Topic 4 Capital Budgeting Part 2

The NPV Investment Evaluation Process

Step 1 - Calculate depreciation

Step 2 - Calculate any gain/loss on disposal

Step 3 - Calculate taxable income, i.e. profit or loss

Step 4 – Calculate the tax item, i.e tax bill or rebate

Step 5 - Calculate net cash flows

Step 6 - Discount the net cash flows

Step 7 – Conclusion – NPV: + accept, - reject

Example

Purchase price $42 000 Salvage value $1 000 at end Year 3 Operating net cash-inflows Year 1 $31 000

Year 2 $29 000 Year 3 $27 000

Feasibility study cost $4 000 – yet to be paid Warehouse previously rented out for $8,000 p.a. will be used for

project New technician will replace existing technician. Existing technician’s salary = $65 000 p.a. New technician’s salary = $70 000 p.a. Old machine can be sold for $2500, book value is $3 000 Tax rate is 30% Depreciation is straight line Required rate of return is 12% p.a.

Solution – depreciation and gain/loss on disposal

Depreciation = cost price/no. of years

= $42,000/3 = $14,000 p.a.

Gain/loss on sale:

Old Machine New Machine

Book value yr 0 3000 Book value yr 3 0

Salvage value yr 0 2500 Salvage value yr 3 1000

Loss on sale 500 Gain on sale 1000

Note: book value = cost price less accumulated depreciation

Solution - taxable income

Profit & Loss Statement

0 1 2 3

Operating

cash flows31 000 29 000 27 000

- Depreciation (14 000) (14 000) (14 000)

- Rent foregone (8 000) (8 000) (8 000)

+ Gain/loss on sale (500) 1 000

- Additional salary (5 000) (5 000) (5 000)

= Taxable income (profit/loss)

(500) 4 000 2 000 1000

Tax Paid (30%) (150) 1 200 600 300

Cash Flow Statement

0 1 2 3

Tax (30%) 150 (1 200) (600) (300)

Oper. cash flows 31 000 29 000 27 000

Rent foregone (8 000) (8 000) (8 000)

Salvage value 2 500 1 000

Additional salary (5 000) (5 000) (5 000)

Initial outlay (42 000)

Net Cash Flows (39 350) 16 800 15 400 14 700

Solution – Cash flows

Solution – Discount The Net Cash Flows

NPV = -$39,350 + $16,800(1.12)-1 + $15,400(1.12)-2 + $14,700(1.12)-3

= ($1,610)

Conclusion: NPV < 0 – therefore, reject the project.

Finance costs

Finance costs should not be included as an explicit cash flow in the analysis.

Finance costs:

cost of debt (interest expense),

cost of equity (dividends)

Finance costs are included in the required rate of return (discount rate) used to evaluate the project.

Incremental Cash-Flow Example

In NPV analysis we are only interested in incremental cash-flows.

Example: A firm is currently considering replacing a machine purchased 2 years ago with an original estimated useful life of 5 years. The replacement machine has an economic life of 3 years.

Solution – depreciation and gain/loss on disposal

Depreciation: old machine = $48,000 p.a.,new machine = $120,000 p.a.

Gain/loss on sale:Old Machine New Machine

Book value yr 0 144,000* Book value yr 0

Salvage value yr 0 80,000 Salvage value yr 3 100,000

Loss on sale 64,000 Gain on sale 100,000

Book value = cost price less accumulated depreciation

*Book value of old machine = 240,000 – 96,000 = 144,000

Solution - taxable incomeProfit & Loss Statement

0 1 2 3

Incremental

cash revenues50 000 50 000 50 000

- Incremental

cash expenses(10 000) (10 000) (10 000)

- Incremental depn (72 000) (72 000) (72 000)

- Loss on sale (old) (64 000)

+ Gain on sale (new) 100 000

= Taxable income (64 000) (32 000) (32 000) 68 000

Tax Paid (30%) (19 200) (9 600) (9 600) 20 400

Solution – cash flows

Cash Flow Statement

0 1 2 3

Tax Paid (30%) 19 200 9 600 9 600 (20 400)

Incremental

cash revenues50 000 50 000 50 000

Incremental

cash expenses(10 000) (10 000) (10 000)

Salvage values 80 000 100 000

Initial outlay (360 000)

Net Cash Flows (260 800) 49 600 49 600 119 600

Solution – discount net cash-flows

Conclusion: NPV < 0, therefore reject the project.

NPV = ($260,800) + $49,600(1.1)-1 + $49,600(1.1)-2 +

$119,600(1.1)-3

= ($84,860)

Summary: Which items appear in P/L Statement and which appear in Cash-Flow Statement?

