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### FINC3131Business Finance

Chapter 12: Cash Flow Estimation in Capital Budgeting

Learning Objectives

- Know the guidelines by which cash flows should be measured.
- Calculate a project’s incremental after-tax cash flows.
- Describe the difference between independent and mutually exclusive projects.
- Compare projects with different lives using the equivalent annual series technique.

Estimating project cash flows 1

- For this chapter, we focus on the NPV, IRR capital budgeting rules.
- To apply these rules, we need the project’s cash flows and the appropriate discount rate.
- In this chapter, you will learn how to estimate a project’s cash flows. The discount rate will still be given to you.

Estimating project cash flows 2

- Guidelines:
- Add back depreciation to net income.
- Ignore interest expense.
- All project cash flows must be incremental.
- Ignore allocated costs and sunk costs.
- Include opportunity costs.
- Net working capital.

Add back depreciation

- Depreciation is a non-cash charge and must be added to net income to estimate cash flow.

Cash flow

= net income + depreciation expense

= (revenue – cost)x(1-tc) + (tc x depreciation)

tc: corporate tax rate

Note: Cost = all costs except depreciation

Ignore interest expense

- WACC includes the interest expenses.
- In determining a project’s cash flows, we ignore it’s financing cost, i.e., the interest expense.

All project cash flows must be incremental

- To evaluate a project, we look at the cash flows which it contributes towards the firm’s existing cash flows. In other words, we look at project’s incremental cash flows.

How to determine incremental cash flows?

- Look at the firm’s cash flows without the project.
- Look at the firm’s cash flows with the project.
- The difference is the incremental cash flows.

Ignore allocated costsand sunk costs

- Allocated costs: rent, supervisory salaries, administrative costs, and various overhead expenses.
- These costs are not incremental. They don’t change if the project is undertaken. Thus, they should not be considered in estimating the project’s incremental cash flows.
- Sunk (irrecoverable) costs: costs which cannot be recovered regardless of whether the firm undertakes the project.
- Examples: R&D expenses, consultant fees.

Include opportunity costs

- Suppose the project requires the use of some asset owned by the firm.
- If the asset is not used by the project, the firm can sell the asset for $X. This $X is the opportunity cost of the asset. Such a cost should be included in the project’s cost.
- An asset’s opportunity cost is the money that the firm can receive if the asset is put to the next best use. The ‘next best’ use may be to sell the asset.

Net working capital 1

In general, the change in net working capital

= change in current assets – change in current liabilities.

- Very often, a project will require an initial increase in net working capital. This increase in net working capital must be added to the project’s costs. (changes in AR, Inv, AP, accruals, minimum cash balance)
- Assume that this additional working capital is liquidated (sold for cash) at the end of the project’s life.
- This liquidation is a cash inflow in the last period.

Net working capital 2

- The opposite pattern is also possible.
- In other words, if taking on a project REDUCES the net working capital, then the size of this reduction is subtracted from
- the project’s initial cost.
- the last period cash inflow.

Question

Thompson Company has to decide whether to build a new factory. Management has collected various cost data to use to make the decision. Some of the items collected are listed below. Which of the following should Thompson consider as being relevant for computing cash flows for the new factory project?

- $500,000 was spent last year to upgrade a piece of property on which the company is planning to build the new factory.
- It will cost $10,000,000 to construct the factory and new equipment costing $3,250,000 will need to be purchased and installed to begin production of the product to be sold.
- The factory construction costs of $10,000,000 will be financed entirely with new long-term debt (specifically a new bond issue). The company estimates that the interest costs of this new debt will be $850,000 per year.
- The variable cost of production is estimated to be 65% of annual sales.
- The accounting department plans to allocate supervisory and management costs of $25,000 per year to the project. No new supervisory or management personnel will be required.

Question

Investment in land and building: 200,000

Changes in net working capital: 8,000 increase in inventory, 3,500 increase in minimum cash balance, 18,000 increase in account receivable, 2,500 increase in account payable, 500 increase in accruals. The total amount will be recovered at the end of life of project. What is the initial change in net working capital?

Answer: 8000+3500+18000-2500-500=26,500

Capital budgeting example 1

You are given the responsibility of conducting the project selection analysis in your firm. You have to calculate the NPV of a given project. The appropriate cost of capital is 12 percent and the firm is in the 30 percent tax bracket. You are provided the following pieces of information regarding the project:

Details

- The project is going to be built on a piece of land that the firm already owns. The market value of the land is $1 million.
- If the project is undertaken, prior to construction, an amount of $100,000 would have to be spent to make the land usable for construction purposes.
- In order to come up with the project concept, the company had hired a marketing research firm for $200,000.
- The firm has spent another $250,000 on R&D for this project.

