ANS

1) Net Present Value

Net Present Value(NPV) is a formula used to determine the present value of an investment by the discounted sum of all cash flows received from the project. When a company or investor takes on a project or investment, it is important to calculate an

estimate of how profitable the project or investment will be. In the formula, the -C0 is the initial investment, which is a negative cash flow showing that money is going out as opposed to coming in. Considering that the money going out is subtracted from the discounted sum of cash flows coming in, the net present value would need to be positive in order to be considered a valuable investment.

Present Value NPV Machine A 12.41 -12.59 Machine B 13.61 -26.39

Accept the project only if its NPV is positive or zero. Reject the project having negative NPV. While comparing two or more exclusive projects having positive NPVs, accept the one with highest NPV.

NPV =R1

+R2

+R3

+ ... − Initial Investment(1 + i)1 (1 + i)2 (1 + i)3

Decision: Both the machine doesn’t give positive NPV, so replacement can’t considered.

2) Profitability Index

Profitability index is an investment appraisal technique calculated by dividing the present value of future cash flows of a project by the initial investment required for the project. Profitability index is actually a modification of the net present value method. While present value is an absolute measure (i.e. it gives as the total Rupee figure for a project), the profitability index is a relative measure (i.e. it gives as the figure as a ratio).

Decision Rule

Accept a project if the profitability index is greater than 1, stay indifferent if the profitability index

is zero and don't accept a project if the profitability index is below 1.

Profitability index is sometimes called benefit-cost ratio too and is useful in capital rationing since it helps in ranking projects based on their per dollar return.

Profitability Index

Machine A 0.50

Machine B 0.34

Decision: Both the machine doesn’t give greater than one , so replacement can’t considered.

3) Pay Back Period

The payback period formula is used to determine the length of time it will take to recoup the initial amount invested on a project or investment. The payback period formula is used for quick calculations and is generally not considered an end-all for evaluating whether to invest in a particular situation. One issue is that the payback period formula

does not look at the value of all returns.

Payback PeriodMachine A 0.47Machine B 0.56

Decision: Shorter payback period for Machine A, so option available with Machine A.

4) Discounted payback method:

In discounted payback period we have to calculate the present value of each cash inflow taking the start of the first period as zero point.

Discounted Payback Period = A + BC

Where,

   A = Last period with a negative discounted cumulative cash flow;

   B = Absolute value of discounted cumulative cash flow at the end of the period A;

   C = Discounted cash flow during the period after A.

Machine A: 3 Years + -5.842/9.562 =3 yrs +.61 = 3.61

Machine B = 3 years +-7.3186/11.611 = 3 years +.63 = 3.63 Years

Decision Rule

If the discounted payback period is less that the target period, accept the project. Otherwise reject.

Discounted payback period is more reliable than simple payback period since it accounts for time value of money. It is interesting to note that if a project has negative net present value it won't pay back the initial investment.

Since Disocounted payback period is less in the case of Machine A, Machine A can select.

Calculation.

Outflow 1 2 3 4 5 Machine A 25 0 5 20 14 14 Machine B 40 10 14 16 17 15 Present value 0.9091 0.8264 0.7513 0.683 0.6209 PV Machine A 0 4.132 15.026 9.562 8.6926 PV Machine B 9.091 11.5696 12.0208 11.611 9.3135 Cumulative DCF A -25 -25 -20.868 -5.842 3.72 12.4126

Cumulative DCF B -40 -30.909-

19.3394 -7.3186 4.2924 13.6059

Discounted Payback A 3 to 4 Years

Discounted Payback B 3 to 4 Years