Capital Budgeting Examples -Solutions Capital Budgeting Example -Payback PDF

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Capital Budgeting Example - Payback You are analyzing the following two mutually exclusive projects, where Project A is a 4- year project and Project B is a 3-year project: Project A Project B Year Cash Flows Cash Flows 0 -$1,000 -$ 800 1 +350 +350 2 +400 +400 3 +400 +400 4 +400 ----- Assuming that ...

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Capital Budgeting Example - Payback You are analyzing the following two mutually exclusive projects, where Project A is a 4year project and Project B is a 3-year project: Year 0 1 2 3 4

Project A Cash Flows -$1,000 +350 +400 +400 +400

Project B Cash Flows -$ 800 +350 +400 +400 -----

Assuming that cash flows are received evenly throughout the year, what are the payback periods for Projects A and B?

PBA = 2 + (250/400) = 2.625 years PBB = 2 + (50/400) = 2.125 years

Capital Budgeting Examples - Solutions

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Capital Budgeting Example - NPV, IRR and PI You are analyzing the following two mutually exclusive projects, where Project A is a 4year project and Project B is a 3-year project: Project A Cash Flows -$1,000 +350 +400 +400 +400

Year 0 1 2 3 4

Project B Cash Flows -$ 800 +350 +400 +400 -----

Assuming a discount rate of 15%, calculate the net present values, internal rates of return, and profitability ratios for projects A and B.

Project A CFj CFj CFj CFj CFj

= = = = =

-$1,000 $ 350 $ 400 $ 400 $ 400

I/YR = 15 Solve for NPV = $98.51 Solve for IRR = 19.68% Solve for PI = $1,098.51 / $1,000 = 1.09851 Solve for PI = $98.51 / $1,000 = .09851 Project B CFj CFj CFj CFj

= = = =

-$ $ $ $

800 350 400 400

I/YR = 15 Solve for NPV = $69.81 Solve for IRR = 20.07% Solve for PI = $869.81 / $800.00 = 1.0873 Solve for PI = $69.81 / $800.00 = 0.0873

Capital Budgeting Examples - Solutions

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Capital Budgeting Example - EAA You are analyzing the following two mutually exclusive projects, where Project A is a 4year project and Project B is a 3-year project: Project A Cash Flows -$1,000 +350 +400 +400 +400

Year 0 1 2 3 4

Project B Cash Flows -$ 800 +350 +400 +400 -----

Assume that the cost of capital is 15% and that you use the Equivalent Annual Annuity (EAA) method to evaluate these projects under infinite replication. Which project will dominate in terms of NPV and by how much?

Project A CFj CFj CFj CFj CFj

= = = = =

-$1,000 $ 350 $ 400 $ 400 $ 400

I/YR = 15 Solve for NPV = $98.51 _____ N = 4 I/YR = 15 PV = -98.51 FV = 0 Solve for PMT = $34.51 = EAA Solve for NPV of EAA = $34.51 / 0.15 = $230.04 Project B CFj CFj CFj CFj

= = = =

-$ $ $ $

800 350 400 400

Capital Budgeting Examples - Solutions

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I/YR = 15 Solve for NPV = $69.81 _____ N = 3 I/YR = 15 PV = -69.81 FV = 0 Solve for PMT = $30.58 = EAA Solve for NPV of EAA = $30.58 / 0.15 = $203.84 Project A dominates by $230.04 - $203.84 = $26.20

Capital Budgeting Examples - Solutions

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Capital Budgeting Example - MIRR You are analyzing the following project. Assuming that the cost of capital is 10%, determine the IRR and MIRR for Project A Project A Cash Flows -$1,000 +350 +400 +400 +400

Year 0 1 2 3 4

Solve for IRR: CFj CFj CFj CFj CFj

= = = = =

-$1,000 $ 350 $ 400 $ 400 $ 400

Solve for IRR = 19.68% Alternatively, CFj CFj CFj Nj

= -$1,000 = $ 350 = $ 400 = 3

Solve for IRR = 19.68% Solve for MIRR: TV = ($400)(1.10)0 + ($400)(1.10)1 + ($400)(1.10)2 + ($350)(1.10)3 TV = $400.00 + $440.00 + $484.00 + $465.85 = $1,789.85 N = 4; PV = -1,000; FV = 1,789.85; Solve for MIRR = 15.67%

Capital Budgeting Examples - Solutions

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Capital Budgeting Example - MIRR Two projects being considered by a firm have the following projected cash flows: Year 0 1 2 3

Project A Cash Flows ($150,000) $ 75,000 $ 75,000 $ 75,000

Project B Cash Flows ($150,000) 0 0 $251,867

Based on this information you should be able to determine at what cost of capital Projects A and B will have the same MIRR. (Hint: after you convert the cash flows for Project A, what will they have to be equivalent to so that they will have the same MIRR as Project B?) What is the NPV for Project A at this cost of capital and what is its MIRR?

