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### CHAPTER 12

### Graphical Illustration of NPV and IRR

THE CAPITAL BUDGETING DECISION

Capital Expenditures Decision

- CE usually require initial cash outflows in hope of future benefits or cash inflows
- Examples: new plant construction, acquisition of business, purchase of new machine, etc.
- Projects often last for more than a year
- The longer the time horizon, the greater the uncertainty

Areas of Uncertainty in CE Decision

- Expected cash flows
- Product life
- Interest rates
- Economic conditions
- Technological change

Capital Budgeting

- To see if the CE is economically acceptable - if it creates or adds value to the firm
- To examine the CE from an investment perspective
- The basic concept is to determine if it makes sense to commit to an initial cash outflows in order to receive future cash inflows

Project Evaluation

- Discount Rate = Cost of Capital
- Positive NPV indicates that the yield or rate of return on the project exceeds the cost of capital (thus add value to the firm)
- Project is financially acceptable when the PV of the total cash inflows greater than the PV of the total cash outflows ( +ve NPV)

Project B cont’

- Both projects A and B require an initial capital outflow of $10000
- Both of them will generate a total return of $12000 in the next three years
- However, project A has a positive NPV while project B has a negative NPV
- Why?

Project A

Yr 0 -$10,000

Yr 1 $5,000

Yr 2 $5,000

Yr 3 $2,000

Project B

Yr 0 -$10,000

Yr 1 $2,000

Yr 2 $5,000

Yr 3 $5,000

Cash Flows of Project A & BReasons

- For Project A, the cash inflows mainly occur at the first two years
- For Project B, the cash inflows mainly come in at the last two years
- Due to the time value of money, money received earlier has higher value than that received later
- Hence, Project B is not acceptable -(negative NPV)

Flexibility of NPV - Using various discount rates across time

- The longer the time horizon, the higher the risk
- Sometimes, we may have to use a higher discount rate for income in the latest year
- Instead of 10%, we may use 12% to discount the latest cash inflow at the end of third year
- NPV method provides such a flexibility

Flexibility of NPV – allow reversal of cash flows

- NPV method can be applied to any type of cash flows even cash flows with reversal
- Cash flows with reversal means that there are more than one cash outflows
- Example: a 2-year project with cash flows:
- Yr 0 – Initial cash outflow – (-$1000)
- Yr 1 – Cash inflow – (+$5000)
- Yr 2 – Another cash outflow – (-$3000)

Profitability Index

- It is a variation of the NPV method
- Profitability index (PI)

= PV of cash inflows/PV of cash outflows

- If PI > 1, PV of cash inflows is greater than PV of cash outflows. That is NPV > 0
- Hence project with PI > 1 is financially viable

Another method - IRR

- IRR = Internal Rate of Return
- The IRR is the discount rate at which the PV of cash inflows = PV of the cash outflows
- I.E., IRR is the discount rate which makes the NPV = 0
- Project is financially acceptable when the IRR is greater than the cost of capital

Project Evaluation

- Project A has an IRR of 11.16% which is higher than the cost of capital, 10%. Hence project A is financially acceptable.
- Project B has an IRR of 8.53% which is lower than the cost of capital, 10%. Hence project B is financially not acceptable.

Why bother to use IRR?

- Since both NPV and IRR generate similar results, why bother to use IRR
- Yield derived from IRR may be more comprehensible than the absolute value derived from NPV
- In fact, we use IRR when we cannot use the cost of capital (the risk of the project differs from the risk of the firm)

Limitations of IRR method

- A single discount rate (the IRR) throughout the project life – inability to account for cash flows of different risk levels
- Possibly unrealistic to assume reinvestment of the generated cash inflow at the IRR
- Inapplicable when more than one reversal of cash flows exists – will generate multiple IRRs in that case

See Examples Below

Investment A

Yr 0 -10000

Yr 1 5000

Yr 2 5000

Yr 3 2000

Investment B

Yr 0 -10000

Yr 1 1500

Yr 2 2000

Yr 3 2500

Yr 4 5000

Yr 5 5000

Cash Flows of Investment A&B6000

4000

2000

IRR= 14.33%

0

15

5

10

IRR= 11.16%

Discount Rate

NPV Profile – NPVs at different Discounting rateINV. B

INV. A

Investment B

Yr 0 -10000

Yr 1 1500

Yr 2 2000

Yr 3 2500

Yr 4 5000

Yr 5 5000

Investment C

Yr 0 -10000

Yr 1 9000

Yr 2 3000

Yr 3 1200

Cash Flows of Investment B & CNPV Profile with crossover

NPV

6000

Crossover point

INV.B

4000

2000

INV.C

IRR= 14.33%

0

15

20

5

10

IRR= 22.49%

Discount Rate

Where are we?

- How to raise capital?
- We have learned the three ways of raising long-term capital for a firm. What are they?
- How to use the capital to generate more money?
- Underlying principle – to generate an investment return that is greater than cost of capital
- The lowest required rate of return = cost of capital

Project Valuation

- Similar to the valuation of financial instruments, we must assess the fair market value for any capital expenditure project.
- The highest price we pay is the present value of expected cash flows (derived from the project) discounted at the rate equivalent to the cost of capital
- Basic concept – lowest rate of return = highest price to be paid

Cash Flows Determination

- Net of tax i.e. after tax net cash flow
- Gross of all financing costs (they have been reflected in the discount rate)
- Shortfalls:

- Future projection may base on extrapolation

- Bias built into the cash flows estimation

- Over/under estimate of the inflation

- Neglect other qualitative factors such as better corporate image, fairer treatment of employee, etc

Capital Rationing

- Management, for some reasons, may impose a dollar constraint in certain kind of investment
- Projects become mutually exclusive
- Project is selected based on the amount of benefit generated by the project
- That is, projects with the greatest NPV or the highest IRR

Net

Total Present

Project Investment Investment Value

- CapitalA $2,000,000 400,000 rationing B 2,000,000 380,000
- solution C 1,000,000 $5M 150,000
- Best D 1,000,000 100,000
- solution E 800,000 $6.8M 40,000
- F 800,000 (30,000.)

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