Project Analysis and Forecast Risk

ADVANCE-Managerial Finance

Class Notes for Chapter 11

D.B. Hamm—updated Jan. 2006

Evaluating NPV Estimates—The Basic Problem

Basic Problem—How reliable is our NPV estimate for new project(s) under consideration?– Projected vs. actual cash flows– Forecasting risk—possibility that errors in

projected cash flows will lead to incorrect decisions

– Also called “estimation risk” (same) “What If” analysis may help us evaluate and

minimize forecasting/estimation risk

“What If” Analysis (overview)

Scenario analysis– Ask basic “What if?” questions and rework NPV

estimates• Worst case—good start point—what is the

minimum NPV for the project?• Best case—upper limit bound of project NPV• Base case—most likely outcome assumed

(probably some midpoint between best & worst)

“What If” Analysis (continued)

Sensitivity analysis—– Impact on NPV and/or IRR when one variable is

changed (up or down) and other variables remain at “base case”

– If our estimate of NPV or IRR is very sensitive (changes significantly) to relatively small changes in some component, forecasting risk for that variable is high

“What If” Analysis (slide 3):

Simulation analysis– Combine scenario and sensitivity analysis to

calculate impact of varying changes – Use of a computer (spreadsheet or other software)

is essential– Still may be impossible to forecast every possible

combination of variables, but should give us some trends

Illustration:Wally's Widget WorksNew Project Estimate Scenario

Base Worst BestUnit Sales 6,000 4,500 7,500x Selling price per unit $15 $15 $15Sales Revenue $90,000 $67,500 $112,500-Variable Costs at $8 per unit -$48,000 -$36,000 -$60,000Contribution Margin $42,000 $31,500 $52,500- Fixed costs (other than depr.) -$12,000 -$12,000 -$12,000- Depreciation -$11,000 -$11,000 -$11,000EBIT $19,000 $8,500 $29,500Taxes @ 40% -$7,600 -$3,400 -$11,800Net Income $11,400 $5,100 $17,700

OCF (EBIT+ Depr-Taxes) $22,400 $16,100 $28,700

Pres. Value (4 yrs x above at 12%) $68,037 $48,901 $87,172Less Original Investment -$60,000 -$60,000 -$60,000NPV $8,037 ($11,099) $27,172

IRR 18.22% 2.89% 32.15%

Once our template is set up we may rerun with any variations required

Break-Even Analysis (1):

Fixed and Variable Costs– VC varies with quantity produced/sold– FC remains constant (in relevant range)– Separate depreciation (D) for cash flow purposes

TC = VC + FC + D– Or S = v x Q + FC+D

Therefore S – VC – FC – D = 0 at break even point (“accounting break even”)

Accounting break even occurs where net income from project = 0

Break Even Analysis (2):

Since S – VC – FC – D = 0 at break even And since S = p x Q (selling price x quantity) And VC = v x Q (vc per unit x Q) Then (p x Q)-(v x Q) – FC – D = 0 Finally accounting break even quantity is:

Q = FC + D

p - v

Accounting Break Even (illustration)

Selling price per unit = $20, variable cost = $11 per unit, fixed costs other than depreciation = $60,000 and depreciation = $20,000. Find accounting break even quantity:

Q = FC + D / p - v

Q = 60,000 + 20,000 / 20 -11

Q = 80,000 / 9

Q = 8,889 units

Cash Flow Break Even:Operating cash flow: OCF = EBIT + Depr – Taxes

In these illustrations we will assume Taxes = 0 (calculating break even on a pre-tax basis), so

OCF = EBIT + D

OCF =( S –VC – FC – D) + D

OCF = (P x Q)-(v x Q) – FC

OCF = Q (p-v) - FC

Q (break even) = FC (without depr.)

p – v

Cash flow break even occurs where project OCF = 0

Cash Flow B/E (illustration):Using previous illustration:

Selling price per unit = $20, variable cost = $11 per unit, fixed costs other than depreciation = $60,000 and depreciation = $20,000. Find cash flow break even quantity

Q = FC / p – v

Q = 60,000 / 20 – 11

Q = 60,000 / 9

Q = 6,667 units

Note: B/E quantity for cash flow is less than required for accounting break even, but project at cash b/e only can never pay back its original investment. IRR = -100%

Financial Break Even: Financial break even occurs when NPV of

project = 0 – Discounted payback = project life– Project NPV = 0– Project IRR = required rate of return

Formula for break even:

Q = FC + OCF*

p – v

*Where OCF results in a zero NPV

Financial B/E (illustration):

Our previous project seeks a 12% return over 5 years. Original investment was $100,000. Required OCF per year would therefore be OCF = 100,000 / 3.6048 (see table for PV annuity factor @ 12% for 5 periods)

OCF = $27,741 ( 100,000 / 3.6048 rounded to nearest $1)

Q = FC + OCF / p – v

Q = 60,000 + 27,741 / 20 – 11

Q = 87,741 / 9

Q = 9,749 units (considerably more than cash flow b/e, even more than accounting b/e, but this now factors recovery of original capital investment at 12% over 5 yrs)

Problems (group case):

PAUSE FOR CLASS CASE:

Operating Leverage

Operating leverage is the degree to which a project relies on fixed costs

Degree of operating leverage = % change in OCF relative to % change in quantity sold

DOL = 1 + (FC/OCF)

Operating Leverage (illustration)

In the case just worked, OCF at base case = $30,000 and FC=$40,000 (output is 14,000 units)

DOL = 1 + (40,000/30,000)

DOL = 1 + 1.3333

DOL = 2.333

Thus a 1% increase in units sold would generate a 2.33% increase in OCF in the base case range. Vice versa, a 1% decrease in sales = 2.33% decrease in OCF.

Operating Leverage (conclusion)

DOL will decline if Q increases substantially. At best case scenario DOL = 1+(40,000/45,000) = 1.889 Conversely at worst case scenario DOL = 1 +(40,000 / 15,000)=3.667

This is because as fixed costs decline as a percent of operating cash flow (quantities sold increases and OCF therefore increases, but fixed costs stay constant), the leverage effect diminishes. If fixed costs as a % of OCF increases (as when sales decline, thus OCF declines, but fixed costs don’t change), leverage effect increases.

End of Ch. 11 Presentation