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FIN 5823 FINANCIAL MODELING ______________________________________________ Inventory and Investment Management

Inventory Management

What is inventory?

Inventory is the raw materials, component parts, work-in-process, or finished products that are held at a location in the supply chain.

Why do we care?

At the macro level:

Investment in inventory is currently over $1.25 Trillion (U.S. Department of Commerce).

This figure accounts for almost 25% of GNP.

Enormous potential for efficiency increase by controlling inventories

Inventory is one of the biggest corporate assets ($).

Sales growth: right inventory at the right place at the right time

Cost reduction: less money tied up in inventory, inventory management, obsolescence

Higher profit

Why do we care?

At the firm level:

Why do we care?

Each of Solectron’s big customers, which include Cisco, Ericsson, and Lucent was expecting explosive growth for wireless phones and networking gear….when the bottom finally fell out, it was too late for Solectron to halt orders from all of its 4,000 suppliers. Now, Solectron has $4.7 billion in inventory. (BW, March 19, 2001)

“When Palm formally reported its quarterly numbers in June, the damage was gruesome. Its loss totaled $392 million, a big chunk of which was attributable to writing down excess inventory - piles of unsold devices.” (The Industry Standard, June 16, 2001)

“Liz Claiborne said its unexpected earnings decline is the consequence of higher than anticipated excess inventories”. (WSJ, August 1993)

How do you manage your inventory? How much do you buy? When?

Soda

Milk

Toilet paper

Gas

Cereal

Cash

What Do you Consider?

Cost of not having it.

Cost of going to the grocery or gas station (time, money), cost of drawing money.

Cost of holding and storing, lost interest.

Price discounts.

How much you consume.

Some safety against uncertainty.

Costs of Inventory

Physical holding costs:

out of pocket expenses for storing inventory (insurance, security, warehouse rental, cooling)

All costs that may be entailed before you sell it (obsolescence, spoilage, rework...)

Opportunity cost of inventory: foregone return on the funds invested.

Operational costs:

Delay in detection of quality problems.

Delay the introduction of new products.

Increase throughput times.

Hedge against uncertain demand

Hedge against uncertain supply

Economize on ordering costs

Smoothing

Benefits of Inventory

To summarize, we build and keep inventory in order to match supply and demand in the most cost effective way.

Modeling Inventory in a Supply Chain…

Warehouse

Retail

Supplier

Home Depot

“Our inventory consists of up to 35,000 different kinds of building materials, home improvement supplies, and lawn and garden products.”

“We currently offer thousands of products in our online store.”

“We offer approximately 250,000 more products through our special order services.”

Different types of inventory models

Multi-period model

Repeat business, multiple orders

Single period models

Single selling season, single order

Multiperiod model

Key questions:

How often to review?

When to place an order?

How much to order?

How much stock to keep?

orders

Supply

On-hand

inventory

Ordering costs

Holding costs

Consider the following setting: customer demand is satisfied from on-hand inventory. For replenishment, we review our stocks on a periodic basis (say, every week) and place orders to an upstream supplier. There is a non-negligible lead time for replenishment. We refer to the total of on-hand stock (that can be used to meet customer demand) and the pipeline stock (inventory on the trucks) as the inventory position.

To balance out inventory cost with customer service, we have three decisions to make: how often to review the stock, when to place a replenishment order, and how much to order. Together, these three decisions constitute an inventory control policy.

Multiperiod model – The Economic Order Quantity

Demand is known and deterministic: D units/year

We have a known ordering cost, S, and immediate replenishment

Annual holding cost of average inventory is H per unit

Purchasing cost C per unit

Supplier

Demand

Retailer

What is the optimal quantity to order?

Total Cost = Purchasing Cost + Ordering Cost + Inventory Cost

Purchasing Cost = (total units) x (cost per unit)

Ordering Cost = (number of orders) x (cost per order)

Inventory Cost = (average inventory) x (holding cost)

Finding the optimal quantity to order…

Let’s say we decide to order in batches of Q…

Number of periods will be

Time

Total Time

Period over which demand for Q has occurred

Inventory position

The average inventory for each period is…

Finding the optimal quantity to order…

Purchasing cost = D x C

Inventory cost =

Ordering cost =

x S

x H

So what is the total cost?

TC = D C +

In order now to find the optimal quantity we need to optimize the total cost with respect to the decision variable (the variable we control)

Which one is the decision variable?

What is the main insight from EOQ?

There is a tradeoff between holding costs and ordering costs

Order Quantity (Q*)

Cost

Total cost

Holding costs

Ordering costs

Economic Order Quantity - EOQ

Q* =

2SD

Example:

Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size?

Receive order

Time

Inventory

Order

Quantity

Place

order

Lead Time

If delivery is not instantaneous, but there is a lead time L: When to order? How much to order?

ROP = LxD

Receive order

Time

Inventory

Order

Quantity

Place

order

Lead Time

Reorder

Point

(ROP)

If demand is known exactly, place an order when inventory equals demand during lead time.

D: demand per period

L: Lead time in periods

Q: When shall we order?

A: When inventory = ROP

Q: How much shall we order?

A: Q = EOQ

Example (continued)…

What if the lead time to receive cars is 10 days? (when should you place your order?)

365

D =

R =

365

5000

= 137

So, when the number of cars on the lot reaches 137, order 548 more cars.

Since D is given in years, first convert: 10 days = 10/365yrs

Receive order

Place

order

Lead Time

ROP = ???

Stockout

Point

Unfilled demand

Receive

order

Time

Inventory

Order

Quantity

Place

order

Lead Time

If Actual Demand > Expected, we Stock Out

To reduce stockouts we add safety stock

Receive

order

Time

Place

order

Lead Time

Expected

Lead-time

Demand

Inventory

Level

ROP =

Safety

Stock +

Expected

Demand

Order Quantity

Q = EOQ

Expected

LT Demand

Safety Stock

Service level

Safety

Stock

Probability

of stock-out

Decide what Service Level you want to provide

(Service level = probability of NOT stocking out)

Service level

Safety

Stock

Probability

of stock-out

Safety stock =

(safety factor z)(std deviation in LT demand)

Read z from Normal table for a given service level

Caution: Std deviation in LT demand

Variance over multiple periods = the sum of

the variances of each period (assuming

independence)

Standard deviation over multiple periods is

the square root of the sum of the variances,

not the sum of the standard deviations!!!

