1. Chapter – 5 & 6: NPV & Other Investment Rules, Cash flows
NPV Rule
Determining Cash flows
Payback period Rule
Discounted Payback Period
Internal Rate of Return
Independent VS Mutually Exclusive
Profitability Index

2. Net Present Value Rule
Investment decisions from the perspective of corporate finance is known as capital budgeting.
Net present value is one of the criteria to choose between capital budgeting projects.
NPV is the difference between intrinsic value and the cost of the project
NPV = (PV of future cash flows) – cost
NPV Rule: Accept the project if NPV is positive, reject if NPV is negative.

3. Net Present Value Rule
Example: The Alpha Corporation is considering investing in a riskless project costing $100. The project receives $107 in one year and has no other cash flows. The discount rate is 6%. The NPV is
This example deals with a riskless project which is impossible in reality. To incorporate the risk in calculation the discount rate can be increased, which will be discussed in later chapter

4. Net Present Value Rule Benefits of NPV:
One way of determining the value of a firm is to add the values of different projects, divisions, or other entities within the firm.
This property is called “value additivity” and it implies that the contribution of any project to the firm’s value is the NPV of the project.
NPV uses cash flows and not accounting profit
NPV uses all cash flows of the project including the initial cost and salvage value
NPV discounts the cash flows properly

5. Determining the Cash Flows
The cash flows that should be included in a capital budgeting analysis are those that will only occur if the project is accepted
These cash flows are called incremental cash flows
Cash basis calculation is needed not accrual basis
The stand-alone principle allows us to analyze each project in isolation from the firm simply by focusing on incremental cash flows

6. Determining the Cash Flows
Sunk costs – costs that have already been incurred in the past and cannot be removed
Should not be considered in investment decision
Opportunity costs – the most valuable alternative that is given up if a particular investment is undertaken.
Should be included in investment decision calculations
Always an outflow (negative) adjusted with initial outlay
Side effects
Positive side effects – benefits to other existing projects
Negative side effects (a.k.a. erosion) – costs to other existing projects

7. Determining the Cash Flows
Changes in net working capital – the extra amount of cash required for daily operations of the project
Should be included in the investment decision
Financing costs – interest expense, dividends, principal paid etc.
Should not be included in investment decision
These cashflow do not depend on operation.
Taxes – If a particular component is taxed then after-tax cashflow needs to be considered.

8. Determining the Cash Flows
Incremental project cash flows with all these components suggest that it is the Free Cash Flow (FCF) of the project
Another name is Cash Flow From Asset (CFFA)
FCF = EBIT(1-T) + Depreciation – Change in NWC – Change in capital expenditure

9. Payback Period Rule
Payback Period is the method for measuring the time it takes to recover the initial cost of a project
If a project requires an initial investment of $50,000 and the following cash flows of $30,000; $25,000; and $10,000 then its payback period is
-$50,000 + $30,000 + $20,000 (out of $25,000)= 0
Payback = 1 + (20,000/25,000) = 1.8 years
Payback period rule: Set a cutoff date and select projects with payback shorter than cutoff.

10. Payback Period Rule Problems of Payback Period:
Payback period does not consider time value of money
Payback period does not consider the cash flows after the payback
The choice of the cutoff date is random and does not have any proper standard.

11. Discounted Payback Period
To address the timing issue of the payback period an alternative method used is discounted payback period.
Discounted payback period is the method for measuring the time it takes to recover the initial cost of a project with the present value of all the future cash flows.

12. Discounted Payback Period
Suppose the discount rate is 10% and the cash flows on a project are given by - $100, $50, $50, $20.
The discounted cash flows are: [-$100, ($50/1.1), ($50/1.12), ($20/1.13)] = (-$100, $45.45, $41.32, $15.03)
Discounted period is 2 + [( )/15.03] = 2.88 years

13. Internal Rate of Return (IRR)
A project’s IRR is the discount rate that forces the PV of cash inflows to equal the cost
This is equivalent to forcing the NPV to equal zero.
Thus IRR does not depend on market interest rate. It is completely intrinsic.
There is no fixed formula to calculate IRR other than the trial and error methods to make NPV zero.
IRR Rule: Accept the project if IRR is greater than discount rate, reject it if IRR is less than discount rate.

14. Internal Rate of Return (IRR)
The IRR rule mentioned in the previous slide is applicable only to projects which has the cash flow pattern of a single outflow followed by several inflows.
In this sequence the decision of NPV and IRR almost always match
If the pattern of cash flow is an inflow followed by outflows then the rule is reversed.
If the pattern involves several changes of cash flow signs (i.e. outflow, inflow, inflow, outflow etc.) then there are multiple IRRs for a single project

15. Internal Rate of Return (IRR)
IRR= Ra (NPVa) * (Rb - Ra)
(NPVa - NPVb)
Here,
Ra = discount rate that gives the positive net present value
NPVa = positive NPV
NPVb = negative NPV
Rb = discount rate that gives the negative net present value

16. Modified IRR (MIRR)
When multiple IRR arises an alternative method can be modified IRR (MIRR)
MIRR combines multiple cash flows until only one change of sign remains and then the IRR rule is applied.
Using the discount rate the future cash outflows are discounted to present time
They are then added with the initial investment to have single negative cash flow while the others are positive.
Then the IRR method is applied

17. The Rule Chart

18. Independent VS Mutually Exclusive
The rules of capital budgeting decisions discussed so far are applicable to choose in between independent projects only.
Independent projects are those whose acceptance or rejection is independent of each other or any other projects.
These rules will be different in cases of mutually exclusive projects.
If two projects are mutually exclusive then you can accept either one and have to reject the other or reject both. You cannot accept both projects.

19. Independent VS Mutually Exclusive
Mutually Exclusive Investment Rules:
Accept the project with the higher NPV if both NPV are positive.
If both are negative then reject both
Accept the project with the shorter payback or discounted payback period if both are below cutoff date.
If both are above cutoff date then reject both
Accept the project with higher IRR if both are above discount rate.
If both are below discount rate then reject both

20. Profitability Index
Profitability Index (PI) = (PV of cash flows after initial investment)/Initial investment
Very similar to NPV
Does not work with mutually exclusive projects. Then revert back to NPV.
PI Rule: Accept project if PI>1, reject if PI<1