Question

A firm is considering the purchase of one of two

new machines. The data on each are given.

Machine A Machine B

Initial cost 3400 6500

Service life 3 years 6 years

Salvage value 100 500

Net operating cost 2000/year 1800/year

If the MARR is 12%, which alternative should be

selected when using the following methods?

a. Annual equivalent cost approach ( method 2)

b. Present Worth comparison (method 2)

c. Incremental IRR comparison ( method 2)

Answer 1

given

Project A

Initial cost P=3400

Service life n=3 years

Salvage value S=100

Operating cost C=2000

Project B

Initial cost P=6500

Service life n=6 years

Salvage value S=500

Operating cost C=1800

Question 1)

ECA of alternate A=- Equivalent annual cost of initial investment P for 3 years+Equivalent annual cost of Salvage value S for 3 years-Annual cost C=-P*r/(1-(1+r)^-n)+S*r/((1+r)^n-1)-C=-1367.19+30.21-2000=3336.97 Eq1

ECA of alternate B=- Equivalent annual cost of initial investment P for 6 years+Equivalent annual cost of Salvage value S for 6 years-Annual cost C=-P*r/(1-(1+r)^-n)+S*r/((1+r)^n-1)-C=-1492.45+64.80-1800=-3227.64 Eq2

From equation 1 and 2 it is clear that project B will be chosen because ECAb>ECAa.

Question 2) Since two projects have different life span so to compare the NPV So the lifespan of project A needs to be doubled to equal the six-year lifespan of Machine B by assuming that company reinvest same amount in third year of project A and cash flow for year 4, &6 will be same as year 1,2,&3.So new cashflow will be

PV of annuity =PMT*{1-(1+r)^-n}/r

PV=FV/(1+r)^n

where PMT =payment per period

n=period

r=MARR

NPV=PV -I

I=initial investment

NPV for project A=14533.41 Eq3

NPV for project B=14057.23   Eq4

From equation 3 and 4 it is clear that project B will be chosen because PVb>PVa.

Question 3)

For incremental cashflow we need to subtract cash flow of project lower initial investment amount (project A) from higher initial investment amount (project B) and calculate for IRR.

PMT*{1-(1+IRR)^-n}/IRR=I

Following table will be obtained for incremental cash flow and IRR.

From above table it is clear that incremental IRR for project B is greater that MARR(10%) so we will choose project B.