Average Inventory =

(Order Qty)/2 + Safety Stock

Receive

order

Time

Place

order

Lead Time

Inventory

Level

Order

Quantity

Safety Stock (SS)

EOQ/2

Average

Inventory

How to find ROP & Q

Order quantity Q =

To find ROP, determine the service level (i.e., the probability of NOT stocking out.)

Find the safety factor from a z-table or from the graph.

Find std deviation in LT demand: square root law.

Safety stock is given by:

SS = (safety factor)(std dev in LT demand)

Reorder point is: ROP = Expected LT demand + SS

Average Inventory is: SS + EOQ/2

Example (continued)…

Back to the car lot… recall that the lead time is 10 days and the expected yearly demand is 5000. You estimate the standard deviation of daily demand demand to be d = 6. When should you re-order if you want to be 95% sure you don’t run out of cars?

Since the expected yearly demand is 5000, the expected demand over the lead time is 5000(10/365) = 137. The z-value corresponding to a service level of 0.95 is 1.65. So

Order 548 cars when the inventory level drops to 168.

Investment Evaluation

INVESTMENT EVALUATION

Investment Evaluation

The Finance Function

Financial Markets

(Investors)

Operations

(Plant, Equipment, Projects, etc.)

Financial

Manager

(1a) Raise

Funds

(1b) Obligations

(Stocks, Debt, IOUs)

(2) Investment

(3) Cash from

Operations

(5) Dividends or

Interest Payments

The finance function manages the cash flow

(4) Reinvest

Investment Evaluation

The Finance Function

Financial Markets

Operations

Financial

Manager

Investment

Decision

Financing

Decision

How much to invest and in what assets?

Where is the $ going to come from?

Capital Budgeting

Finance focuses on these two decisions

Investment Evaluation

Interaction between Financing & Investment Decisions

Financial Markets

Operations

Financial

Manager

Investment

Decision

Financing

Decision

The interplay of the decisions determines the cost of capital

Cost of Capital

Characteristics

of the

Investment

Investment Evaluation

The Finance Function

The objective of the financial manager and the corporation is to MAXIMIZE THE CURRENT VALUE OF SHAREHOLDERS' WEALTH.

(Taken literally, this means that a firm should pursue policies that maximize its today's quotation in the Wall Street Journal.)

By making investing and financing decisions, the financial manager is attempting to achieve the following objective:

Investment Evaluation

Investment Evaluation in 3 Basic Steps

1) Forecast all relevant after tax expected cash flows generated by the project

2) Estimate the opportunity cost of capital--r (reflects the time value of money and the risk)

3) Evaluation

DCF (discounted cash flows)

NPV (net present value)

Accept project if NPV is positive

Reject project if NPV is negative

IRR (internal rate of return

Accept project if IRR > r

Payback, Profitability Index

ROA, ROFE, ROI, ROCE

ROE

EVA

Investment Evaluation

Forecasting Cash Flows

First, forecast all relevant after-tax expected cash flows

Key is that cash flows must be (a) relevant, costs and income directly affected by the project, and (b) after-tax, cash into the owner’s pocket

Investment Evaluation

Forecasting Cash Flows

This is done by estimating operational parameters

These are based on actual reported performance

This represents a “best guess” about the company’s future performance

Obviously, there is an uncertainty problem but history is used as a guide for what to expect in the future

Investment Evaluation

Evaluating investments involves the following:

1) Forecast all relevant after tax expected cash flows generated by the project

2) Estimate the opportunity cost of capital--r (reflects the time value of money and the risk)

3) Evaluation

DCF (discounted cash flows)

NPV (net present value)

Accept project if NPV is positive

Reject project if NPV is negative

IRR (internal rate of return

Accept project if IRR > r

Payback , Profitability Index

ROA, ROFE, ROI, ROCE

ROE

EVA

Investment Evaluation

1) Depreciation is not a cash flow, but it affects taxation

2) Do not ignore investment in fixed assets (Capital Expenditures)

Do not ignore investment in net working capital

Include only changes in operating working capital. Short-term debt, excess cash and marketable securities should not be accounted for.

Separate investment and financing decisions: Evaluate as if entirely equity financed

5) Estimate flows on a incremental basis

Forget sunk costs: cost incurred in the past and irreversible

Include all externalities - the effects of the project on the rest of the firm - e.g., cannibalization or erosion, enhancement

6) Opportunity costs cannot be ignored

Forecasting Cash Flows: The Ten Commandments

Investment Evaluation

7) Do not forget continuing value (residual or terminal value)

Liquidation value: Estimate the proceeds from the sale of assets after the explicit forecast period. (Recover investment in working capital, tax-shield or fixed assets but missing the intangibles and value of on-going business)

Perpetual growth: Assume cash flows are expected to grow at a constant rate perpetually.

8) Be consistent in your treatment of inflation

Nominal cash flows (including inflation) -- use a nominal cost of capital R

Real cash flows (without inflation) -- use a real cost of capital r

9) Overhead costs

10) Include excess cash, excess real estate, unfunded (over-funded) pension fund, large stock option obligations, and other relevant off balance sheet items.

Forecasting Cash Flows: The Ten Commandments

Investment Evaluation

Forecasting Cash Flows

Cash Flows from Operations

Revenue

- Cost of Goods Sold

- Depreciation (may be in CGS)

- Selling, General & Admin.

= Operating Profit

- Cash Taxes on Operating Profit

= Net Operating Profit After Tax

+ Depreciation

- Capital Expenditures

- Increase in Working Capital

= Cash Flow from Operations

Investment Evaluation

Forecasting Cash Flows

1) Depreciation is not a cash flow, but it affects taxation

Revenue

- Cost of Goods Sold

- Depreciation

- Selling, General & Admin.

