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Lecture Fourteen Cash Flow Estimation and Other Topics in Capital Budgeting. Relevant cash flows Working capital in capital budgeting Unequal project lives Inflation. Proposed Project. Cost: $200,000 + $10,000 shipping + $30,000 installation. Depreciable cost: $240,000.

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lecture fourteen cash flow estimation and other topics in capital budgeting
Lecture FourteenCash Flow Estimation and Other Topics in Capital Budgeting
  • Relevant cash flows
  • Working capital in capital budgeting
  • Unequal project lives
  • Inflation
proposed project
Proposed Project
  • Cost: $200,000 + $10,000 shipping + $30,000 installation. Depreciable cost: $240,000.
  • Inventories will rise by $25,000 and payables by $5,000.
  • Economic life = 4 years.
  • Salvage value = $25,000.
  • MACRS 3-year class.
slide3
Sales: 100,000 units/yr @ $2.
  • Variable cost = 60% of sales.
  • Tax rate = 40%.
  • WACC = 10%.
set up without numbers a time line for the project s cash flows
Set up, without numbers, a time line for the project’s cash flows.

0

1

2

3

4

Initial

Costs

OCF1

OCF2

OCF3

OCF4

+

(CF0)

Terminal

CF

NCF0

NCF1

NCF2

NCF3

NCF4

slide5

Investment at t = 0:

Equipment

-$200

Installation & Shipping

-40

Increase in inventories

-25

Increase in A/P

5

Net CF0

-$260

DNWC = $25 - $5 = $20.

what s the annual depreciation
What’s the annual depreciation?

Year

Rate

x

Basis

Depreciation

1

0.33

$240

$ 79

2

0.45

240

108

3

0.15

240

36

4

0.07

240

17

1.00

$240

Due to 1/2-year convention, a 3-year asset is depreciated over 4 years.

slide11

0

1

2

3

4

5

6

7

8

12%

-82,500

22,800

26,760

22,470

20,160

19,830

18,180

16,200

16,200

slide12

11 - 7

Operating cash flows:

1

2

3

4

Revenues

$200

$200

$200

$200

Op. Cost, 60%

-120

-120

-120

-120

Depreciation

-79

-108

-36

-17

Oper. inc. (BT)

1

-28

44

63

Tax, 40%

--

-11

18

25

1

-17

26

38

Oper. inc. (AT)

Add. Depr’n

79

108

36

17

Op. CF

80

91

62

55

net terminal cf at t 4

11 - 8

Net Terminal CF at t = 4:

Recovery of NWC

$20

Salvage Value

25

Tax on SV (40%)

-10

Net termination CF

$35

Q. Always a tax on SV? Ever a positive tax number?

Q. How is NWC recovered?

should cfs include interest expense dividends

11 - 9

Should CFs include interest expense? Dividends?
  • No. The cost of capital is accounted for by discounting at the 10% WACC, so deducting interest and dividends would be “double counting” financing costs.
slide15

11 - 10

Suppose $50,000 had been spent last year to improve the building. Should this cost be included in the analysis?

No. This is a sunk cost.Analyze incremental investment.

suppose the plant could be leased out for 25 000 a year would this affect the analysis

11 - 11

Suppose the plant could be leased out for $25,000 a year. Would this affect the analysis?
  • Yes. Accepting the project means foregoing the $25,000. This is an opportunity cost, and it should be charged to the project.
  • A.T. opportunity cost = $25,000(1 - T) = $25,000(0.6) = $15,000 annual cost.
slide17

11 - 12

If the new product line would decrease sales of the firm’s other lines, would this affect the analysis?
  • Yes. The effect on other projects’ CFs is an “externality.”
  • Net CF loss per year on other lines would be a cost to this project.
  • Externalities can be positive or negative, i.e., complements or substitutes.
slide18

11 - 13

Here are all the project’s net CFs (in thousands) on a time line:

0

1

2

3

4

k = 10%

-260

79.7

91.2

62.4

54.7

Terminal CF

35.0

89.7

Enter CFs in CF register, and I = 10%.

NPV = -$4.03

IRR = 9.3%

what s the project s mirr

11 - 14

What’s the project’s MIRR?

0

1

2

3

4

-260

79.7

91.2

62.4

89.7

10%

68.6

10%

110.4

10%

106.1

MIRR = ?

374.8

-260

Can we solve using a calculator?

slide20

N

I/YR

PV

PMT

FV

11 - 15

Yes.

CF0 = 0

CF1 = 79.7

CF2 = 91.2

CF3 = 62.4

CF4 = 89.7

I = 10

NPV = 255.97

INPUTS

4 10 -255.97 0

TV = FV = 374.8

OUTPUT

use the fv tv of inputs to find mirr

N

I/YR

PV

PMT

FV

11 - 16

Use the FV = TV of inputs to find MIRR

INPUTS

4 -260 0 374.8

9.6

OUTPUT

MIRR = 9.6%. Since MIRR < k = 10%, reject the project.

what s the payback period

11 - 17

What’s the payback period?

