Question

4. Please find the data of two (2) alternatives to improve a plant's current production system: Machine A Machine B =P= =P= Initial Installment Cost Annual Operating Cost Service Life Salvage Value 20,000 10,000 2 years 0 40,000 8.000 3 years 0 At 12% interest, which alternative should be selected using the a) Annual Equivalent Cost Method, and b) Present Value Method.

with CASH FLOW DIAGRAM PLEASE

Answer 1

A. Annual equivalant cost.

The cashflows and EAC cost are shown below. Explanation follows.

Year Option A -20000 Option B -40000 0 1 -10000 -8000 2 -10000 -8000 3 -8000 4 -8000 NPV -36900.51 ($21,833.96) -64298.79 ($21,169.38) EAC

For EAC, we need NPV first.
NPV has been calculated by the formula =NPV(rate,cashflow)+initial investment.
EAC has been calculated by the formula =PMT(rate,no of years,NPV)

EAC can also be calculated manually by the following formula-

Equivalent Annual Cost NPV xr 1- (1 + r)"

Where, NPV can be calculated by

NPV CF1 (1 + r) CF2 (1 + r)2 + .... + CFn (1 + r)" - 1

As can be seen, EAC of option B is lower, hence Option B should be chosen by EAC method.

The cashflow diagram is shown below-

Option A-

Cashflow 0 0 2 -5000 -10000 -10000 -10000 Cashflow - 15000 -20000 -20000 -25000 Year

Option B-

B. Now we will use the NPV method. But the issue here is that NPVs cant be compared directly as the number of years for both are different. So we need to repeat the methods till their number of years match. This happens in 6 years, where we have to repeat option A thrice and Option B twice. The cashflow and NPVs are shown below

Year Option A -20000 Option B -40000 0 1 -10000 -8000 2 -8000 -30000 -10000 3 4 -30000 -10000 -48000 -8000 -8000 5 6 -10000 -8000 NPV -89768.31 -101362.47

As can be seen, initial costs for option A have been added to year 2, 4 and 6. Similarly, initial cost for Option B is added in year 3.

As can be seen, NPV of Option A is lower, hence Option A will be chosen by NPV method.