= Operating Profit

- Cash Taxes on Operating Profit

= Net Operating Profit After Tax

+ Depreciation

- Capital Expenditures

- Increase in Working Capital

= Cash Flow from Operations

Investment Evaluation

Forecasting Cash Flows

2) Do not ignore investment in fixed assets.

Revenue

- Cost of Goods Sold

- Depreciation

- Selling, General & Admin.

= Operating Profit

- Cash Taxes on Operating Profit

= Net Operating Profit After Tax

+ Depreciation

- Capital Expenditures

- Increase in Working Capital

= Cash Flow from Operations

Investment Evaluation

Forecasting Cash Flows

3) Do not ignore investment in net working capital.

Revenue

- Cost of Goods Sold

- Depreciation

- Selling, General & Admin.

= Operating Profit

- Cash Taxes on Operating Profit

= Net Operating Profit After Tax

+ Depreciation

- Capital Expenditures

- Increase in Working Capital

= Cash Flow from Operations

Investment Evaluation

Forecasting Cash Flows

There is an important distinction between the accounting definition of working capital and the economic/finance definition relevant to cash flows forecast.

The distinction is a direct result of the 4th commandment above: We need the operating working capital, not the operating and financial working capital.

Investment Evaluation

Current assets include operating assets (above dotted line). However, excess cash and marketable securities not required for operations (below dotted line) are not operating working capital and accounted separately for value (see 10th commandment).

Current liabilities include both operating liabilities (above the dotted line) and non-operating short-term debt (below the dotted line).

Accounting Definition of Working Capital

Accounts receivable

Inventory

Cash (required for operations)

Excess Cash & marketable securities

Accounts payable

Accrued taxes

Accrued wages

short-term debt

Working Capital =

Current Assets -

Current Liabilities

Investment Evaluation

Forecasting Cash Flows

4) Separate investment and financing decisions

Revenue

- Cost of Goods Sold

- Depreciation

- Selling, General & Admin.

= Operating Profit

- Cash Taxes on Operating Profit

= Net Operating Profit After Tax

+ Depreciation

- Capital Expenditures

- Increase in Working Capital

= Cash Flow from Operations

Evaluate as if entirely equity financed

Ignore financing/

no interest line item

Investment Evaluation

Forecasting Cash Flows

5) Estimate flows on an incremental basis

Incremental = total firm cash flow - total firm cash flow

Cash Flow WITH the project WITHOUT the project

Forget Sunk Costs –

costs incurred in the past and irreversible

Include all effects of the project on the rest of the firm (e.g., cannibalization, erosion, enhancement, etc.)

Investment Evaluation

Forecasting Cash Flows

6) Opportunity costs cannot be ignored

What other

uses could

resources be

put to?

The cost of any resource is the foregone opportunity of employing this resources in the next best alternative use.

Investment Evaluation

Forecasting Cash Flows

7) Do not forget continuing value (residual or terminal)

Two approaches are available:

Liquidation value: Estimate the proceeds from the sale of assets after the explicit forecast period. (Include the recovery of investment in working capital, tax-shield on the undepreciated fixed assets and any revenue from assets sale).

This approach results in under-valuation since it misses the value of on-going business. It ignores the value of intangibles.

Investment Evaluation

Forecasting Cash Flows

Perpetual growth: Assumes that after time n cash flows are expected to grow at a constant rate perpetually.

Year 1

CF1

Year 2

CF2

Year n

CFn

. . .

Terminal Value

Year n+1 & on

CFn+1/(r-g)

Investment Evaluation

8) Be consistent in the treatment of inflation

Discount nominal cash flows with nominal cost of capital

Discount real cash flows with real cost of capital

Nominal Rate » Real Rate + Inflation

Common Mistake: Nominal (inflation adjusted) discount rate used to discount real cash flows

Bias towards short-term investment

Nominal vs. Real Interest Rate

Nominal

Inflation

Real

{

Forecasting Cash Flows

Investment Evaluation

Nominal vs. Real Cash Flows

Note: Depreciation is based on historical costs and therefore is not adjusted for inflation

Forecasting Cash Flows

Investment Evaluation

Forecasting Cash Flows

9) Overhead costs

Revenue

- Cost of Goods Sold

- Depreciation

- Selling, General & Admin.

= Operating Profit

- Cash Taxes on Operating Profit

= Net Operating Profit After Tax

+ Depreciation

- Capital Expenditures

- Increase in Working Capital

= Cash Flow from Operations

Do not forget overheads and other indirect costs that increase due to the project

Investment Evaluation

Forecasting Cash Flows

10) Include excess cash, excess real estate, unfunded (over-funded) pension funds, large stock option obligations

Year 1

CF1

Year 2

CF2

Year 3

CF3

Year 4

CF4

Year 5

CF5

Terminal

CFn+1/(r-g)

. . .

PV(Operating Cash Flows)

+ Excess cash balance

+ Excess marketable securities

+ Excess real estate

- Under-funded pension

=Value of the FIRM

Assets/Liabilities not required to support operations

Investment Evaluation

Value of the Firm

-Value of Debt

=Value of Equity

To calculate share price-divide by the number of shares outstanding

Value of Equity

Investment Evaluation

Evaluating investments involves the following:

1) Forecast all relevant after tax expected cash flows generated by the project

2) Estimate the opportunity cost of capital--r (reflects the time value of money and the risk)

3) Evaluation

DCF (discounted cash flows)

NPV (net present value)

Accept project if NPV is positive

Reject project if NPV is negative

IRR (internal rate of return

Accept project if IRR > r

Payback , Profitability Index

ROA, ROFE, ROI, ROCE

ROE

EVA

Investment Evaluation

Evaluation Methods: NPV

Net Present Value (NPV) is the sum of all cash flows adjusted by the discount rate

Example:

Future cash flows are discounted “penalized” for time and risk

Investment Evaluation

Evaluation Methods: NPV

Net Present Value (NPV) is the sum of all cash flows adjusted by the discount rate

Example:

Investment Evaluation

Evaluation Methods: IRR

As the discount rate increases, the PV of future cash flows is lower and the NPV is reduced

Example:

Internal rate of return (IRR) is the discount rate that sets the NPV to zero

IRR: Discount rate at which the project has a NPV of zero

Investment Evaluation

Calculation of IRR

The IRR is the r that solves

Decision Rule: Accept the project if

IRR > Opportunity Cost of Capital

Investment Evaluation

Evaluation Methods: NPV vs. IRR

NPV is a measure of absolute performance, whereas IRR measures relative performance:

1) Independent Projects

Accept if NPV > 0

Accept if IRR > Opportunity Cost of Capital

Investment Evaluation

Evaluation Methods: NPV vs. IRR

2) Mutually Exclusive Projects (Ranking)

Problems with IRR:

A) Scale

B) Timing of Cash Flows: Bias against long-term investments

Highest (NPVa, NPVb, NPVc)

Highest (IRRa, IRRb, IRRc)

Obviously, the return in absolute

dollars must be considered

Preference for CF early!