0

1

2

3

4

-260

79.7

91.2

62.4

89.7

Cumulative:

-260

-180.3

-89.1

-26.7

63.0

Payback = 3 + 26.7/89.7 = 3.3 years.

if this were a replacement rather than a new project would the analysis change

11 - 18

If this were a replacement rather than a new project, would the analysis change?

Yes. The old equipment would be sold, and the incremental CFs would be the changes from the old to the new situation.

slide24

11 - 19

  • The relevant depreciation would be the change with the new equipment.
  • Also, if the firm sold the old machine now, it would not receive the SV at the end of the machine’s life. This is an opportunity cost for the replacement project.
slide25

11 - 20

Q. If E(INFL) = 5%, is NPV biased?

A. YES.

k = k* + IP + DRP + LP + MRP.

Inflation is in denominator but not in

numerator, so downward bias to NPV.

Should build inflation into CF forecasts.

slide26

11 - 21

Consider project with 5% inflation. Investment remains same, $260. Terminal CF remains same, $35.

Operating cash flows:

1 2 3 4

Revenues $210 $220 $232 $243

Op. cost 60% -126 -132 -139 -146

Depr’n -79 -108 -36 -17

Oper. inc. (BT) 5 -20 57 80

Tax, 40% 2 -8 23 32

Oper. inc. (AT) 3 -12 34 48

Add Depr’n 79 108 36 17

Op. CF 82 96 70 65

slide27

NPV = $15.0

IRR = 12.6%

11 - 22

Here are all the project’s net CFs (in thousands) when inflation is considered.

0

1

2

3

4

k = 10%

-260

82.1

96.1

70.0

65.0

Terminal CF

35.0

100.0

Enter CFs in CF register, and I = 10%.

Project should be accepted.

s and l are mutually exclusive and will be repeated k 10 which is better

11 - 23

S and L are mutually exclusive and will be repeated. k = 10%. Which is better?

Expected Net CFs

Year

Project S

Project L

($100,000)

0

($100,000)

60,000

1

33,500

60,000

2

33,500

--

3

33,500

--

4

33,500

slide29

11 - 24

S

L

CF

-100,000

-100,000

0

CF

60,000

33,500

1

N

2

4

j

I

10

10

NPV

4,132

6,190

Q. NPVL > NPVS. Is L better?

A. Can’t say. Need replacement chain analysis.

slide30

11 - 25

  • Note that Project S could be repeated after 2 years to generate additional profits.
  • Use replacement chain to calculate extended NPVS to a common life.
  • Since S has a 2-year life and L has a 4-year life, the common life is 4 years.
slide31

11 - 26

L:

0

1

2

3

4

10%

-100,000

33,500

33,500

33,500

33,500

NPVL = $6,190 (already to Year 4)

S:

0

1

2

3

4

10%

-100,000

60,000

60,000

60,000

60,000

-100,000

-40,000

NPVS = $7,547 (on extended basis)

slide32

1

11 - 27

Equivalent Annual Annuity (EAA)

That annuity PMT whose PV equals the project’s NPV.

S:

2

0

10%

10%

EAAS

EAAS

PV1

PV2

4,132 = Previously determined NPVS.

slide33

N

I/YR

PV

PMT

FV

N

I/YR

PV

PMT

FV

11 - 28

Project S (EAA):

INPUTS

2 10 -4132 0

EAAS = 2380.82

OUTPUT

Project L (EAA):

INPUTS

4 10 -6190 0

EAAL = 1952.76

OUTPUT

The higher annuity is better.

slide34

11 - 29

  • The project, in effect, provides an annuity of EAA.
  • EAAS > EAAL , so pick S.
  • Replacement chains and EAA always lead to the same decision.
if the cost to repeat s in two years rises to 105 000 which would be best

2

3

60,000

-105,000

-45,000

11 - 30

If the cost to repeat S in two years rises to $105,000, which would be best?

4

0

1

10%

-100,000

60,000

60,000

60,000

NPVS = 3,415 < NPVL = 6,190.

Now choose L.

11 11
11-11

The Erley Equipment Company purchased a machine 5 years ago at a cost of $100,000. The machine had an expected life of 10 years at the time of purchase, and an expected salvage value of $10,000 at the end of 10 years. It is being depreciated by the straight line method toward a salvage value of $10,000, or by $9,000 per year.

A new machine can be purchased for $150,000, including installation costs. During its 5-year life, it will reduce cash operating expenses by $50,000 per year. Sales are not expected to change. At the end of its useful life, the machine is estimated to be worthless. MACRS depreciation will be used, and the machine will be depreciated over its 3-year class life rather than its 5-year economic life. (See Table 11A-2 for MACRS recovery allowance percentages.)

The old machine can be sold today for $65,000. The firm’s tax rate is 35 percent. The appropriate discount rate is 16 percent.

a) If the machine is purchased, what is the amount of the initial cash flow at Year 0?

b) What incremental operating cash flows will occur at the end of Years 1 through 5 as a result of replacing the old machine?

c) What incremental terminal cash flow will occur at the end of Year 5 if the new machine is purchased?

d) What is the NPV of this project? Should Erley replace the old machine?

slide38

0

1

2

3

4

5

16%

(88,500)

46,675

52,975

37,225

33,025

29,350

(10,000)

19,350

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