Problem #1 1. 2 3 4 5 Investment Criteria Summary Ranking by Investment Criterion

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Problem #1

Year 0 Year l Year 2 Year 3

A. Investment 10,000Revenue 21,000Operating expenses 11,000Depreciation 10,000Operating Income 0Taxes 0EBIT(1-t) 0Depreciation 10,000OCF 10,000FCF 10,000 10,000

Payback 0ROI 0IRR 0NPV

@10% 909@35% 2,593

Project Type of Cash Flow

Year of Cash Flow

2


B. Investment 10,000Revenue 15,000 17,000Operating expenses 5,833 7,833Depreciation 5,000 5,000Operating Income 4,167 4,167Taxes 1,667 1,667EBIT(1-t) 2,500 2,500Depreciation 5,000 5,000OCF 7,500 7,500FCF 10,000 7,500 7,500

Payback 2,500 5,000ROI 50%IRR 31.9%NPV

@10% 3,017@35% 329


Year of Cash Flow

3


C. Investment 10,000Revenue 10,000 11,000 30,000Operating expenses 5,555 4,889 15,555Depreciation 3,333 3,333 3,333Operating Income 1,112 2,778 11,112Taxes 445 1,111 4,445EBIT(1-t) 667 1,667 6,667Depreciation 3,333 3,333 3,333OCF 4,000 5,000 10,000FCF 10,000 4,000 5,000 10,000

Payback 6,000 1,000 9,001ROI 60%IRR 33.5%NPV

@10% 5,282@35% 229


Year of Cash Flow

4


D. Investment 10,000Revenue 30,000 10,000 5,000Operating expenses 15,555 5,555 2,222Depreciation 3333.333 3333.333 3333.333Operating Income 11,112 1,112 555Taxes 4,445 445 222EBIT(1-t) 6,667 667 333Depreciation 3,333 3,333 3,333OCF 10,000 4,000 3,000FCF 10,000 10,000 4,000 3,000

Payback 0 4,001 7,001ROI 47%IRR 42.7%NPV

@10% 4,651@35% 822


Year of Cash Flow

5

A B C D

Payback 1 2 3 1ROI 0 50% 60% 47%IRR 0 31.9% 33.5% 42.7%NPV

@10% 909 3,017 5,282 4,651@35% 2,593 329 229 822

Project

Criteria

@10% @35%

A,D C D C DB B C D CC D B B B

A A A A

Payback

NPV

ROI IRR

Investment Criteria Summary

Ranking by Investment Criterion

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What explains the differences in the rankings?– Payback method• Reflects the relative timing of cash flows but

is insensitive to the total amount of cash flow beyond the payback horizon

• Ignores the time value of money and the riskiness of the cash flows

• If a company is operating under binding capital constraints, the payback period is a crude indicator of how quickly funds are recovered to fund other projects in the queue

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– Accounting ROI• Provides some indication of how a project

will affect some traditional measures of performance

• Does not reflect true cash flow, time value of money, and risk

– NPV– Reflects time value of money and risk– Gives us a $ measure of the value of a

project– IRR will give a similar decision as NPV (i.e.,

“accept” or “reject”, as long as cash flows are conventional

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What project should be accepted?– If projects are independent, should

accept according to NPV ranking until capital runs out

– If projects are mutually exclusive, should accept either C or D, depending on the hurdle rate• The differences in the NPV rankings reflect

the relative timing of the cash flows. Such timing differences are not captured by the IRR (e.g. the IRR assumes for project D that the $10 million inflow in year 1 is reinvested at a rate equal to the IRR)

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Problem #2Pro forma income statement

0 1 2 3 4 5Sales 10000 13000 13000 8666.6667 4333.3333Cost of Sales 6000 7800 7800 5200 2600SG&A 2350 3055 3055 2036.6667 1018.3333Introductory Expenses 200Depreciation 100 100 100 100 100Profit before taxes 1350 2045 2045 1330 615Taxes 540 818 818 532 246Profit after taxes 810 1227 1227 798 369

AssumptionsCost of sales = 60%

SG&A = 23.5%Change in NWC = 27%

ROR = 20%

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FCFsAfter tax profits 810 1227 1227 798 369Depreciation 100 100 100 100 100OCF 910 1327 1327 898 469Cap Ex -500Change in Sales 10000 3000 0 -4333.3333 -4333.3333 -4333.3333Change in NWC 2700 810 0 -1170 -1170 -1170FCF -3200 100 1327 2497 2068 1639

IRR = 29.55%NPV @20% = $905.86

• Yes, the project should be undertaken because it has a positive NPV of $905, 861.• $1 million of development costs are sunk costs and should not be includedin the analysis

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Management discloses it will issue new shares to finance a new project– Project NPV = $100,000– The market knows this and it is immediately

reflected on the stock price. That is, the stock price will rise to $110

– Thus, only 1,000 new shares need to be issued to fund the $110,ooo cost of the new project.

– The market value of VAI will rise to $1,210,000– Current shareholders will gain the full value of

the project (i.e. 10%), new shareholders will pay full (but fair) price for ownership in the firm

Problem #3

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Problem #4

End of Year Time "Index" Investment Production Costs Revenues Sum PV

1967 0 ($100) ($100) (100.00)1968 1 ($200) ($200) (181.82)1969 2 ($200) ($200) (165.29)1970 3 ($200) 140 ($60) (45.08)1971 4 ($200) (490.00) 140 ($550) (375.66)1972 5 (490.00) 560 $70 43.461973 6 (490.00) 560 $70 39.511974 7 (490.00) 560 $70 35.921975 8 (490.00) 560 $70 32.661976 9 (490.00) 420 ($70) (29.69)1977 10 420 $420 161.93

Total ($900) ($2,940) $3,360 ($480) ($584)

At 210 units

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1967 0 ($100) ($100) (100.00)1968 1 ($200) ($200) (181.82)1969 2 ($200) ($200) (165.29)1970 3 ($200) 200 $0 0.001971 4 ($200) (625.00) 200 ($625) (426.88)1972 5 (625.00) 800 $175 108.661973 6 (625.00) 800 $175 98.781974 7 (625.00) 800 $175 89.801975 8 (625.00) 800 $175 81.641976 9 (625.00) 600 ($25) (10.60)1977 10 600 $600 231.33

Total ($900) ($3,750) $4,800 $150 ($274)

At 300 units

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1967 0 ($100) ($100) (100.00)1968 1 ($200) ($200) (181.82)1969 2 ($200) ($200) (165.29)1970 3 ($200) 320 $120 90.161971 4 ($200) (1000.00) 320 ($880) (601.05)1972 5 (1000.00) 1280 $280 173.861973 6 (1000.00) 1280 $280 158.051974 7 (1000.00) 1280 $280 143.681975 8 (1000.00) 1280 $280 130.621976 9 (1000.00) 960 ($40) (16.96)1977 10 960 $960 370.12

Total ($900) ($6,000) $7,680 $780 $1

Economic break-even at approximately 480 units

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• At originally planned production levels, the project would have destroyed value for the firm

• Economic break-even is closer to 480 units (compared with total world market of 323 – 775 planes)

Lockheed Martin’s stock price

Documents

Problem #1 1. 2 3 4 5 Investment Criteria Summary Ranking by Investment Criterion