When In P/L

In CF

Initial investment or cost Yr 0 No Yes

Depreciation Yr 1 to Yr n Yes No

Salvage value Yr 0 and/or Yr n No Yes

Gain on disposal Yr 0 and/or Yr n Yes No

Loss on disposal Yr 0 and/or Yr n Yes No

Cash revenues Yr 1 to Yr n Yes Yes

Cash expenses Yr 1 to Yr n Yes Yes

Working capital Yr 0 and Yr n No Yes

Rent rev. foregone Yr 1 to Yr n Yes Yes

One Step Process

•Rather than adopt a two step process to Project Evaluation (i.e. P & L Statement and Cash-Flow Statement) a one step process can be undertaken (Cash-Flow Statement only).

•Rather than work out taxable income (profit or loss) and tax in step 1 (P & L Statement) and cash flows in step 2 (Cash-Flow Statement) one can directly work out after tax cash flows for each item (in the Cash-Flow Statement).

•We will go on to illustrate by doing the second worked example just undertaken in one step

Relevant Cash Flows

One-Step Process Revenue::

cash inflow due to sale of goods and services revenue is taxable, therefore net cash-inflow after-tax equals:

REV - (REV * (tREV - (REV * (tcc)) )) oror REV (1 - t REV (1 - tcc))

where twhere tcc = corporate tax-rate = corporate tax-rate

Expenses:cash outflow due to expenditures of production, etcexpenses represent a tax saving (they are tax deductible,

therefore they reduce tax payable (they provide a tax-shield))net cash-outflow after-tax equals: EXP – (EXP * tEXP – (EXP * tcc ) ) oror EXP * ( 1 - t EXP * ( 1 - tcc))

Non-Cash Flow Items

Depreciation Tax Shield

Depreciation is a non-cash expense that is an allowable tax deduction (it provides a tax-shield). Thus it reduces the tax payable by:

Depreciation * (tc)Depreciation * (tc)

This represents a cash inflow (a tax rebate).cash inflow (a tax rebate).

Book Gain/Loss on DisposalBook Gain/Loss on Disposal• salvage value (SV) = sale price (market value) received on disposal of asset

• asset has a book value (BV) = purchase price less accumulated depreciation

if SV > BV we have a book gain

– a taxable profit arisesTax on profit = book gain * tc

This leads to a tax liability (a cash-outflow)

– The net after-tax cash-inflow from disposal will be:

SVSV lessless ((book gain * tc)

if SV < BV we have a book loss

- a deductible loss arises Tax saving on loss = book loss * tc

This leads to a tax rebate (a cash-inflow)

– The net after-tax cash-inflow from disposal will be:

SV plusplus (book loss * tc)

One-Step Process: Cash-Flow StatementAfter tax cash flows

0 1 2 3

Depreciation tax saving

21,600 i.e. 72,000 x 0.30

21,600 21,600

Incremental after

tax cash revenues35, 000

i.e. 50,000 x

(1 - 0.30)

35, 000 35, 000

Incremental after

tax cash expenses(7, 000)

i.e.

10,000 x (1 – 0.30)

(7, 000) (7, 000)

Initial outlay (360 000)

Net after tax cash flow asset disposal

99,200

i.e. 80,000 +

(64,000 x 0.30)

70 000

i.e. 100,000 –

(100,000 x 0.30)

After tax net cash flows

(260 800) 49 600 49 600 119 600

NPV (84,860)

Evaluating Projects with Different Lives

If two projects are mutually exclusive they are competing projects

A choice between the projects must be made

Evaluation of the projects is complicated if they differ in life span i.e. are each over a different number of years

A common base is required for comparison

Evaluating Projects with Different Lives

Two methods of evaluating projects with different livespans:

Equivalent Annual Annuity

Approach (EAA)

2.2.

Lowest Common Life Approach

(LCL)

1.1.

Lowest Common Life Approach

Involves choosing the lowest common multiple of lives

NPV of each project is calculated assuming each is replaced with itself until the lowest common multiple life is reached:

e.g.e.g. Project A has a life of Project A has a life of 99 years yearsProject B has a life of Project B has a life of 1111 years yearsTherefore LCL = 9 x 11 years = 99 yearsTherefore LCL = 9 x 11 years = 99 years

Replace Replace Project A Project A 11 times11 times with another project of an with another project of an identical identical cash flow patterncash flow pattern

Replace Replace Project Project BB 9 times9 times with another project of an with another project of an identical identical cash flow pattern.cash flow pattern.