But, it depends.

Investment Evaluation

The ranking of the projects depends on the discount rate

A is a LT project and when discount rate PV ¯

B is a ST project and when discount rate PV ¯ drops less

Evaluation Methods: NPV vs. IRR

Investment Evaluation

Other Evaluation Methods

Payback: How long does it take for the project to payback?

Problems:

No discounting the first 3 years

Infinite discounting of later years

Biases against long-term projects.

ROA (return on assets)

ROI (return on investment)

ROFE (return on funds employed)

ROCE (return on capital employed)

ROE =

}

Earnings

Investment

Problems:

Investment not valued at market

Earnings vs. cash flows

Net Income

Shareholders’ Equity

Book Value

Profitability Index: PV/I. Problem: Biases against large-scale projects.

Investment Evaluation

Use of Capital Budgeting Rules in Practice.

548

500

)

000

)(

000

(

Time

Inventory

Level

Order

Quantity

But demand is rarely predictable!

Demand???

But demand is rarely predictable!

Time

Inventory

Level

Order

Quantity

Demand???

Inventory at time of receipt

Receive

order

Time

Inventory

Level

Order

Quantity

Place

order

Lead Time

Actual Demand < Expected Demand

ROP

Lead Time Demand

Actual Demand < Expected Demand

Inventory at time of receipt

Receive
order

Time

Inventory

Level

Order

Quantity

Place

order

Lead Time

ROP

Lead Time Demand

ROP = Expected Demand

Average

Time

Inventory

Level

Order

Quantity

If ROP = expected demand, service level is

50%. Inventory left 50% of the time, stock

outs 50% of the time.

Uncertain Demand

If ROP = expected demand, service level is 50%. Inventory left 50% of the time, stock outs 50% of the time.

ROP = Expected Demand

Average

Time

Inventory

Level

Order

Quantity

Uncertain Demand

EOQ

( )

LTD

stddevinLTdemandstddevindailydemanddaysi

nLT

s=s

168

)

(

137

ROP

Actual

B. Operating Income1998199920002001200220032004

1Sales1,356.1 1,535.0 1,660.0 1,759.6 1,865.2 1,958.4 2,056.4

2Operating Costs(1,143.2) (1,304.8) (1,402.7) (1,478.1) (1,566.7) (1,645.1) (1,727.3)

3Depreciation(67.5) (77.0) (83.0) (80.0) (75.0) (70.0) (65.0)

4EBIT 145.4 153.3 174.3 201.5 223.4 243.3 264.0

5Taxes(50.6) (61.3) (69.7) (80.6) (89.4) (97.3) (105.6)

6EBIAT94.8 92.0 104.6 120.9 134.1 146.0 158.4

Actual

C. Cash Flows from Operations1998199920002001200220032004

7EBIAT94.8 92.0 104.6 120.9 134.1 146.0 158.4

8Depreciation67.5 77.0 83.0 80.0 75.0 70.0 65.0

9Changes in WC(87.7) (30.3) (75.0) (19.9) (21.1) (18.7) (19.6)

10Capital Investment(59.7) (46.2) (48.4) (50.0) (50.0) (50.0) (50.0)

11Free Cash Flows14.9 92.4 64.2 131.0 137.9 147.4 153.8

ProForma

Sample Corporation VALUATION

Basic Parameters

Sample Corporation Basic Parameters
	Basic Parameters for Corporate Valuation
	Line Description	Value
	Company Name:
	Sample Corporation
	Year (Last Actual):	1998
	Rates:
	Risk-free Rate(rf)	5.25%
	Debt Yield/Return on Debt (rd)	7.90%
	Market Risk Premium (MRP)	7.40%
	Company's Beta (B)	1.10
	Return on Equity (re)	13.39%
	Financial:
	# of Shares Outstanding	22,900,000
	Long-term Debt Outstanding	217,300,000
	Stock Price	35.00
	Tax Rate	35.00%
	Weighted Average Cost of Capital (WACC)	11.63%
	Valuation Per Share	50.15
	Yellow denotes some discretion required in estimation
	Blue denotes readily available fact from public sources