Given that the projects are of the same scale, the terminal values of their cash flows must be equal for them to have the same MIRR. Therefore, we must find the COC that will give Project A’s cash inflows a terminal value equal to $251,867: N = 3 PV = $0 PMT = -$75,000 FV = $251,867 Solve for I/YR = 11.50% Now solve for MIRRA N=3 PV = -$150,000 PMT = 0 FV = $251,867 Solve for I/YR = MIRRA = 18.86% Note: MIRRA = MIRRB Alternatively, CFj -$150,000 CFj $ 75,000 Nj 3 I/YR

11.5

Now solve for NPVA = $31,696.45

Capital Budgeting Examples - Solutions

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Alternatively, CFj CFj CFj CFj

-$150,000 $ 0 $ 0 $251,867

Now solve for IRRA = MIRRA = 18.86%

Capital Budgeting Examples - Solutions

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Capital Budgeting Example - Decision Trees You are analyzing a project that has the following distribution of potential cash flows (initial and conditional probabilities are in parentheses): Year 0

Year 1

Year 2

$ 500 (.4)

$ 300 (.2) $ 500 (.6) $ 700 (.2)

$1,200 (.6)

$1,000 (.3) $1,200 (.4) $1,400 (.3)

-$ 800

If the appropriate risk-adjusted discount rate to use for this project is 15 percent, then what are the net present value (NPV) and internal rate of return (IRR) for this project?

Calculate expected cash flows: Year 0 = -$800 Year 1 = ($500)(.4) + ($1,200)(.6) = $920 Year 2 = [($300)(.2) + ($500)(.6) + ($700)(.2)][.4] + [($1,000)(.3) + ($1,200)(.4) + ($1,400)(.3)][.6] = [$500][.4] + [$1,200][.6] = $920

CFj = -$800 CFj = $920 CFj = $920 I/YR = 15 Solve for NPV = $695.65 Solve for IRR = 79.18%

Capital Budgeting Examples - Solutions

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Capital Budgeting Example - Cash Flow Estimation Your company is thinking about taking on a new project. In analyzing the project, the financial staff has brought together the following information: • • • •

•

• • •

The new project will require an initial capital outlay of $10 million at Year 0. This outlay will be used to purchase new equipment. This equipment will be depreciated using a MACRS 3-year class life. The equipment will have a salvage value of $400,000 at the end of four years. Inventories will rise by $1,000,000 at Year 0, and accounts payable will rise by $500,000 at Year 0. This increase in net operating working capital will be recovered at the end of the project’s life, Year 4. The new business is expected to have an economic life of four years. The business is expected to generate sales of $10 million at Year 1, $12 million at Year 2, $8 million at Year 3, and $6 million at Year 4. Each year, operating costs (excluding depreciation) are expected to be 60 percent of sales. The company’s tax rate is 40 percent. The company is very profitable, so any accounting losses on this project can be used to reduce the company’s overall tax burden. The project’s weighted average cost of capital (WACC) is 10 percent.

What is the expected net present value (NPV) of this project? (Note: the following tables are to help you organize your calculations; a few values have been included. However, you are not required to use these tables and there are other ways of calculating the cash flows.)

Capital Budgeting Examples - Solutions

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Item Cost Depreciation Rate Depreciation

Item Operating Cash Flows: Sales Less: Operating Costs Less: Depreciation EBIT Less: Taxes (40%) Net Income Plus: Depreciation Operating Cash Flows

Year 0 $10,000,000

Year 2

33.0%

Year 0

Year 1

Year 3

45.0%

Year 2

-$280,000

Year 1

Year 4

15.0%

Year 3

$10,000,000 $12,000,000

Year 0 Other Cash Flows: Initial Capital Outlay Salvage Value Tax Effect of Salvage Net Working Capital Inventories Accounts Payable Recovery of NWC Total Other Cash Flows

Year 1

-$120,000

Year 2

7.0%

Year 4

$8,000,000

$6,000,000

-$680,000

-$680,000

Year 3

Year 4

-$10,000,000 $400,000

$500,000 $0

$0

$0

Total Net Cash Flow Present Value at 10% Net Present Value

Capital Budgeting Examples - Solutions

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Item Cost Depreciation Rate Depreciation

Item Operating Cash Flows: Sales Less: Operating Costs Less: Depreciation EBIT Less: Taxes (40%) Net Income Plus: Depreciation Operating Cash Flows

Year 0 $10,000,000

Year 0

Year 0

Year 1

Year 2

Year 3

Year 4

33.0% $3,300,000

45.0% $4,500,000

15.0% $1,500,000

Year 1

Year 2

Year 3

Year 4

$10,000,000 $12,000,000 -$6,000,000 -$7,200,000 -$3,300,000 -$4,500,000 $700,000 $300,000 -$280,000 -$120,000 $420,000 $180,000 $3,300,000 $4,500,000 $3,720,000 $4,680,000

$8,000,000 -$4,800,000 -$1,500,000 $1,700,000 -$680,000 $1,020,000 $1,500,000 $2,520,000

Year 1

Year 3

Year 2

7.0% $700,000

$6,000,000 -$3,600,000 -$700,000 $1,700,000 -$680,000 $1,020,000 $700,000 $1,720,000

Year 4

Other Cash Flows: Initial Capital Outlay Salvage Value Tax Effect of Salvage Net Working Capital Inventories Accounts Payable Recovery of NWC Total Other Cash Flows

-$10,500,000

$0

$0

$0

$500,000 $740,000

Total Net Cash Flow

-$10,500,000

$3,720,000

$4,680,000

$2,520,000

$2,460,000

Present Value at 10% Net Present Value

-$10,500,000 $323,113

$3,381,818

$3,867,769

$1,893,313

$1,680,213

-$10,000,000 $400,000 -$160,000 -$1,000,000 $500,000

Capital Budgeting Examples - Solutions

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