Details

- The project will require an initial outlay of $20 million for plant and machinery.
- The sales from this project will be $15 million per year of which 20 percent will be from lost sales of existing products.
- The variable costs of manufacturing for this level of sales will be $9 million per year.
- The company uses straight-line depreciation. The project has an economic life of ten years and will have a salvage value of $3 million at the end.

Details

- Because of the project the company will need additional working capital of $1 million which can be liquidated at the end of ten years.
- The project will require additional supervisory and managerial manpower that will cost $200,000 per year.
- The accounting department has allocated $350,000 as allocated overhead cost for supervisory and managerial salaries.

Calculate initial cost

- Initial cost is the sum of:
- Market value of land: $1 mil (opportunity cost)
- Land improvement $100 k
- Plant & machinery: $20 mil
- Incremental working capital: $1 mil

Initial cost

= 1,000,000 + 100,000 + 20,000,000 + 1,000,000

= $22,100,000

Calculate the annual incremental cash flow: step 1

- Calculate the annual depreciation expense

For this project, fixed assets refer to $20mil plant & machinery. Therefore,

Depreciation

= (20,000,000 – 3,000,000)/10

= $1,700,000

- Calculate incremental sales

Incremental sales = 0.8 x 15,000,000 = $12,000,000

Calculate the annual incremental cash flow: step 2

Draw up the incremental income statement

Consider other cash flows

- At the end of project’s life (t=10), company
- Recovers $1 mil additional working capital (item 9)
- Receives $3 mil salvage value from plant & machinery (item 8)

Additional cash flows at end of project

= 1,000,000 + 3,000,000

= $4,000,000

Let’s bring all the cash flows together 1

- CF0 (initial cost) = $22,100,000
- Annual incremental after-tax cash flow (Year 1 through Year 10) = $2,470,000
- Additional cash flow in Year 10 = $4,000,000
- So in year 10, the company receives a total of = 2,470,000 + 4,000,000 = $6,470,000

Let’s bring all the cash flows together 2

To compute NPV, enter cash flows in this way:

CF0 = -22,100,000

C01 = 2,470,000, F01=9

C02 = 6,470,000, F02=1

Then press NPV, enter I = 12, press CPT and NPV.

NPV = -$6,856,056.17

Decision: reject the project.

Capital budgeting example 2

- ABC Corp. manufactures television sets and computer monitors. The company is considering introducing a new 40” flat screen television/monitor. The company’s CFO has collected the following information about the proposed product.

Details

1) The project has an anticipated economic life of 5 years.

2) The company will have to purchase a new machine to produce the screens. The machine has an up front cost (t = 0) of $4,000,000. The machine will be depreciated on a straight-line basis over 5 years. The company anticipates that the machine will last for five years and then have no salvage value (that is, it will be worthless).

Details

3) If the company goes ahead with the proposed product, it will have to increase inventory by $280,000 and accounts payable by $80,000. At t = 5, the net working capital will be recovered after the project is completed.

4) The screen is expected to generate sales revenue of $2,000,000 the first year; $4,500,000 the second through fourth years and $3,000,000 in the fifth year. Each year the operating costs (excluding depreciation) are expected to equal 50% of sales revenue.

Details

5) The company’s interest expense each year will be $350,000.

6) The new screens are expected to reduce the sales of the company’s large screen TV’s by $500,000 per year.

7) The company’s cost of capital is 12%.

8) The company’s tax rate is 30%.

Questions

- What is the initial investment for the project?
- What is the 3rd year expected incremental operating cash flow? (i.e., the incremental after tax cash flow)
- What is the 5th year incremental non-operating cash flow?

Q1: initial investment

- To answer Q1, you need points 2 & 3.

Initial investment

= machine cost + change in net working capital

= 4,000,000 + (change in current assets

– change in current liabilities)

= 4,000,000 + (280,000 – 80,000)

= $4,200,000

Q2: 3rd incremental operating cash flow

To answer Q2, you need points 2,4,6,8.