&L&"Arial,Bold Italic"&14Corporate Valuation Model&"Arial,Regular"&10 &A

&L&11Raviv&RPage: &p of &n File: &f Date: &d

Historical Performance

Sample Corporation Past Financial Performance
			Actual										Projected
E. Historical Performance (Value Line)			1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000
1		Sales ($ millions)	429.0	448.7	458.8	511.6	545.3	588.2	712.8	862.3	906.3	1,356.1	1,535.0	1,660.0
2	G	Sales Growth (%)		4.6%	2.3%	11.5%	6.6%	7.9%	21.2%	21.0%	5.1%	49.6%	13.2%	8.1%
3		Operating Costs	358.6	374.7	387.2	428.2	454.2	483.5	590.2	689.8	722.3	1,143.2	1,304.8	1,402.7
4	P	Operating Margin (%)	16.4%	16.5%	15.6%	16.3%	16.7%	17.8%	17.2%	20.0%	20.3%	15.7%	15.0%	15.5%
5	D	Depreciation	17.0	18.4	22.5	28.6	30.3	33.0	37.3	45.0	49.2	67.5	77.0	83.0
6		Net Profit	36.9	39.5	34.9	39.4	40.9	47.1	55.6	79.3	81.6	74.6	76.8	84.7
7	T	Income Tax Rate	34.8%	35.0%	35.0%	34.0%	34.0%	36.0%	36.8%	38.4%	39.5%	39.9%	40.0%	40.0%
8		Net Profit Margin (%)	8.6%	8.8%	7.6%	7.7%	7.5%	8.0%	7.8%	9.2%	9.0%	5.5%	5.0%	5.1%
9		Working Capital	138.3	137.6	141.4	152.2	157.9	183.4	193.2	206.2	149.2	236.9	260.0	335.0
10	W	Working Capital Increase (%)		-3.6%	37.6%	20.5%	16.9%	59.4%	7.9%	8.7%	-129.5%	19.5%	16.9%	60.0%
11		Debt	20.5	20.2	19.8	26.0	25.2	23.5	25.6	30.6	24.5	428.2	440.0	440.0
12		Capital Spending Per Share	0.72	1.15	0.93	0.74	0.72	0.76	1.13	1.31	0.86	1.38	1.10	1.15
13		Outstanding Shares (millions)	42.34	42.87	43.44	45.21	44.12	44.79	45.38	45.59	45.77	43.27	42.00	42.10
14	C	Capital Expenditures	30.5	49.3	40.4	33.5	31.8	34.0	51.3	59.7	39.4	59.7	46.2	48.4

&L&"Arial,Bold Italic"&14Corporate Valuation Model&"Arial,Regular"&10 &A

&L&11Raviv&RPage: &p of &n File: &f Date: &d

WACC Calculation

Weighted Average Cost of Capital Calculation
for Sample Corporation
	Market Value of Equity
		Current Share Price	35.00
		Outstanding Shares	22,900,000
		Total	801,500,000
	Market Value of Debt (use book as proxy)		217,300,000
	Firm Value		1,018,800,000
		Debt	217
		Debt + Equity	1,019	21%
		Equity	802
		Debt + Equity	1,019	79%
	Using CAPM to estimate the cost of equity (re) as follows:
		re = rf + (Beta * Market Risk Premium)
		rf =	5.25%
		Beta =	1.1
		Market Risk Premium =	7.40%
		re=	13.39%
	Therefore the Weighted Average Cost of Capital is as follows:
		WACC = [(D/(D+E))rd(1-t)]+[(E/(D+E))*re]
		D/(D+E) =	21%
		rd =	7.90%
		t (tax rate) =	35%
		E/(D+E) =	79%
		re =	13.39%
		WACC	11.63%

&L&"Arial,Bold Italic"&14Corporate Valuation Model&"Arial,Regular"&10 &A

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Valuation Worksheet

Sample Corporation VALUATION
		Actual	ProForma
A. Operating Parameters		1998	1999	2000	2001	2002	2003	2004	2005	Terminal
S	Sales Growth (%)	49.6%	13%	8%	6%	6%	5%	5%	5%
P	Operating Profit Margin (%)	15.7%	15.0%	15.5%	16.0%	16.0%	16.0%	16.0%	16.0%
T	Tax Rate (%)	39.9%	40.0%	40.0%	40.0%	40.0%	40.0%	40.0%	40.0%
D	Depreciation ($)	67.5	77.0	83.0	80.0	75.0	70.0	65.0	65.0
C	Capital Expenditure ($)	59.7	46.2	48.4	50.0	50.0	50.0	50.0	50.0
W	Working Capital as % of Sales (%)	19.5%	16.9%	60.0%	20.0%	20.0%	20.0%	20.0%	20.0%
	Excess Cash	- 0
	Market Value of Debt	217.3
	# of Outstanding Shares	22.9
	Perpetual Growth Rate	5.0%
Sample Corporation VALUATION
		Actual	ProForma
B. Operating Income		1998	1999	2000	2001	2002	2003	2004	2005	Terminal
1	Sales	1,356.1	1,535.0	1,660.0	1,759.6	1,865.2	1,958.4	2,056.4	2,159.2
2	Operating Costs	(1,143.2)	(1,304.7)	(1,402.7)	(1,478.1)	(1,566.7)	(1,645.1)	(1,727.3)	(1,813.7)
3	Depreciation	(67.5)	(77.0)	(83.0)	(80.0)	(75.0)	(70.0)	(65.0)	(65.0)
4	EBIT	145.4	153.3	174.3	201.5	223.4	243.3	264.0	280.5
5	Taxes	(50.6)	(61.3)	(69.7)	(80.6)	(89.4)	(97.3)	(105.6)	(112.2)
6	EBIAT	94.8	91.9	104.6	120.9	134.1	146.0	158.4	168.3	168.3
		Actual	ProForma
C. Cash Flows from Operations		1998	1999	2000	2001	2002	2003	2004	2005	Terminal
7	EBIAT	94.8	91.9	104.6	120.9	134.1	146.0	158.4	168.3	168.3
8	Depreciation	67.5	77.0	83.0	80.0	75.0	70.0	65.0	65.0	- 0
9	Changes in WC	(87.7)	(30.3)	(75.0)	(19.9)	(21.1)	(18.7)	(19.6)	(20.6)	- 0
10	Capital Investment	(59.7)	(46.2)	(48.4)	(50.0)	(50.0)	(50.0)	(50.0)	(50.0)	(52.5)
11	Free Cash Flows	14.9	92.4	64.2	131.0	137.9	147.4	153.8	162.7	115.8
D. Value of Sample Corporation
12	Present Value of First 7 Years Cash Flows	557
13	Terminal Value at 5.0% Perpetual Growth	809
14	Add: Excess Cash	- 0
15	TOTAL VALUE	1,366
16	Less: Long-term Debt	(217)
17	TOTAL EQUITY VALUE	1,148
18	* VALUE PER SHARE *	50.15

&L&"Arial,Bold Italic"&14Corporate Valuation Model&"Arial,Regular"&10 &A

&L&11Raviv&RPage: &p of &n File: &f Date: &d

Equity

turn

Rate

Tax

Corporate

Rate

Interest

term

Long

Debt,

Return

Equity

Outstandin

Value

Market

Debt

Amount

where

)

