Assuming a specific single project with normal cash flows and a cost of capital

Question

Assuming a specific single project with normal cash flows and a cost of capital of 10%, which of the following statements will ALWAYS be true: (Note: more than one of the following statements may be true; you must record ALL of the statements that are true to receive any credit. That is, if statements a, b and c are ALWAYS true, you must record, A, B, C as the correct answers to this problem to receive any credit. Any other letter or combination of letters will be marked wrong). If NPV > 0, then a simple sum of the cash inflows of the project will always be greater than the cost of the project (i.e, the year 0 cash flow). If NPV > 0 at the stated cost of capital (i.e., 10%), then NPV will also be > 0 at a cost of capital of 12%. If NPV>0, then Profitability Index >O O If NPV > 0, then Payback Period > 0. If NPV > 0, then IRR > 0

Explanation / Answer

NPV=-Initial Investment+PV of cash inflows
So, If NPV >0 then PV of cash inflows>Initial Investment
Then
CF1/(1+r)+CF2/(1+r)^2...........>CF0
So, CF1+CF2+.........>CF0
Simple sum of cash inflows must be greater than initial investment

Payback period is the time required to cover the initial investment
Payback cannot be less than zero
Hence, if NPV>0 then Payback period>0

PI=NPV/Initial Investment+1
So, if NPV>0, then PI>1
if PI>1 then PI is also greater than 0

If NPV is greater than 0 at 10%, it need not necessarily be greater than 0 at 12% as well

If NPV is greater than 0 then IRR must be greater than the cost of capital
Hence, if NPV>0 then IRR>cost of capital and hence if NPV>0 then IRR>0

Accept all projects which are having positive NPV

Hence, accept B,C,D& E

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