U8-1

UNIT 8Project Valuation

Should we build this

plant?

U8-2

What is capital budgeting? Analysis of potential additions to

fixed assets. Long-term decisions; involve

large expenditures. Very important to firm’s future.

U8-3

Steps to capital budgeting

1. Estimate CFs (inflows & outflows).2. Assess riskiness of CFs.3. Determine the appropriate cost of

capital.4. Find NPV and/or IRR.5. Accept if NPV > 0 and/or IRR > WACC.

U8-4

What is the difference between independent and mutually exclusive projects?

Independent projects – if the cash flows of one are unaffected by the acceptance of the other.

Mutually exclusive projects – if the cash flows of one can be adversely impacted by the acceptance of the other.

U8-5

What is the difference between normal and nonnormal cash flow streams?

Normal cash flow stream – Cost (negative CF) followed by a series of positive cash inflows. One change of signs.

Nonnormal cash flow stream – Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. Nuclear power plant, strip mine, etc.

U8-6

Net Present Value (NPV) Sum of the PVs of all cash inflows and

outflows of a project:

N

0tt

t

)r 1 (CF

NPV

U8-7

What is Project L’s NPV?

Year CFt PV of CFt

0 -100 -$100 1 10 9.09 2 60 49.59 3 80 60.11

NPVL = $18.79

NPVS = $19.98

U8-8

Excel NPV Reminder

You may use Excel’s NPV function to calculate NPV but be careful!

Use Excel’s NPV function to find NPV of CF1-n and then subtract CF0 from this result.

U8-9

Rationale for the NPV methodNPV = PV of inflows – Cost

= Net gain in wealth If projects are independent, accept if

the project NPV > 0. If projects are mutually exclusive,

accept projects with the highest positive NPV, those that add the most value.

In this example, accept S if mutually exclusive (NPVs > NPVL), and accept both if independent.

U8-10

Internal Rate of Return (IRR) IRR is the discount rate that forces PV of

inflows equal to cost, and the NPV = 0:

Use Excel’s IRR function.

N

0tt

t

) IRR 1 (CF

0

U8-11

How is a project’s IRR similar to a bond’s YTM? They are the same thing. Think of a bond as a project. The

YTM on the bond would be the IRR of the “bond” project.

EXAMPLE: Suppose a 10-year bond with a 9% annual coupon and $1,000 par value sells for $1,134.20. Solve for IRR = YTM = 7.08%, the

annual return for this project/bond.

U8-12

Rationale for the IRR method If IRR > WACC, the project’s return

exceeds its costs and there is some return left over to boost stockholders’ returns.

If IRR > WACC, accept project.If IRR < WACC, reject project.

If projects are independent, accept both projects, as both IRR > WACC = 10%.

If projects are mutually exclusive, accept S, because IRRs > IRRL.

U8-13

NPV Profiles A graphical representation of project

NPVs at various different costs of capital.

WACC NPVL NPVS

0 $50 $40 5 33 2910 19 2015 7 1220 (4) 5

U8-14

Drawing NPV profiles

-10

0

10

20

30

40

50

60

5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

SL

.

.

...

.

..

.

. .

U8-15

Comparing the NPV and IRR methods

If projects are independent, the two methods always lead to the same accept/reject decisions.

If projects are mutually exclusive … If WACC > crossover rate, the

methods lead to the same decision and there is no conflict.

If WACC < crossover rate, the methods lead to different accept/reject decisions.

U8-16

Reasons why NPV profiles cross

Size (scale) differences – the smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so a high WACC favors small projects.

Timing differences – the project with faster payback provides more CF in early years for reinvestment. If WACC is high, early CF especially good, NPVS > NPVL.

U8-17

Reinvestment rate assumptions NPV method assumes CFs are

reinvested at the WACC. IRR method assumes CFs are reinvested

at IRR. Assuming CFs are reinvested at the

opportunity cost of capital is more realistic, so NPV method is the best. NPV method should be used to choose between mutually exclusive projects.

Perhaps a hybrid of the IRR that assumes cost of capital reinvestment is needed.

U8-18

What is the payback period?

The number of years required to recover a project’s cost, or “How long does it take to get our money back?”

Calculated by adding project’s cash inflows to its cost until the cumulative cash flow for the project turns positive.

