Chapter 7: Capital Budgeting Cash Flows

 In this chapter, we forecast the annual cash flows for a project. After all the cash flows are forecasted, then we can calculate the NPV or IRR (as covered in Chapter 6) and recommend that the project be either

accepted

or

rejected

.



As in Chapter 6, the relevant cash flows that we consider are always after-tax cash flows.

 Note the similarity between project after-tax cash flows and the Free Cash Flow model that is covered in Chapter 5.

11-1

Issues associated with capital budgeting cash flows

 The key to analyzing a new project is to always think

incrementally

. We calculate the incremental cash flows that are associated with the project, i.e., how will the corporation’s total

after-tax

cash flows change if this project is accepted.

 Don’t forget about future inflation when estimating future cash flows!

   Include all side effects within the corporation: the project may either cannibalize or enhance existing operations.

Do not include

sunk

costs: any money spent in the past is irrelevant. The only cash flows that matter are those that occur now and in the future.

Include any

opportunity

costs. Any asset used for a project might have a higher value in some alternative use.

11-2

The two types of investment in business assets

  Business investment requires investment in two types of assets:

long-term

and

short-term

assets.   The

long-term

assets are the plant, property, and equipment, i.e., assets that will be

depreciated

over the coming years. The

short-term

receivable, or inventory that are necessary to support a project.

assets include the increased cash, accounts Any increase in financed with investor’s (debt or equity) capital is called

short-term Net Working Capital

assets that is funded or and must be included in the calculation of a project’s NPV.

11-3

An Example: Analysis of a proposed five-year project

 If accepted today (t=0), the project is expected to generate positive net cash flows for each of the

following

five years (t=1 through t=5).   A new machine will be put into operation. The new machine costs $1,000,000. Shipping and installation will cost an additional $500,000. Thus the

Installed Cost

is

$1,500,000

. This new machine will be sold five years from today when this project is completed. We believe that it can be sold for an estimated

$100,000

salvage value in five years (t=5).   The project will increase annual revenues and operating expenses (before depreciation) by

$800,000

and

$300,000

each year, for years 1 through 5. in Continued on next slide.

11-4

Analysis of a proposed five-year project,

continued

 More information:  A

$50,000

initial increase in

Net Working Capital

will be required during the project’s life.

(NWC) is required today and this amount will be recovered in 5 years when the project is terminated. No other changes in NWC    If project is accepted, then an old, fully depreciated machine must be removed and sold. It can be sold today for

$50,000

.

This project’s 5.76%.

Installed Cost

will be

depreciated

using an IRS 5-year MACRS schedule: year 1, 20%; year 2, 32%; year 3, 19.2%; year 4, 11.52%; year 5, 11.52%; and year 6, Note that this schedule actually covers a sixth year.

The project’s cost of capita is

r=11%

. The corporate tax rate is 40%.

11-5

Calculating the annual depreciation of the project’s Installed Cost of $1,500,000  This project’s Installed Cost must be depreciated using a

5-year MACRS schedule

(schedule actually covers 6 years). Below are the annual depreciation amounts.

 The year 6 depreciation amount of $86,400 will never be realized,

since the project will terminate with year 5

.

Project Year 1 2 3 4 5 6 IRS MACRS % 20% 32% 19.2% 11.52% 11.52% 5.76% Project’s annual depreciation expense $300,000 $480,000 $288,000 $172,800 $172,800 $86,400 Remaining acct. book value

$1,200,000 $720,000 $432,000 $259,200 $86,400 0 11-6

Issues related to the project’s depreciation and project’s liquidation

 The project has a five year life. However, the IRS MACRS depreciation schedule spills over into a sixth year.

 When the project is liquidated at year 5, the remaining accounting book value of the machine will be $86,400, the amount that would have been expensed in year 6.

 Today, we believe the asset can be sold for an estimated $100,000 salvage value in five years. The estimated tax on the sale of the asset at t=5 years is estimated as follows:

TAX

=

[tax rate][sale price – remaining book value]

[0.40][100,000 – 86,400] =

$5400, paid at year t=5.

= 11-7

Issues related to the t=0 disposal of the old, fully depreciated machine

 If project is accepted today, then an existing, fully depreciated machine must immediately be removed and sold. This existing machine can be sold today for

$50,000

.

