Question

4. (15 points) Which option should be selected based on a present worth comparison at an interest rate of 10%? First cost, $ Annual operating & maintenance cost, $/year Salvage value, $ Life, in years Option X Option Y -230,000 -380,000 -9,000 -12,000 12,000 140,000 a. Draw the cash flow diagram for Option X. b. Calculate the present worth for Option X. c. Which option should be selected? Why?

Answer 1

Option X's life is 3 years, but that of option Y is 6 years. Thus, to compare the two options, the cash flow of option X will also be made for 6 years. $230,000 is the first cost of option X and the salvage value is $12000 which is received after 3 years. To draw the cash flow for 6 years, first cost will be considered again at the end of the 3rd year, whose salvage value will be received at the end of the 6th year. Annual operating & maintenance cost remains $9000 throughout. Thus, the cash flow for option X is shown below: -230,000 +12,000 +12,000 -230,000 - 9,000 -9,000 -9,000 -9,000 -9,000 -9,000 Year 1 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Calculate the Present Worth (PW) of option X as follows: PW =-Initial Cost - Annual operating & maintenance cost (P/A,1%,1)+ (Salvage value - Initial cost)(P/F.%.n)+Salvage value (P/F,1%,) --230,000 - 9000 (P/4,10%,6)+(12,000 - 230,000)(P/F 10%,3) +12,000 (P/F,10%,6) --230,000 - 9000 (4.355 )+(-218.000) (0.7513 ) +12,000( 0.5645 ) =-230,000 - 39,195-163,783.4+6774 PW, = -426,204.4 Thus, the present worth for option X is $426,204.4.

To find out which option should be selected, find the present worth of option Y and compare it with that of option X. Present worth of option X is: PW, --Initial Cost - Annual operating & maintenance cost (P/4,1%,n) + Salvage value (P/F,1%.n) =-380,000-12,000 (P/ 4,10%,6)+140,000 (P/F,10%,6) =-380,000-12,000 (4 355 ) +140,000(0.5645) =-380,000-52.260+79,030 PW, =-353,230 Thus, the present worth for option Y is $353,230. Since the present worth of cost of option Y is less than that of option X, option Y should be selected.