Question

a) Cmpare altematives shown below on the basis of preent worth analysis Ue n rate of 10% per year. (20 Marks) an interest Initial Cost 100.000- Alternative AHernative ーAnnual Operating Co,t®..| Annual Repair Cost () 200/XX 38/xo 10.000 11300 0,000 A,, "ual Maintenance Cost (5)- 12,0 Annual Income () Salvage Value( Life (Years) C o ワー70K 24十 88,51 ってae l 7A8

Answer 1

Answer:

PW=PV of all future cashflow+PV of Salavge value- Initial investment (P)

PV for equal cash flow each year= A*(1-(1+r)^-n)/r

PV of Salvage value=S/(1+r)^n

r=rate of interest

n=number of period

A=Net cash flow each year

S= salvage value

Net Cash flow A=Annual Income-Annual operating cost-Annual repair cost-Annual Maintenance cost

Since all the project has different life cycles so the comparison will be made over a time period equal to the least common multiple of the life spans of the alternatives. In this case the least common multiple of the life spans is 72 years.

For Alternative X

Since it has life =8 years

so there will 72/8=9 cycles of cash flow

Here A=35000-10000-0-11300=$13700

r=10%

n=8 years

P=$100,000

So NPV for 1 cycle= 13700*(1-(1+10%)^-8)/10%+60000/(1+10%)^8-100000=$1078.93

So NPV for 9 cycles = NPV+NPV/(1+10%)^8+NPV/(1+10%)^16+NPV/(1+10%)^24+NPV/(1+10%)^32+NPV/(1+10%)^40+NPV/(1+10%)^48+NPV/(1+10%)^56+NPV/(1+10%)^64

NPV for 9 cycles=1078.93+1078.9/(1+10%)^8+1078.93/(1+10%)^16+1078.93/(1+10%)^24+1078.93/(1+10%)^32+1078.93/(1+10%)^40+1078.93/(1+10%)^48+1078.93/(1+10%)^56+1078.93/(1+10%)^64

NPV for 9 cycles=$2020.27 Eq 1

For Alternative Y

Since it has life =12 years

so there will 72/12=6 cycles of cash flow

Here A=57800-7000-8000-18000=$24800

r=10%

n=12 years

P=$200,000

So NPV for 1 cycle= 24800*(1-(1+10%)^-12)/10%+100000/(1+10%)^12-200000=$842.63

So NPV for 6 cycles = NPV+NPV/(1+10%)^12+NPV/(1+10%)^24+NPV/(1+10%)^36+NPV/(1+10%)^48+NPV/(1+10%)^60

NPV for 6 cycles=842.63+842.6/(1+10%)^12+842.63/(1+10%)^24+842.63/(1+10%)^36+842.63/(1+10%)^48+842.63/(1+10%)^60

NPV for 6 cycles=$1235.40 Eq 2

For Alternative Z

Since it has life =128 years

so there will 72/18=4 cycles of cash flow

Here A=89000-12000-8000-35000=$34000

r=10%

n=18 years

P=$300,000

So NPV for 1 cycle= 34000*(1-(1+10%)^-18)/10%+120000/(1+10%)^18-300000=$431.07

So NPV for 4 cycles = NPV+NPV/(1+10%)^18+NPV/(1+10%)^36+NPV/(1+10%)^54

NPV for 4 cycles=431.07+431.07/(1+10%)^18+431.07/(1+10%)^36+431.07/(1+10%)^54

NPV for 4 cycles=$525.04 Eq 3

From equation 1 ,2, and 3 we find that alternate x has highest PW.