 The estimated tax on the sale of the (fully depreciated) asset today is estimated as follows:

TAX value]

=

[tax rate][sale price – remaining book

= [0.40][50,000 – 0] =

$20,000, paid at today at t=0.

11-8

Estimating the project’s Initial Investment or Capital Expenditure

 We estimate of the new project’s initial cost. There are two asset costs:

Installed Cost

and

Net Working Capital

.

Purchase of Machine + Installation and Shipping Installed Cost + Initial increase in Net Working Capital (NWC) - Proceeds from existing asset sales Net investment before taxes + tax on sale of existing assets Total Initial Net Investment (an outflow of cash) 1,000,000 500,000

1,500,000

50,000 50,000 1,500,000 20,000

$1,520,000

11-9

Estimating the project’s annual

incremental

operating

Cash Flows

for years 1 through 5   These are essentially

incremental

(FCF). Free Cash Flow estimation was covered earlier in Chapter 5 (in Addendum 2).

Free Cash Flows The project Net Cash Flows must always ignore the interest costs associated with any debt financing. Thus these Free Cash Flows appear as if the project were all equity financed. The actual interest cost of any debt financing is actually reflected in the cost of capital

r

that is used to calculate the NPV.

 The project cost of capital

r=11%

represents a weighted average of the equity and debt costs of financing this project. 11-10

Estimating the project’s annual

incremental

operating Cash Flows for years 1 through 5    For each operating year of this project (years 1 through 5), the annual net after-tax

incremental

cash flows ΔCF 1 through ΔCF 5 must be estimated. The general formula follows: ΔCF i =

ΔNOPAT

+ Δdepreciation – ΔNWC +/– Salvage or Terminal cash flows , otherwise expressed as shown below ΔCF i = [Δrevenue – Δcosts – Δdepreciation][1 – tax rate] + Δdepreciation – ΔNWC (a) +/– Salvage or Terminal cash flows (b) 

(a)

ΔNWC represents changes in Net Working Capital. ΔNWC is

positive

when additional investment in NWC is needed. 

(b)

The Salvage or Terminal cash flows include such items as: sale of assets and taxes on the sale of those assets, and costs associated with the disposal of a project, e.g., environmental cleanup costs. 11-11

Estimating the project’s annual

incremental

operating Cash Flows for years 1 through 5      ΔCF i = [Δrevenue – Δcosts – Δdepreciation][1 – tax rate] + Δdepreciation – ΔNWC +/– Salvage or Terminal cash flows ΔCF 1 = [800,000 – 300,000 – 300,000][1 – 0.4] + 300,000 – 0 =

$420,000

ΔCF 2 = [800,000 – 300,000 – 480,000][1 – 0.4] + 480,000 – 0 =

$492,000

ΔCF 3 = [800,000 – 300,000 – 288,000][1 – 0.4] + 288,000 – 0 =

$415,200

ΔCF 4 = [800,000 – 300,000 – 172,800][1 – 0.4] + 172,800 – 0 =

$369,120

11-12

Estimating the project’s annual

incremental

operating Cash Flows for years 1 through 5  Note that

CF 5 $50,000

must include the recovery of the original of NWC, final sale of machine for

$100,000

, and tax payment of

$5440

on the sale of the machine.

ΔCF 5 = [Δrevenue – Δcosts – Δdepreciation][1 – tax rate] + Δdepreciation – ΔNWC +/– Salvage or Terminal cash flows ΔCF 5 = [800,000 – 300,000 – 172,800][1 – 0.4] + 172,800 – ( –50,000 ) + 100,000 – [0.40][100,000 – 86,400] =

$513,680

11-13

Final NPV and IRR analysis of the five-year project

  This five-year project has the following estimated after-tax cash flows.The project also has a cost of capital r=11%.

Now this example becomes a Chapter 6 NPV/IRR analysis.

Year 0 1 2 3 4 5 Incremental Cash Flow -1,520,000 420,000 492,000 415,200 369,120 513,680

11-14

Final NPV and IRR analysis of the five-year project

  Using a financial calculator, at a cost of capital of r=11%, the

NPV

is

$109,282

. The

IRR

is

13.8%

, which is greater than

r=11%

.

If this is an independent project, then it should be

accepted

.