Steps:

1) Incremental sales

= 4,500,000 – 500,000 = 4,000,000

2) Annual depreciation = (4,000,000)/5 = 800,000

3) Incremental operating cost for 3rd year

= 0.5 x 4,500,000 = 2,250,000

Next, draw up the incremental income statement

Q2: 3rd incremental operating cash flow

Draw up the incremental income statement

Q3: 5th year incremental non-operating cash flow

- Very simple. The only incremental non-operating cash flow is the cash flow from liquidating the increase in net working capital (point 3).
- 5th year incremental non-operating cash flow = $200,000

Mutually Exclusive Projects

- Projects are mutually exclusive if accepting one implies that the other projects will be foregone.
- When projects are mutually exclusive and have equal lives, you have to
- rank the projects based on their NPVs
- choose the best project, provided the project’s NPV is positive
- With mutually exclusive projects, choosing the project with the highest NPV is always correct.

Question

- Consider the following mutually exclusive projects, for a firm using a discount rate of 10%:

Which project(s) should the firm accept and why?

Another question

Your company is considering 5 projects: A, B, C, D, & E. Project A and Project B are independent projects. Project C, Project D and Project E are mutually exclusive (to each other, but independent from Project A and Project B). Your company’s cost of capital is 16%.

- The IRR of Project A is 14.4% (the NPV of Project A was not provided)
- The NPV of Project B is $3,286 (the IRR of Project B was not provided)
- The NPV of Project C is $1,812 (the IRR of Project C was not provided)
- The IRR of Project D is 15.2% (the NPV of Project D was not provided)
- The NPV of Project E is $2,436 (the IRR of Project F was not provided)

Which project(s) should be chosen?

Comparing projects with unequal lives: Equivalent annual series (EAS)

- When projects are mutually exclusive but have unequal lives
- We construct the equivalent annual series (EAS) of each project and
- We choose the project with the highest EAS
- A project’s EAS is the payment on an annuity whose life is the same as that of the project and whose present value, using the discount rate of the project, is equal to the project’s NPV.

Calculating EAS

- Consider Projects J & K, with the following cash flows. The discount rate is 10%.

EAS for Project J

- To compute Project J’s EAS, do the following:
- Compute Project J’s NPV
- Verify that NPV(J) = $2,921.11
- Find the payment on the 3-year (life of project J) annuity whose PV is equal to $2,921.11.

Enter the following values:

N=3, I/Y=10, PV=-2921.11, FV=0, Then CPT, PMT.

PMT = 1,174.62, which is Project J’s EAS.

So, finding EAS is nothing more than finding the payment of an annuity.

EAS for Project K

- Verify that Project K’s NPV= $4,189.06
- Find the payment on the 4-year (life of project K) annuity whose PV is equal to $ 4,189.06.

Enter the following values:

N=4, I/Y=10, PV=- 4,189.06, FV=0, Then CPT, PMT.

PMT = 1,321.53, which is Project K’s EAS.

Recall that Project J’s EAS=1174.62

So, choose Project K since it has the higher EAS.

Another application of EAS

- We can use the EAS concept to choose between two machines that do the same job but have different costs and lives.
- Consider the following problem.

Problem

- Suppose that your firm is trying to decide between two machines, that will do the same job. Machine A costs $90,000, will last for ten years and will require operating costs of $5,000 per year. At the end of ten years it will be scrapped for $10,000. Machine B costs $60,000, will last for seven years and will require operating costs of $6,000 per year. At the end of seven years it will be scrapped for $5,000. Which is a better machine? (discount rate is 10 percent)

Step 1: compute the PV of the costs of each machine

PV of costs (A)

= $90,000 + PV of $5,000 annuity for ten years - PV of the scrap (at t = 10) value of $10,000

= 90000 + 30722.84 – 3855.43 = $116,867.41

PV of costs (B)

= $60,000 + PV of $6,000 annuity for seven years - PV of the scrap (at t = 7) value of $5,000

= $60,000 + $29,210.51 - $2,565.79 =$86,644.72

Step 2: compute equivalent annual cost (EAC) series of each machine

- The equivalent annual cost series is the payment of an annuity that has the same present value as the PV of the machine’s cost.

EAC of machine A, EAC(A):

- N = 10, I/Y = 10, PV = -116867.41, FV = 0. Then CPT, PMT. This yields EAC(A) = $19,019.63.

EAC of machine B, EAC(B):

- N = 7, I/Y = 10, PV = -86644.72, FV = 0. Then CPT, PMT. This yields EAC(B) = $17,797.30.
- Choose machine B because it has the lower cost.

Summary

- Estimating a project’s after-tax incremental cash flows.
- Choosing between mutually exclusive projects.
- Comparing projects with unequal lives using the EAS technique.

Assignment

Problems: 1 2 3

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