Appunti di Corporate Finance

THREE POINTS ABOUT NPV

1. The NPV rule recognizes that a dollar today is worth more than a dollar tomorrow

2. Net present value depends solely on the forecasted cash flows from the project and the opportunity cost of capital

3. Because present values are all measured in today's dollars, you can add them up

Stock Price Impact of Good vs. Bad Investment Decisions

(Assume P = $100; EPS = 10; g=0; & a t=1 new project costs $10)

Project costs $10.00 (EPS ) NPV=-10+C/r, where r=.101

Cost of project wipes out dividend for year 1; NPV is calculated at year 1. To find the impact on P , discount for one year at r=.10

Payback

Payback period: The number of years it takes before the cumulative cash flow equals the initial

investmentPayback rule: Accept a project if its payback period is less than some specified cutoff period

Consider the following three projects

Project C C C C Payback Period NPV at0 1 2 3 (years) 10%

A -2,000 500 500 5,000 3 +2,624

B -2,000 500 1,800 0 2 -58

C -2,000 1,800 500 0 2 +50

In NPV rule, which project we will accept and reject ? accept +2,624 and +50; reject -58

How about in Payback rule?  If a cutoff period of two years B) 2 (payback period); C) 2 (payback period); NO accept A) 3 (payback period)

If a cutoff period of three or more years I accept A,B,C so 3,2,2

Regardless of the choice of cutoff period, the payback rule gives different answers from the NPV rule

Payback Rule cutoff date: 2 years

1. The Payback rule ignores all cash flows after the cutoff date

2. The payback rule gives equal weight to all cash flows before the cutoff date

INTERNAL (OR DISCOUNTED-CASH-FLOW) RATE OF RETURN

• The discounted – cash-flow (DCF) rate of return or internal rate of return

(IRR) is the project rate of return that gives a zero NPV

Internal Rate of Return Example:

You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

2,000 4,000 = - + = NPV

4,000 0 IRR 28.08% + +1 2(1 IRR ) (1 IRR )

THE IRR RULE

1. Pitfall 1 – Lending or Borrowing? A→B →NPV A 4→NPV B→or ←borrowing? Are you lending

2. Pitfall 2 – Multiple Rates of return What’s the project’s IRR? → YOU ARE WRONG!!! Certain cash flows can generate NPV=0 at two different discount rates.

3. Pitfall 3 – Mutual Exclusive Projects In IRR rule, which project you will choose? How about NPV rule?

4. Pitfall 4 – What Happens When There is More than One Opportunity Cost of Capital

• Term Structure Assumption

• We assume that discount rates are stable during the term of the project.

• This assumption implies that

All funds are reinvested at the IRR.

This is a false assumption.

CAPITAL RATIONING

Capital Rationing - Limit set on the amount of funds available for investment.

Soft Rationing - Limits on available funds imposed by management.

Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market.

PROFITABILITY INDEX

When resources are limited, the profitability index (PI) provides a tool for selecting among various project combinations and alternatives.

A set of limited resources and projects can yield various combinations.

The highest weighted average PI can indicate which projects to select.

Survey Data on CFO Use of Investment Evaluation Techniques

04E - MAKING INVESTMENT DECISIONS WITH NET PRESENT VALUE RULE

MERRICK -

Applying the Net Present Value Rule

An Example Project

Investment Timing

Equivalent Annual Cash Flows

Implementing Capital Budgeting Decision Rules

Most capital budgeting decision

flowsAsking the Right Question

• You should always ask yourself "Will this cash flow occur ONLY if we accept the project?"
• If the answer is "yes", it should be included in the analysis because it is incremental
• If the answer is "no", it should not be included in the analysis because it will occur anyway
• If the answer is "part of it", then we should include the part that occurs because of the project

What To Discount

• Estimate Cash Flows on an Incremental Basis
• Do not confuse average with incremental payoffs
• Include all incidental effects
• Forecast Sales Today and Recognize After-Sales Cash Flows to come Later
• Do not forget working capital requirements
• Include opportunity costs
• Forget sunk costs
• Beware of allocated overhead costs
• Remember salvage value (Positive vs negative salvage value Cleaning up expenditures could be the huge negative cost)

Treat Inflation Consistently

• Use nominal

rates to discount nominate cash flows

• Use real rates to discount real cash flows
• You will get the same results, whether you use nominal or real figures

Inflation

Example:

You invest in a project that will produce real cash flows of -$100 in year 0 and then $35, $50, and $30 in the three respective years. If the nominal discount rate is 15% and the inflation rate is 10%, what is the NPV of the project?

-1+ nominal discount rate 1 real discount rate = 1+ inflation rate

Example – using “real” figures

Example – using nominal figures

IM&C’s FERTILIZER PROJECT

• As the newly appointed financial manager of International Mulch and Compost Company (IM&C), you are about to analyze a proposal for marketing guano as a garden fertilizer.
• The equipment needed for this projects costs $10,000,000. The engineering department expects the project will take one year to dismantle and the equipment can be sold for $1,949,000 in year 7. Use straight line

Depreciation in the first analysis with a six-year life and the equipment depreciated to an arbitrary salvage value of $500,000, which is less than your forecasted salvage value of $1,949,000.

• Any remaining working capital will be recovered in year 7.
• You have received the forecasts presented in Table 1 from various departments. The sales forecast came from the marketing department and the cost of goods sold (COGS) forecast is from the operations and production department.
• "Other costs" include miscellaneous start-up costs in years 0 & 1 and general and administrative costs in years 1 - 6.
• The tax rate is 35% and the Cost of Capital is 20%. Assume all tax credits can be used at the time they occur.

Example - IM&C's Fertilizer Project

The project's income statement ($ thousands):

FCF at time 0 (Initial Investment)

FCF during Operations (Operating Cash Flows)

Use the Straight-Line Depreciation: OCF = (Sales -

project's cash-flow forecast in year 3 ($ thousands) :FCF at Project End (Non-Operating Cash Flows)

Example – IM&C's Fertilizer Project's initial cash-flow analysis ($ thousands) :IM&C's Guano Project

• NPV using nominal net cash flows from previous slide @ 20% discount rate

Investment Timing

Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision.

A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow.

Example: You own a large tract of inaccessible timber. To harvest it, you have to invest a substantial amount in access roads and other facilities. The longer you wait, the higher the investment required. On the other hand, lumber prices will rise as you wait, and the trees will keep growing, although at a gradually decreasing rate. Given the following data and a 10% discount rate,