(

)

(

)

(

WACC

Equityon turn Rer

RateTax Corporatet

RateInterest term-Long Debt,on Return r

Equity gOutstandin of ValueMarket E

Debt ofAmount D

where

)(

)1(**

)(

WACC

MBD00533C67.unknown

Actual

A. Operating Parameters19981999200020012002200320042005Terminal

SSales Growth (%)49.6%13%8%6%6%5%5%5%

POperating Profit Margin (%)15.7%15.0%15.5%16.0%16.0%16.0%16.0%16.0%

TTax Rate (%)39.9%40.0%40.0%40.0%40.0%40.0%40.0%40.0%

DDepreciation ($)67.5 77.0 83.0 80.0 75.0 70.0 65.0 65.0

CCapital Expenditure ($)59.7 46.2 48.4 50.0 50.0 50.0 50.0 50.0

WWorking Capital as % of Sales (%)19.5%16.9%60.0%20.0%20.0%20.0%20.0%20.0%

Excess Cash-

Market Value of Debt217.3

# of Outstanding Shares22.9

Perpetual Growth Rate5.0%

Sample Corporation VALUATION

ProForma

Basic Parameters

Sample Corporation Basic Parameters
	Basic Parameters for Corporate Valuation
	Line Description	Value
	Company Name:
	Sample Corporation
	Year (Last Actual):	1998
	Rates:
	Risk-free Rate(rf)	5.25%
	Debt Yield/Return on Debt (rd)	7.90%
	Market Risk Premium (MRP)	7.40%
	Company's Beta (B)	1.10
	Return on Equity (re)	13.39%
	Financial:
	# of Shares Outstanding	22,900,000
	Long-term Debt Outstanding	217,300,000
	Stock Price	35.00
	Tax Rate	35.00%
	Weighted Average Cost of Capital (WACC)	11.63%
	Valuation Per Share	50.15
	Yellow denotes some discretion required in estimation
	Blue denotes readily available fact from public sources

&L&"Arial,Bold Italic"&14Corporate Valuation Model&"Arial,Regular"&10 &A

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Historical Performance

Sample Corporation Past Financial Performance
			Actual										Projected
E. Historical Performance (Value Line)			1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000
1		Sales ($ millions)	429.0	448.7	458.8	511.6	545.3	588.2	712.8	862.3	906.3	1,356.1	1,535.0	1,660.0
2	G	Sales Growth (%)		4.6%	2.3%	11.5%	6.6%	7.9%	21.2%	21.0%	5.1%	49.6%	13.2%	8.1%
3		Operating Costs	358.6	374.7	387.2	428.2	454.2	483.5	590.2	689.8	722.3	1,143.2	1,304.8	1,402.7
4	P	Operating Margin (%)	16.4%	16.5%	15.6%	16.3%	16.7%	17.8%	17.2%	20.0%	20.3%	15.7%	15.0%	15.5%
5	D	Depreciation	17.0	18.4	22.5	28.6	30.3	33.0	37.3	45.0	49.2	67.5	77.0	83.0
6		Net Profit	36.9	39.5	34.9	39.4	40.9	47.1	55.6	79.3	81.6	74.6	76.8	84.7
7	T	Income Tax Rate	34.8%	35.0%	35.0%	34.0%	34.0%	36.0%	36.8%	38.4%	39.5%	39.9%	40.0%	40.0%
8		Net Profit Margin (%)	8.6%	8.8%	7.6%	7.7%	7.5%	8.0%	7.8%	9.2%	9.0%	5.5%	5.0%	5.1%
9		Working Capital	138.3	137.6	141.4	152.2	157.9	183.4	193.2	206.2	149.2	236.9	260.0	335.0
10	W	Working Capital Increase (%)		-3.6%	37.6%	20.5%	16.9%	59.4%	7.9%	8.7%	-129.5%	19.5%	16.9%	60.0%
11		Debt	20.5	20.2	19.8	26.0	25.2	23.5	25.6	30.6	24.5	428.2	440.0	440.0
12		Capital Spending Per Share	0.72	1.15	0.93	0.74	0.72	0.76	1.13	1.31	0.86	1.38	1.10	1.15
13		Outstanding Shares (millions)	42.34	42.87	43.44	45.21	44.12	44.79	45.38	45.59	45.77	43.27	42.00	42.10
14	C	Capital Expenditures	30.5	49.3	40.4	33.5	31.8	34.0	51.3	59.7	39.4	59.7	46.2	48.4

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WACC Calculation

Weighted Average Cost of Capital Calculation
for Sample Corporation
	Market Value of Equity
		Current Share Price	35.00
		Outstanding Shares	22,900,000
		Total	801,500,000
	Market Value of Debt (use book as proxy)		217,300,000
	Firm Value		1,018,800,000
		Debt	217
		Debt + Equity	1,019	21%
		Equity	802
		Debt + Equity	1,019	79%
	Using CAPM to estimate the cost of equity (re) as follows:
		re = rf + (Beta * Market Risk Premium)
		rf =	5.25%
		Beta =	1.1
		Market Risk Premium =	7.40%
		re=	13.39%
	Therefore the Weighted Average Cost of Capital is as follows:
		WACC = [(D/(D+E))rd(1-t)]+[(E/(D+E))*re]
		D/(D+E) =	21%
		rd =	7.90%
		t (tax rate) =	35%
		E/(D+E) =	79%
		re =	13.39%
		WACC	11.63%

