW(B,C) = 19000000+23000000(P/A, 12%,15) +16000000(P/A, 12%,10) +250000(P/F, 12%, 10) + 350000(P/G,12%, 4) + 450000(P/G, 12%, 10) = 19000000+23000000* 6.8109 + 16000000* 5.6502 +250000* .3220 +350000* 4.1273 +

450000*20.2541= $276693300

Present worth of benefits of alternative B is

PW(B,B) = $1600000

Net present worth of alternative A = PW(A,B) - PW(A,C)= 900000-20023528=

                                                                     $-19123528

Also net present worth of alternative B = PW(B,B)- PW(B,C)

                                                        = $1600000-$276693300 = $-275093300

As net present worth of alternative A is higher than alternative B, alternative A should be undertaken.

2. The net present worth of Alternative A = PW(A,C)-PW(A,B) = 20023528-900000= $19123528