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# Chapter 8 - PowerPoint PPT Presentation

Chapter 8. Using Discounted Cash Flow Analysis to Make Investment Decisions. Topics Covered. Discounted Cash Flows, Not Profits Incremental Cash Flows (Ping King Example) Treatment of Inflation Separate Investment & Financing Decisions Calculating Cash Flows Wednesday Example: TBA.

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### Chapter 8

Using Discounted Cash Flow Analysis to Make Investment Decisions

• Discounted Cash Flows, Not Profits

• Incremental Cash Flows (Ping King Example)

• Treatment of Inflation

• Separate Investment & Financing Decisions

• Calculating Cash Flows

• Wednesday Example: TBA

• 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.

• For a potential project:

• Forecast the project cash flows.

• Estimate the opportunity cost of capital

• Discount the future cash flows at the opportunity cost of capital.

• Find NPV of project = PV of future cash flows – required investment, and accept if NPV > 0.

cash flow with project

cash flow without project

-

=

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

IMPORTANT

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.

• Total Cash Flow =

• Cash Flow from Investment in Plant & Equipment +

• Cash Flow from Investments in Working Capital +

• Cash Flow from Operations

• 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 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 for Ping Kings

• 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 for Ping Kings

• (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.

• 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 4860

WC need 640 960 486 0

WC 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) for Ping Kings Project (\$000s)

• Method 1: Oper. CF = revenues – cash expenses – taxes

• Method 2: Oper. CF = net accounting profit + depreciation

• Method 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. for Ping Kings Project (\$000s)

• 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) for Ping Kings Project (\$000s)

Year 1 2 3

Unit Sales 10,000 15,000 9,000

\$/Unit \$640 \$640 \$540

VC/Unit \$350 \$350 \$350

Sales(\$000) 6,400 9,600 4,860

-Variable Costs 3,500 5,250 3,150

-Fixed Costs 300 300 300

-Depreciation 900 900 900

Pre-tax Profit 1,700 3,150 510

-Tax(40%) 680 1,260 204

Net Profit 1,020 1,890 306

+Depreciation 900 900 900

Operating Cash Flow 1,920 2,790 1,206

Year 1 Ping King CF from Operations using Methods 1 & 3 for Ping Kings Project (\$000s)

• 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

Year 0 1 2 3

Cap Inv (4500) 1200

WC Inv (640) (320) 474 486

Oper CF 1920 2790 1206

Total CF (5140) 1600 3264 2892

CF0 C01 C02 C03

NPV at 18% = 320.247 or \$320,247

IRR = 21.5%

Indirect CF Effects (\$000s)

• 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.

• 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.

Year Orig 1 Change New 1

Revenue(\$000) 6,400 (1,000) 5,400

-Variable Costs 3,500 (500) 3,000

-Fixed Costs 300 300

-Depreciation 900 900

Pre-tax Profit 1,700 (500) 1,200

Tax(40%) 680 (200) 480

Net Profit 1,020 (300) 720

+Depreciation 900 900

Oper 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 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 & Effect 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.

• 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 of

Year 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

Year 1 2 3

Unit Sales 10,000 15,000 9,000

\$/Unit \$640 \$640 \$540

VC/Unit \$350 \$350 \$350

Sales(\$000) 6,400 9,600 4,860

-Variable Costs 3,500 5,250 3,150

-Fixed Costs 300 300 300

-Depreciation 900 1,440 864

Pre-tax Profit 1,700 2,610 546

-Tax(40%) 680 1,044 218

Net Profit 1,020 1,566 328

+Depreciation 900 1,440 864

Operating Cash Flow 1,920 3,006 1,192

WC Cash Flow (320) 474 486

After-Tax SV 998

Total Cash Flow 1,600 3,480 2,676

Initial CF (T=0) = 5140

NPV at 18% = \$343,910 vs. \$320,247 under straight-line depreciation

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