&L&"Arial,Bold Italic"&14Corporate Valuation Model&"Arial,Regular"&10 &A

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Valuation Worksheet

Sample Corporation VALUATION
		Actual	ProForma
A. Operating Parameters		1998	1999	2000	2001	2002	2003	2004	2005	Terminal
S	Sales Growth (%)	49.6%	13%	8%	6%	6%	5%	5%	5%
P	Operating Profit Margin (%)	15.7%	15.0%	15.5%	16.0%	16.0%	16.0%	16.0%	16.0%
T	Tax Rate (%)	39.9%	40.0%	40.0%	40.0%	40.0%	40.0%	40.0%	40.0%
D	Depreciation ($)	67.5	77.0	83.0	80.0	75.0	70.0	65.0	65.0
C	Capital Expenditure ($)	59.7	46.2	48.4	50.0	50.0	50.0	50.0	50.0
W	Working Capital as % of Sales (%)	19.5%	16.9%	60.0%	20.0%	20.0%	20.0%	20.0%	20.0%
	Excess Cash	- 0
	Market Value of Debt	217.3
	# of Outstanding Shares	22.9
	Perpetual Growth Rate	5.0%
Sample Corporation VALUATION
		Actual	ProForma
B. Operating Income		1998	1999	2000	2001	2002	2003	2004	2005	Terminal
1	Sales	1,356.1	1,535.0	1,660.0	1,759.6	1,865.2	1,958.4	2,056.4	2,159.2
2	Operating Costs	(1,143.2)	(1,304.7)	(1,402.7)	(1,478.1)	(1,566.7)	(1,645.1)	(1,727.3)	(1,813.7)
3	Depreciation	(67.5)	(77.0)	(83.0)	(80.0)	(75.0)	(70.0)	(65.0)	(65.0)
4	EBIT	145.4	153.3	174.3	201.5	223.4	243.3	264.0	280.5
5	Taxes	(50.6)	(61.3)	(69.7)	(80.6)	(89.4)	(97.3)	(105.6)	(112.2)
6	EBIAT	94.8	91.9	104.6	120.9	134.1	146.0	158.4	168.3	168.3
		Actual	ProForma
C. Cash Flows from Operations		1998	1999	2000	2001	2002	2003	2004	2005	Terminal
7	EBIAT	94.8	91.9	104.6	120.9	134.1	146.0	158.4	168.3	168.3
8	Depreciation	(67.5)	77.0	83.0	80.0	75.0	70.0	65.0	65.0	- 0
9	Changes in WC	87.7	(30.3)	(75.0)	(19.9)	(21.1)	(18.7)	(19.6)	(20.6)	- 0
10	Capital Investment	(59.7)	(46.2)	(48.4)	(50.0)	(50.0)	(50.0)	(50.0)	(50.0)	(52.5)
11	Free Cash Flows	55.3	92.4	64.2	131.0	137.9	147.4	153.8	162.7	115.8
D. Value of Sample Corporation
12	Present Value of First 7 Years Cash Flows	557
13	Terminal Value at 5.0% Perpetual Growth	809
14	Add: Excess Cash	- 0
15	TOTAL VALUE	1,366
16	Less: Long-term Debt	(217)
17	TOTAL EQUITY VALUE	1,148
18	* VALUE PER SHARE *	50.15

&L&"Arial,Bold Italic"&14Corporate Valuation Model&"Arial,Regular"&10 &A

&L&11Raviv&RPage: &p of &n File: &f Date: &d

Equity

turn

Rate

Tax

Corporate

Rate

Interest

term

Long

Debt,

Return

Equity

Outstandin

Value

Market

Debt

Amount

where

)

(

)

(

)

(

WACC

Equityon turn Rer

RateTax Corporatet

RateInterest term-Long Debt,on Return r

Equity gOutstandin of ValueMarket E

Debt ofAmount D

where

)(

)1(**

)(

WACC

MBD00533C67.unknown

Value

Continuing

123

Nominal2.00 2.08 2.16

Real2.00 2.00 2.00

Inflation @ 4%

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Time Period:	0	1	IRR
Project A	-1¢	5¢	400%
Project B	-100B	120B	20%
Time Period:	0	1	2	IRR	NPV@0%	NPV@10%
Project A	-100	20	120	20%	40	17.3
Project B	-100	100	31.25	25%	31.25	16.7
Discount Rate	Project A	Project B
0%	40	31.25
2%	34.9480968858	28.0757401
4%	30.1775147929	25.0462278107
6%	25.66749733	22.152011392
8%	21.3991769547	19.384430727
10%	17.3553719008	16.7355371901
12%	13.5204081633	14.1980229592
14%	9.8799630656	11.7651585103
16%	6.4209274673	9.4307372176
18%	3.1312841138	7.1890261419
20%	0	5.0347222222
22%	-2.9830690675	2.9629131954
24%	-5.8272632674	0.9690426639
26%	-8.5411942555	-0.9511211892
28%	-11.1328125	-2.8015136719
30%	-13.6094674556	-4.5857988166

Sheet2

0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0
0	0

Project A

Project B

Discount Rate

NPV

Project Comparison

Sheet3

	1	2	3
Nominal	2.00	2.08	2.16
Real	2.00	2.00	2.00
Inflation @ 4%

Time Period012

Activity

Buy Hot Dog CartSell Hot DogsSell Hot Dogs

Cash Flows

-187110121

Discount Rate

10%

100

187

)

(

121

)

(

110

187

NPV

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Sheet3

Time Period012

Activity

Buy Hot Dog CartSell Hot DogsSell Hot Dogs

Cash Flows

-200110121

Discount Rate

10%

100

200

)

(

121

)

(

110

200

NPV

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs
Cash Flows	-200	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Sheet3

Hot Dog Cart Valuation

-30

-20

-10

0%2%4%6%8%

10%12%14%16%18%20%22%24%

Discount Rate (%)

NPV ($)

Chart2

0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
0.25

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

40.5267130673

37.1445597847

33.85022151

30.6405325444

27.5124716553

24.4631541474

21.4898244388

18.5898491084

15.7607103779

10.3054135216

7.674744898

5.1058814316

2.5967990151

0.145557656

-2.2497027348

-4.5907663087

-6.8793450158

-9.117082127

-11.3055555556

-13.4462809917

-15.5407148616

-17.5902571221

-19.5962539022

-21.56

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Sheet3

)

(

....