U8-19

Calculating payback

PaybackL = 2 + / = 2.375 years

CFt -100 10 60Cumulative -100 -90 50

0 1 2 3

= 30 80

80

-30

Project L’s Payback Calculation

PaybackL = 2.375 years

PaybackS = 1.600 years

U8-20

Strengths and weaknesses of payback

Strengths Provides an indication of a project’s

risk and liquidity. Easy to calculate and understand.

Weaknesses Ignores the time value of money. Ignores CFs occurring after the

payback period.

U8-21

Proposed Project Total depreciable cost

Equipment: $200,000 Shipping: $10,000 Installation: $30,000

Changes in working capital Inventories will rise by $25,000 Accounts payable will rise by $5,000

Effect on operations New sales: 100,000 units/year @

$2/unit Variable cost: 60% of sales

U8-22

Proposed Project

Life of the project Economic life: 4 years Depreciable life: MACRS 3-year class Salvage value: $25,000

Tax rate: 40% WACC: 10%

U8-23

Determining project value Estimate relevant cash flows

Calculating annual operating cash flows. Identifying changes in working capital. Calculating terminal cash flows.

0 1 2 3 4

Initial OCF1 OCF2 OCF3 OCF4 Costs +

Terminal CFs

NCF0 NCF1 NCF2 NCF3 NCF4

U8-24

Initial year net cash flow Find Δ NOWC.

⇧ in inventories of $25,000 Funded partly by an ⇧ in A/P of $5,000 Δ NOWC = $25,000 - $5,000 = $20,000

Combine Δ NOWC with initial costs.

Equipment -$200,000 Installation -40,000 Δ NOWC -20,000

Net CF0 -$260,000

U8-25

Determining annual depreciation expense

Year Rate x Basis Depr 1 0.33 x $240 $ 79 2 0.45 x 240 108 3 0.15 x 240 36 4 0.07 x 240 17

1.00 $240

Due to the MACRS ½-year convention, a 3-year asset is depreciated over 4 years.

U8-26

Annual operating cash flows

1 2 3 4

Revenues 200.0 200.0 200.0 200.0

- Op Costs -120.0

-120.0

-120.0

-120.0

- Depr’n Expense -79.2 -108.0

-36.0 -16.8

Operating Income (BT)

0.8 -28.0 44.0 63.2

- Tax (40%) 0.3 -11.2 17.6 25.3

Operating Income (AT)

0.5 -16.8 26.4 37.9

+ Depr’n Expense 79.2 108.0 36.0 16.8

Operating CF 79.7 91.2 62.4 54.7(Thousands of dollars)

U8-27

Terminal net cash flow

Recovery of NOWC $20,000Salvage value 25,000Tax on SV (40%) -10,000Terminal CF $35,000

Q. How is NOWC recovered?Q. Is there always a tax on SV?Q. Is the tax on SV ever a positive cash

flow?

U8-28

Should financing effects be included in cash flows? No, dividends and interest

expense should not be included in the analysis.

Financing effects have already been taken into account by discounting cash flows at the WACC of 10%.

Deducting interest expense and dividends would be “double counting” financing costs.

U8-29

Should a $50,000 improvement cost from the previous year be included in the analysis?

No, the building improvement cost is a sunk cost and should not be considered.

This analysis should only include incremental investment.

U8-30

If the facility could be leased out for $25,000 per year, would this affect the analysis?

Yes, by accepting the project, the firm foregoes a possible annual cash flow of $25,000, which is an opportunity cost to be charged to the project.

The relevant cash flow is the annual after-tax opportunity cost. A-T opportunity cost = $25,000 (1 – T)

= $25,000(0.6) = $15,000

U8-31

If the new product line decreases the 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 (in the case of complements) or negative (substitutes).

U8-32

Proposed project’s cash flow time line0 1 2 3 4

-260 79.7 91.2 62.4 54.7 Terminal CF → 35.0

89.7

Enter CFs into calculator CFLO register and enter I/YR = 10%. NPV = -$4.03 million IRR = 9.3% Payback = 3.3 years

U8-33

What is real option analysis? Real options exist when managers can

influence the size and riskiness of a project’s cash flows by taking different actions during the project’s life.

Real option analysis incorporates typical NPV budgeting analysis with an analysis for opportunities resulting from managers’ decisions.

U8-34

What are some examples of real options?

Investment timing options Abandonment/shutdown

options Growth/expansion options Flexibility options