NPV 0  CF 0  1 CF 1  r 1 CF 2  r 1 CF 3  r 1 CF 4 CF 5 5 NPV 0  1,550,000   420,000 1  0.11

1   492,000 1  0.11

  415,200 1  0.11

  369,120 1  0.11

  513,680 1  0.11

 5 NPV 0  1,520,000  1,629,282 NPV 0  $109,282 11-15

A further look at the five-year project’s Net Working Capital

   $50,000 is initially spent on NWC if the project is accepted. This $50,000 is considered to be recovered at t=5 years, when the project is liquidated or terminated.

For five years, this $50,000 is tied up for the project and cannot be used elsewhere in the firm, and thus represents an opportunity cost. This $50,000 had to be borrowed at r=11% for five years.

Most firms take strong action to minimize investment in inventory and other short-term assets, as these items represent a use of investor’s capital.

11-16

Other issues associated with the capital budgeting process

 The analysis of the five-year project obviously provides a budget for the project, consisting of forecasts of future revenue and costs.

 Over the life of the project, actual performance will be evaluated and then compared to the original capital budgeting forecast.

 Be very aware of the

games

that may be played within firms with the capital budgeting process.

11-17

Investments of unequal lives; an example

    We evaluate a machine, having a four year economic life (t=0 to t=4 years).    The machine costs $12,000 today to purchase.

The machine costs $3000 per year to maintain.

The machine can be sold for $2000 salvage value at the end of year 4 (t=4).

The machine can be replaced with an identical machine, having the same annual costs, at t=4 years.

The real cost of capital is r=6% per year.

We will use the

Equal Annual Cost

Method (EAC).

11-18

Investments of unequal lives; an example,

continued

  The timeline of costs for the 4-year machine is shown below.

In order to estimate the Equivalent Annual Cost or EAC, a two step procedure is required.   Step 1: Calculate the PV 0 of all the (net annual) costs.

Step 2: Express the PV n=4 year annuity and calculate the annual cash flow of this annuity.

0 from Step 1 as the cash flow of an t=0 -12,000 t=1 -3000 t=2 -3000 t=3 -3000 t=4 - 3000 + 2000 = -1000 11-19

Investments of unequal lives; an example,

continued

 Below are Steps 1 and 2, as described in the previous slide. Step 1 calculate the PV 0 converts the PV 0 of the annual net costs, while Step 2 into the cash flows of a 4-year annuity.

PV 0  12,000  3000  1  0.06

PV 0  20,811.13

3000 1  0.06

3000 1  0.06

1000   1  0.06

 4 PV 0  C   1 r r 1  1  r  n    20,811  C   1 0.06

0 .

06  1 1  0.06

 4   C  6005.92

11-20

Investments of unequal lives; an example,

continued

t=0 t=1 t=2 t=3 t=4 -6005.92

-6005.92

-6005.92

-6005.92

 This 4-year machine thus has an Equivalent Annual Cost or EAC=$6005.92 per year.

 What if the firm had to decide between two consecutive 4-year machines

versus

an 8-year machine that has an EAC=$6500 per year.

 In such a case, choose the machine with the lower EAC, in this case the 4-year machine has the lower EAC.

11-21

The decision to replace an existing asset

   An existing machine has the annual maintenance and salvage costs shown below.

This machine performs the same function as the 4-year machine with an EAC=$6005.92

When should the existing machine be replaced with the new 4 year machine?

Year

0 (now) 1 2 3 4 5

Maintenance Costs

0 4000 4500 5000 5500 6000

Salvage Value

8000 6000 4000 2000 1000 0 11-22

The decision to replace an existing asset,

continued

   What is the PV 0 one more year?

of keeping the existing machine in operation for  PV 0 = 8000 + 4000/(1+0.06) – 6000/(1+0.06) =

$6113.21

This

$6113.21

figure still cannot be compared to the new 4-year machine’s

EAC=$6005.92

, as the new machine’s EAC falls from t=1 to t=4 on the timeline. The PV 0 of the old machine must be multiplied by

1+r

to bring it up to t=1 years.

 FV 1 = (6113.21)(1+0.06) =

$6480

The

$6005.92

FV 1

year.

=$6480

EAC of the new machine is

less

than the of allowing the old machine to remain for the next  Replace the existing machine today at t=1.

11-23