)

(

Time Period:01IRR

Project A-15400%

Project B-10012020%

Time Period:012

Project A-10020120

Project B-10010031.25

Time Period:012IRRNPV@0%NPV@10%NPV@20%

Project A-1002012020%4017.30.0

Project B-10010031.2525%31.2516.75.0

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

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0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Time Period:	0	1	IRR
Project A	-1	5	400%
Project B	-100	120	20%

Sheet3

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

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0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Time Period:	0	1	IRR
Project A	-1¢	5¢	400%
Project B	-100B	120B	20%
Time Period:	0	1	2
Project A	-100	20	120
Project B	-100	100	31.25

Sheet3

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
0
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0
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0
0
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0
0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Time Period:	0	1	IRR
Project A	-1¢	5¢	400%
Project B	-100B	120B	20%
Time Period:	0	1	2	IRR	NPV@0%	NPV@10%	NPV@20%
Project A	-100	20	120	20%	40	17.3	0.0
Project B	-100	100	31.25	25%	31.25	16.7	5.0

Sheet3

Time Period:012IRRNPV@0%NPV@10%

Project A-1002012020%4017.3

Project B-10010031.2525%31.2516.7

Project Comparison

-20

-10

Discount Rate

NPV

Project A

Project B

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
0
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0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Time Period:	0	1	IRR
Project A	-1¢	5¢	400%
Project B	-100B	120B	20%
Time Period:	0	1	2	IRR	NPV@0%	NPV@10%
Project A	-100	20	120	20%	40	17.3
Project B	-100	100	31.25	25%	31.25	16.7

Sheet3

Chart3

0	0
0.02	0.02
0.04	0.04
0.06	0.06
0.08	0.08
0.1	0.1
0.12	0.12
0.14	0.14
0.16	0.16
0.18	0.18
0.2	0.2
0.22	0.22
0.24	0.24
0.26	0.26
0.28	0.28
0.3	0.3

Project A

Project B

Discount Rate

NPV

Project Comparison

31.25

34.9480968858

28.0757401

30.1775147929

25.0462278107

25.66749733

22.152011392

21.3991769547

19.384430727

17.3553719008

16.7355371901

13.5204081633

14.1980229592

9.8799630656

11.7651585103

6.4209274673

9.4307372176

3.1312841138

7.1890261419

5.0347222222

-2.9830690675

2.9629131954

-5.8272632674

0.9690426639

-8.5411942555

-0.9511211892

-11.1328125

-2.8015136719

-13.6094674556

-4.5857988166

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
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0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Time Period:	0	1	IRR
Project A	-1¢	5¢	400%
Project B	-100B	120B	20%
Time Period:	0	1	2	IRR	NPV@0%	NPV@10%
Project A	-100	20	120	20%	40	17.3
Project B	-100	100	31.25	25%	31.25	16.7
Discount Rate	Project A	Project B
0%	40	31.25
2%	34.9480968858	28.0757401
4%	30.1775147929	25.0462278107
6%	25.66749733	22.152011392
8%	21.3991769547	19.384430727
10%	17.3553719008	16.7355371901
12%	13.5204081633	14.1980229592
14%	9.8799630656	11.7651585103
16%	6.4209274673	9.4307372176
18%	3.1312841138	7.1890261419
20%	0	5.0347222222
22%	-2.9830690675	2.9629131954
24%	-5.8272632674	0.9690426639
26%	-8.5411942555	-0.9511211892
28%	-11.1328125	-2.8015136719
30%	-13.6094674556	-4.5857988166

Sheet2

0	0
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0	0
0	0

Project A

Project B

Discount Rate

NPV

Project Comparison

Sheet3

Time Period:012345

Project A-100203050Pass

Project B-1022210

Fail

Corporate Rule: Project must payback in at most 3 years!

Sheet1

Time Period	0	1	2
Activity	Buy Hot Dog Cart	Sell Hot Dogs	Sell Hot Dogs (Cubs make the playoffs)
Cash Flows	-187	110	121
Discount Rate	10%
0	44
0.01	40.5267130673
0.02	37.1445597847
0.03	33.85022151
0.04	30.6405325444
0.05	27.5124716553
0.06	24.4631541474
0.07	21.4898244388
0.08	18.5898491084
0.09	15.7607103779
0.1	13
0.11	10.3054135216
0.12	7.674744898
0.13	5.1058814316
0.14	2.5967990151
0.15	0.145557656
0.16	-2.2497027348
0.17	-4.5907663087
0.18	-6.8793450158
0.19	-9.117082127
0.2	-11.3055555556
0.21	-13.4462809917
0.22	-15.5407148616
0.23	-17.5902571221
0.24	-19.5962539022
0.25	-21.56
0.1506011662	-0.0000006742

Sheet1

0
0
0
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0
0
0
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0
0
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0
0
0
0
0
0

Discount Rate (%)

NPV ($)

Hot Dog Cart Valuation

Sheet2

Time Period:	0	1	IRR
Project A	-1¢	5¢	400%
Project B	-100B	120B	20%
Time Period:	0	1	2	IRR	NPV@0%	NPV@10%
Project A	-100	20	120	20%	40	17.3
Project B	-100	100	31.25	25%	31.25	16.7
Discount Rate	Project A	Project B
0%	40	31.25
2%	34.9480968858	28.0757401
4%	30.1775147929	25.0462278107
6%	25.66749733	22.152011392
8%	21.3991769547	19.384430727
10%	17.3553719008	16.7355371901
12%	13.5204081633	14.1980229592
14%	9.8799630656	11.7651585103
16%	6.4209274673	9.4307372176
18%	3.1312841138	7.1890261419
20%	0	5.0347222222
22%	-2.9830690675	2.9629131954
24%	-5.8272632674	0.9690426639
26%	-8.5411942555	-0.9511211892
28%	-11.1328125	-2.8015136719
30%	-13.6094674556	-4.5857988166

Sheet2

0	0
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0	0
0	0

Project A

Project B

Discount Rate

NPV

Project Comparison

Sheet3

	1	2	3
Nominal	2.00	2.04	2.16
Real	2.00	2.00	2.00
Inflation @ 4%
Time Period:	0	1	2	3	4	5
Project A	-100	20	30	50			Pass
Project B	-10	2	2	2	10	5B	Fail
Corporate Rule: Project must payback in at most 3 years!

17.8

22.5

33.8

26.45

2221.95

18.5

NPVIRRPaybackAverage

Return and

Capital Budgeting techniques:

Primary and Secondary Combined

19771986