Lecture 8Lecture 8

Strategy and Analysis in using NPVStrategy and Analysis in using NPV

The NPV analysis then gives a precise formula for deciding whether or not to proceed with the investment project.

Applying NPV analysis requires judgements about revenues, expenses, depreciation tax shields, true economic lives of plant and equipment, and the appropriate discount rate.

Precision of method is not the same as precision of result.

The validity of the assumptions is also critically important.

garbage-in, garbage-out

NPV analysis

Judging the results of an analysis

NPV is best used as part of an iterative procedure :

identify potential positive NPV projects

estimate the components needed for a formal NPV analysis

critically examine the results

Normal profits correspond to zero NPV projects.

introducing a new product that may take time to duplicate

using existing facilities to produce new products more cheaply

using existing facilities more intensively to expand output at a lower cost

creating or exploiting barriers via advertising, dealer network, etc, thereby raising costs for new entrants to market

A high NPV requires impediments to competition such as :

Judging the results of an analysis (continued)

Exploiting legal barriers to limit or prohibit entry (example)(example) patents, licenses, zoning, environmental and safety laws

Introducing new production technologies or management techniques that reduce costs and may take time to duplicate

Finding new uses for existing resources, such as discovering minerals or converting an apartment block to a condominium

Obtaining a change in property rights that raises the value of existing resources (example)(example) getting land re-zoned for commercial cites

A high NPV requires impediments to competition such as : (continued)

Judging the results of an analysis (continued)

Stock market reaction reveals other valuation of the project.

If the reaction disagrees, then the underlying assumptions should be re-examined.

NPV analysis separates assumptions from conclusions, and forces you to present the underlying reasoning that can be viewed by others.

Judging the results of an analysis (continued)

A wide range of NPV’s, with many large negative and many positive values, should make you feel skeptical. Reinvestigate those cases.

Sensitivity analysisSensitivity analysis examines how changes in underlying assumptions affect NPV using a range of values for annual revenues, costs, etc.

The NPV table can also indicate the assumptions having the biggest effect on NPV and where added effort would be most useful.

A table of NPV’s can then be obtained where each variable in turn is allowed to take on its range of values.

Example: Sensitivity analysis

Consider a project with expected cash flows as follows (in $M) :

Revenues in years 1~5 of $6000 derived from a market size of 10000 units, market share of 30% , and price of $2, variable costs of $3000 ( $1 per unit) and annual fixed cost of $1791.

Corporate tax rate of 34% , and appropriate discount rate of 15%

Initial investment is $1500, depreciated on a straight-line basis over 5 years with a zero salvage value, so yearly depreciation = 300

Sensitivity analysis example (continued)

Tax = 0.34 * 909 = 309

Annual cash flow is (-1500, 900, 900, 900, 900, 900)

= ( 1 - TC ) * ( revenues - expenses - depreciation )

+ ( depreciation )

= (net income) + (depreciation)

= (909 - 309) + 300 = 900

94.1516

15.01

9001500

5

1

i

iNPVNPV

Annual taxable income

= revenue - costs (expenses) - depreciation

= ( price*sales ) - ( variable costs + fixed costs ) - depreciation

= (2*3000) - (3000 + 1791) - 300 = 909

Sensitivity analysis example (continued)

Table 1 shows how sensitive the NPV is to separate 1% variations in each of the forecasts underlying this analysis.

Everything else are kept at the expected level.

Variable NPV (-) Change % NPV (+) Change %

Market size $1,450.37 -4.38% $1,583.11 4.38%Market share $1,450.37 -4.38% $1,583.11 4.38%Price $1,383.99 -8.75% $1,649.48 8.75%Variable cost $1,583.11 4.38% $1,450.37 -4.38%Fixed cost $1,556.36 2.61% $1,477.11 -2.61%Investment $1,528.32 0.76% $1,505.16 -0.76%Discount rate $1,527.48 0.71% $1,506.06 -0.71%

1% decrease 1% increase

Judging the results of an analysis (continued)

Scenario AnalysisScenario Analysis alters several variables.

For example, deviations in variable costs and fixed costs are likely to be positively correlated.

Break-even Analysis Break-even Analysis calculates sales needed to make NPV = 0.

Distinguish fixed and variable costs, since variations in output will affect costs differently when more of them are variable. Let :

EAC = annual equivalent cost of initial investment

F = annual fixed cost

V = variable cost per unit of output

P = price of a unit of output

D = annual depreciation allowances (depreciation tax shield)

TC = corporate tax rate

Judging the results of an analysis (continued)

Then the after-tax costs of the project, independent of output, are

CC TDTFEACC 10

And breakeven sales is given by

C

CC

TVP

TDTFEAC

1

1

Decision Tree

A decision treedecision tree breaks complex business into components by setting out key decisions as a series of “yes or no” decision forks and subsequent random outcomes as additional forks with probabilities.

For example, consider an oil drilling :

First choose whether or not to drill an exploratory well.

Depending on the outcome, decide whether to invest further.

Assume the following data for the example :

discount rate for both phases of the project is 10 %

initial investment cost of exploratory well is $10M

production capacity, if desired, will cost $100M in 1 year.

the cash flow from the well starts 2 years from the year 1 investment, and will only be known after the year1 investment has been made

Decision Tree (continued)

The probabilities could be based on statistical analysis of similar past projects, information about seismic experimental studies undertaken prior to drilling exploratory well, etc.

NPV for each outcome is multiplied by the probability

Expected NPV at each chance fork is sum of the products

Choose the highest expected NPV branch at “decision forks”

Expected NPV of experiment is expected NPV for the decision forks times the probabilities of the experimental outcomes

Expected NPV can then be calculated, starting from the right of the decision tree and working back to the left :

Decision Tree (continued)

Future values from the final project were discounted for time taken to conduct the experiment.

Notice that

The discount rate for the experimental decision may be higher than the discount rate for the final investment due to higher risk.

Cash flows starting 2 years from the year 1 investment (I.e. in year 3) are discounted to year 0.