Computations can become tedious (in this example over 99 years!!!)

Lowest Common Life ApproachProject A – 2 year lifeCash flows; yr 0 ($100), yr 1 $80, yr 2 $70Project B – 3 year lifeCash flows; yr 0 ($175), yr 1 $43, yr 2 $50, yr 3 $55

Lowest Common Life = 2 x 3 = 6 yrs Threfore, undertake Project A three times & Project B two timesProject A

0 1 2 3 4 5 6 (100) 80 70

(100) 80 70 (100) 80 70

Project B0 1 2 3 4 5 6

(175) 43 50 55 (175) 43 50 55

LCL Approach – Constant Chain of Replacement Assumption

Implicit assumption with LCL approach is that asset will be replaced continually by itself, and that technology, operating efficiency, sales and costs do not change.

This is supported by: The importance of cash flows further into the future

decreases (time value of money concept), and Cash flows forecasted for the life of an asset are as good as

any other forecast of cash flows (i.e. management’s forecast of cash-flows will be more accurate than any other’s)

Equivalent Annual Annuities (EAA)

When comparing two mutually exclusive projects with different lifespans it is necessary to make comparisons over the same time period.

EAA compares each project’s cash-flows calculated on an annual basis.

We select the project with the highest EAA if the cash-flows are positive

We select the project with the lowest Equivalent Annual Cost (EAC) if the cash-flows are based on costs (i.e. cash-outflows)

Equivalent annual annuity

To calculate the equivalent annual annuity (EAA):

1.1. Calculate NPV of each project over one life - as if it were Calculate NPV of each project over one life - as if it were "one-off""one-off"

2.2. Convert the NPV into an equivalent annuity for the life of Convert the NPV into an equivalent annuity for the life of each project - convert into a series of annual payments or each project - convert into a series of annual payments or annuity payments annuity payments

(i.e find the unknown PMT for the project using the PV of an (i.e find the unknown PMT for the project using the PV of an ordinary annuity formula)ordinary annuity formula)

Suppose our firm has to choose between 2 machines Suppose our firm has to choose between 2 machines that differ in terms of economic life and capacity. that differ in terms of economic life and capacity. Our required return is 14% p.a. The after-tax net Our required return is 14% p.a. The after-tax net cash-flows are:cash-flows are:

YearYear00112233445566

Machine 1(45,000)(45,000)20,00020,00020,00020,00020,00020,000

Machine 2(45,000)(45,000)12,00012,00012,00012,00012,00012,00012,00012,00012,00012,00012,00012,000

How do we decide which

machine to choose?

The unequal life-span problem

NPV1 = $1,432.64

NPV2 = $1,664.01

Does this mean machine 2 is better?

No, the NPVs can’t be compared.

Step 1: Calculate NPVs

64.432,1$64.432,46$000,45$322.2000,20$000,45$14.0

)14.01(1000,20$000,45$

3

01.664,1$01.664,46$000,45$888.3000,12$000,45$14.0

)14.01(1000,12$000,45$

6

We assume each project can be replaced an infinite number of times in the future, and then convert each NPV to its equivalent annuity

The projects’ EAAs can be compared to determine which is the best project

The EAA is the annuity amount (PMT) from the present value formula of an ordinary annuity

Step 2: Calculate The Equivalent Annual Annuities

r

rPMTPV

n11

EAA

EAA Decision EAA1 = $617.08

EAA2 = $427.91

We’ve reduced a problem with different time horizons to a choice between two annuities

Decision rule:Choose the project with the highest EAA

Choose Machine 1

00.617$322.2

64.432,1$322.264.432,1$

14.0

)14.01(164.432,1$

3

PMTPMTPMT

76.427$888.3

01.664,1$888.301.664,1$

14.0

)14.01(101.664,1$

6

PMTPMTPMT

Example – timeline equivalentsMachine 1

Each of these cash flow streams are exactly equivalent (because all three timelines have the same PV or NPV ($1,432.64)

0 1 2 3

(45 000) 20 000 20 000 20 000

0 1 2 3

1432.64

0 1 2 3

617.08 617.08 617.08

Example – timeline equivalents

Machine 2 Each of these cash flow streams are exactly equivalent (because all three timelines have the same PV or NPV ($1,664.01)

0 1 2 3 4 5 6(45 000) 12 000 12 000 12 000 12 000 12 000 12 000

0 1 2 3 4 5 6 1664.01

0 1 2 3 4 5 6

427.91 427.91 427.91 427.91 427.91 427.91

Capital Budgeting And Inflation

In project evaluation not adjusting for inflation may result in material errors in capital budgeting decisions.

