Chapter 8

Using Discounted Cash Flow Analysis to Make Investment

Decisions

Topics Covered

Discounted Cash Flows, Not ProfitsIncremental Cash Flows (Ping King

Example)Treatment of InflationSeparate Investment & Financing

DecisionsCalculating Cash FlowsWednesday Example: TBA

Learning Objectives

Identify the cash flows attributable to a proposed new project.

Calculate the cash flows of a project from standard financial statements.

Understand how the company’s tax bill is affected by depreciation and how this affects project value.

Understand how changes in working capital affect project cash flows.

Capital Budgeting Steps

For a potential project:1. Forecast the project cash flows.2. Estimate the opportunity cost of capital3. Discount the future cash flows at the

opportunity cost of capital.4. Find NPV of project = PV of future cash

flows – required investment, and accept if NPV > 0.

Incremental Cash Flows

Discount incremental cash flows Include All Indirect Effects Forget Sunk Costs Include Opportunity Costs Recognize the Investment in Working Capital Beware of Allocated Overhead Costs

Incremental Cash Flow

cash flow with project

cash flow without project= -

Incremental Cash Flows

IMPORTANTIMPORTANTAsk yourself this question

Would the cash flow still exist if the project does not exist?

If yes, do not include it in your analysis.If no, include it.

Calculating Cash Flow

Total Cash Flow = Cash Flow from Investment in Plant &

Equipment + Cash Flow from Investments in Working Capital

+ Cash Flow from Operations

Cash Flow from Investment in Plant & Equipment Calculations for Ping Kings

In general, initial cost at beginning of project and possible inflow from after-tax salvage (selling) value at end of project.

Ping will need to buy and install new manufacturing equipment costing $4,500,000, which would be depreciated to zero over 5 years using straight-line depreciation.

At the end of the project’s 3-year life, Ping estimates they can sell this equipment for $800,000. (tax rate = 40%)

Cash Flow from Investment Calculations for Ping Kings Initial investment in equipment today (t = 0) = -$4,500,000 For operating cash flow calculation, annual depreciation =

$4,500,000/5 = $900,000 Book Value of Equipment = Original Cost – Total

Depreciation Book Value at end of year 3 (BV) = $4,500,000 –

3($900,000) = $1,800,000 Year 3 Salvage Value (SV) = $800,000 Tax on SV = Tax Rate x (SV – BV) = 0.4($800,000 -

$1,800,000) = $400,000 tax savings Year 3 after-tax salvage value = $800,000+$400,000 =

$1,200,000: year 3 cash flow from investments

Sunk Costs

These are costs that cannot be recovered if a project is rejected.

Examples: Completed Marketing & Feasibility Studies, Previous new product development and testing

For the Ping Kings Project, Ping has already spent $500,000 to research and design the Ping Kings.

This cost is to be ignored because it is a sunk cost.

Investment in Working Capital

(Net) Working Capital = Current Assets – Current Liabilities

Most new projects require additional short-term (current) assets and often additional current liabilities, such as Additional receivables from increased credit sales. Additional inventory (raw materials) necessary to

produce additional new products. Additional trade credit (accounts payables) and taxes

and wages payable. Any needed increase in (net) working capital is

an outflow of cash, but these outflows are recovered at the end of the project.

Calculation of Cash Flow from Investments in Working Capital for Ping Kings Project ($000s)

Ping estimates they will need working capital equal to 10% of sales revenue for the following year. Ping estimates they can sell 10,000 sets of Ping Kings in year 1, 15,000 sets in year 2, and 9,000 in year 3. They also estimate they can sell the Ping Kings for $640 a set in years 1 & 2,

but they will only be able to sell them for $540 a set in year 3. Year 0 1 2 3

Sales 6400 9600 4860WC need 640 960 486 0WC Chg. 640 320 (474) (486) Increase in WC is an outflow, decrease in WC is an

inflow

Methods of Calculating CF from Operations (Oper. CF)Method 1: Oper. CF = revenues – cash

expenses – taxesMethod 2: Oper. CF = net accounting

profit + depreciationMethod 3: (revenues – cash expenses) x

(1 – tax rate) + depreciation x tax rate

All these methods give the same result!

Ping King CF for Operations Info.

Ping estimates they can sell 10,000 sets of Ping Kings in year 1, 15,000 sets in year 2, and 9,000 in year 3. They also estimate they can sell the Ping Kings for $640 a set in years 1 & 2, but they will only be able to sell them for $540 a set in year 3. Variable costs will be $350 a set for all three years and Ping also expects to have $300,000 in fixed manufacturing costs annually for this project.

Ping’s marginal tax rate is 40%.

Cash Flow from Operations for Ping Kings (using Method 2)Year 1 2 3Unit Sales 10,000 15,000 9,000$/Unit $640 $640 $540VC/Unit $350 $350 $350Sales($000) 6,400 9,600 4,860-Variable Costs 3,500 5,250 3,150-Fixed Costs 300 300 300-Depreciation 900 900 900Pre-tax Profit 1,700 3,150 510-Tax(40%) 680 1,260 204Net Profit 1,020 1,890 306+Depreciation 900 900 900Operating Cash Flow 1,920 2,790 1,206

Year 1 Ping King CF from Operations using Methods 1 & 3

Method 1: Oper. CF = revenues – cash expenses – taxes = 6400 – 3800 - 680 = 1920

Method 3: (revenues – cash expenses) x (1 – tax rate) + depreciation x tax rate = (6400 – 3800)(1 – 0.4) + 900(0.4) = 1920

Total Incremental Cash Flows & Decision for Ping Kings ($000s)

Year 0 1 2 3Cap Inv (4500) 1200WC Inv (640) (320) 474 486Oper CF 1920 2790 1206Total CF (5140) 1600 3264 2892

CF0 C01 C02 C03NPV at 18% = 320.247 or $320,247IRR = 21.5%

Indirect CF Effects

Include impact that a new project would have on existing company sales and expenses.

Example: Callaway Golf considers making a new line of irons. They must consider lost sales on existing product line of irons.

What about this?

Ping’s current line of irons is the Ping i3, which have an estimated product life of 1 year remaining. Should Ping go ahead with the Ping Kings project if they thought next year’s Ping i3 sales and variable costs would decrease by $1,000,000 and $500,000 respectively on a BEFORE-TAX basis.

This would affect the year 1 CF from Operations: Indirect Effect

Year Orig 1 Change New 1Revenue($000) 6,400 (1,000) 5,400-Variable Costs 3,500 (500) 3,000-Fixed Costs 300 300-Depreciation 900 900Pre-tax Profit 1,700 (500) 1,200Tax(40%) 680 (200) 480Net Profit 1,020 (300) 720+Depreciation 900 900Oper Cash Flow 1,920 (300) 1,620 New year 1 total cash flow = 1620 – 320 = 1300, NEW NPV at 18% = 66.009 or $66,009 New IRR = 18.7%

Inflation and Projected Cash Flows

INFLATION RULEINFLATION RULE Be consistent in how you handle inflation!! Use nominal interest rates to discount

nominal cash flows. Use real interest rates to discount real cash

flows. You will get the same results, whether you use

nominal or real figures

Separation of Investment & Financing Decisions When valuing a project, ignore how the project is

financed (exclude interest expense from cash flow forecast).

Following the logic from incremental analysis ask yourself the following question: Is the project existence dependent on the financing? If no, you must separate financing and investment decisions.

MACRS Depreciation vs. Straight-Line for Ping Kings

Fastest depreciation method that corporations are allowed to use for tax purposes. Assume our Ping Kings equipment (cost = $4,500,000) falls into the 5-year MACRS

class. (recall tax rate of 40%, r = 18%). Should MACRS be used? Depreciation Tax Shield (Savings) = Deprec. X tax rate

Dep Diff in PV ofYear Dep% M Dep S-L Dep Diff TaxShd TaxShd 1 20.00 900,000 900,000 0 0 0 2 32.00 1,440,000 900,000 540,000 216,000 155,128 3 19.20 864,000 900,000 (36,000) (14,400) (8,764) 4 11.52 518,400 900,000 146,364 5 11.52 518,400 900,000 6 5.76 259,200 MACRS Year 3 Book Value = 1,296,000 Straight-Line Year 3 Book Value = 1,800,000 *Difference in After-tax Salvage Value = .4(1,296,000 – 1,800,000) = -201,600 PV of After-Tax Salvage Value Difference = -201,600/(1.18)3 = -122,700 Change in NPV = 146,364 – 122,700 = 23,664

MACRS Cash Flows for Ping Kings (using Method 2)Year 1 2 3Unit Sales 10,000 15,000 9,000$/Unit $640 $640 $540VC/Unit $350 $350 $350Sales($000) 6,400 9,600 4,860-Variable Costs 3,500 5,250 3,150-Fixed Costs 300 300 300-Depreciation 900 1,440 864Pre-tax Profit 1,700 2,610 546-Tax(40%) 680 1,044 218Net Profit 1,020 1,566 328+Depreciation 900 1,440 864Operating Cash Flow 1,920 3,006 1,192WC Cash Flow (320) 474 486After-Tax SV 998Total Cash Flow 1,600 3,480 2,676Initial CF (T=0) = 5140NPV at 18% = $343,910 vs. $320,247 under straight-line depreciation

Comprehensive Example (Last half of Wednesday’s Lecture)

Will post example on website Monday, that we will work through in Wednesday’s lecture.