Inflation is included implicitly in the discount rate

Nominal interest rate = [(1+ real interest rate)(1+Inflation rate)] – 1

This is known as the Fisher EquationExample:expected inflation rate = 4.72%, real interest rate = 6% nominal interest rate = [(1+0.06)(1+0.0472)] – 1 = 0.1100

= 11.00%

Depreciation And Inflation

Inflation erodes the real value of any depreciation tax deduction and therefore discourages capital investment in an inflationary period.

The further into the future is the depreciation claim the lower is its real present value (time value of money concept).

If we assume no real rate of interest we can work out at varying inflation rates the present value of the depreciation deductions and divide this by the cost of the asset to get an estimate of the effective write-off of the asset (use the formula:

Σ depreciation p.a.(1+r)-n cost of asset

(where r = inflation rate)

Example:Plant and equipment which could be written off over 5 years if the inflation rate is 11%. effectively, only 74% of the assets cost will be written off.

Example: Depreciation - Real Analysis • Acme Ltd., a scrap metal dealer, is considering the acquisition of

a "Crushit" metal compactor at a cost of $25,000.

• The compactor is estimated to have a five-year life.

• Tax allowable depreciation is 20% prime cost per annum

• The company tax rate is 40%

• Expected inflation rate of 8% per annum for the next 5 years

• Depreciation Tax-Shield (nominal):

$25,000 x 0.20 = $5,000 x 0.40 = $2,000 p.a.

Real Depreciation Tax-Shield

Under this approach it is necessary to deflate the depreciation tax shields by the expected inflation rate to take account of the loss of real value (i.e. loss of purchasing power) of the tax shields in an inflationary environment:

Year 1 = $2,000(1.08)-1 = $1,851.85

Year 2 = $2,000(1.08)-2 = $1,714.67

Year 3 = $2,000(1.08)-3 = $1,587.66

Year 4 = $2,000(1.08)-4 = $1,470.05

Year 5 = $2,000(1.08)-5 = $1,361.16

Capital Rationing Capital rationing – where a firm limits the total amount of funds to be invested

in projects. Therefore, even though certain projects may have a postive NPV, they could be

rejected due to capital (financing) constraints

Hard Capital RationingImposed by Capital Markets - markets will not provide sufficient finance

for a project at an acceptable cost. Does this mean capital markets are not efficient as they are not providing

funding to positive NPV projects?

Soft Capital RationingImposed by upper management to ensure subsidiaries prioritise

investments. Ensures discipline by lower level management – subsidiaries to only invest in

highest NPV projects.

Profitability Index (Benefit-Cost Ratio)

A project’s Profitability Index (PI) measures the return of a project relative to cost

PI = Present Value/Cost or

(NPV+Cost)/Cost

If PI > 1 = Accept the project (NPV must be positive)

If PI < 1 = Reject the project (NPV must be negative)

Capital RationingAssume capital constraint = 15 mProject 0 1 2 NPV PI

A -15 30 15 23.7 2.583B -8 4 25 15.5 2.938C -7 6 22 15.9 3.271

Note. PI = (NPV+Cost)/Cost

Cost of Capital = 12%

Combined NPV = 31.4 As compared to A alone 23.7

Capital Rationing

Both Projects B and C have a higher PI than Project A Total cost of Projects B and C = $15million Total cost of Project A = $15million

Rules: Maximise total NPV subject to the capital constraint (i.e. subject to

financing limits).

Use Profitability Index to rank projects as PI measures return relative to cost.

In the above example we would choose Projects B and C as they both have a higher PI than Project A and together B and C meet the capital constraint of $15million.

Optimal Economic Lives

Abandonment ValueCompare a project’s economic value (PV of future net cash-

flows) to its abandonment value (market/selling price at timeperiod T)

If abandonment value is greater than the PV of the future net cash-flows we should abandon the project

Replacement timingUse Equivalent Annual Costs (EAC) to determine the optimal

time to replace assetsEACs are used when a project is evaluated only on its costs

and revenues are ignored

Replacement timing

By comparing EACs over time, the firm can determine the optimal time to replace the asset.

In the following example, the firm should replace the asset at the end of 4 years (because EAC are lowest in Year 4).

Equivalent Annual Costs - Replacement Timing

7,500

7,419

7,372 7,355 7,3677,404

7,463

7,543

7,642

7,758

7,100

7,200

7,300

7,400

7,500

7,600

7,700

7,800

1 2 3 4 5 6 7 8 9 10