Fin351: lecture 4

Other Investment Criteria and discounted Cash Flow

Analysis

Capital Budgeting Decision

Fin351: lecture 4

Today’s agenda

Net Present Value (revisit) Other two investment rules Some points in calculating free cash

flows Free cash flows calculation A specific example

Fin351: lecture 4

Net Present Value rule (NPV)

NPV is the present value of a project minus its cost

If NPV is greater than zero, the firm should go ahead to invest; otherwise forget about this project

A hidden assumption: there is no budget constraint or money constraint.

Fin351: lecture 4

NPV (continue)

In other words:

Managers can increase shareholders’ wealth by accepting all projects that are worth more than they cost.

Therefore, they should accept all projects with a positive net present value if there is no budget constraint.

Fin351: lecture 4

Net Present Value

Example

Q: Suppose we can invest $50 today & receive $60 later today. What is the profit?

Initial Investment

Added Value

$50

$10

A: Profit = - $50 + $60 = $10

Fin351: lecture 4

Net Present Value

Example

Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given a 10% expected return?

This is the definition of NPV

55.4$1.10

60+-50=Value

Initial Investment

Added Value

$50

$4.55

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Net Present Value

NPV = PV - required investment

NPV CC

r

C

r

C

rt

t

01

12

21 1 1( ) ( )...

( )

Fin351: lecture 4

Net Present Value

Terminology

C = Cash Flow

t = time period

r = “opportunity cost of capital” or discount rate

The Cash Flow could be positive or negative at any time period.

Fin351: lecture 4

Net Present Value

ExampleYou have the opportunity to purchase an office building. You have a tenant lined up that will generate $16,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building?

Fin351: lecture 4

Net Present Value

0 1 2 3

$16,000

$16,000$16,000

$450,000

$466,000Example - continued

Fin351: lecture 4

Net Present Value

0 1 2 3

$16,000$16,000$16,000

$450,000

$466,000

Present Value

14,953

14,953

380,395

$409,323

Example - continued

Fin351: lecture 4

Net Present Value

Example - continued

If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?

Fin351: lecture 4

Net Present Value

Example - continued

If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?

NPV

NPV

350 00016 000

107

16 000

107

466 000

107

323

1 2 3,

,

( . )

,

( . )

,

( . )

$59,

Fin351: lecture 4

Another example about NPV

An oil well, if explored, can now produce 100,000 barrels per year. The well will produce forever, but production will decline by 4% per year. Oil prices, however, will increase by 2% per year. The discount rate is 8%. Suppose that the price of oil now is $14 for barrel.

If the cost of oil exploration is $12.8 million, do you want to take this project?

Fin351: lecture 4

Solution

Visualize the cash flow patterns C0=1.4, C1=1.37, C2=1.34, C3=1.31 What is the pattern of the cash flow?

• g=C1/C0 -1 =-0.0208=-2.1%

• PV( the project) =C0+C1/(r-g)=15

• NPV=PV( the project ) -12.8>0

What’s your decision?

Fin351: lecture 4

Two other investment rules

IRR rule Payback period rule

Fin351: lecture 4

IRR rule

Internal Rate of Return (IRR) - Discount rate at which NPV = 0.

IRR rule - Invest in any project offering a IRR that is higher than the opportunity cost of capital or the discount rate.

Fin351: lecture 4

IRR rule

Example

You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

Fin351: lecture 4

Internal Rate of Return

Example

You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

0 350 00016 000

1

16 000

1

466 000

11 2 3

,

,

( )

,

( )

,

( )IRR IRR IRR

Fin351: lecture 4

Internal Rate of Return

Example

You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

0 350 00016 000

1

16 000

1

466 000

11 2 3

,

,

( )

,

( )

,

( )IRR IRR IRR

IRR = 12.96%

Fin351: lecture 4

Internal Rate of Return

-200

-150

-100

-50

0

50

100

150

200

0 5 10 15 20 25 30 35

Discount rate (%)

NP

V (

,000

s)

IRR=12.96%

Fin351: lecture 4

What’s wrong with IRR?

Pitfall 1 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem.

Example

You have two proposals to choose between. The initial proposal (H) has a cash flow that is different from the revised proposal (I). Using IRR, which do you prefer?

Fin351: lecture 4

Internal Rate of Return (1)

Example

You have two proposals to choose between. The initial proposal (H) has a cash flow that is different from the revised proposal (I). Using IRR, which do you prefer?

Project C0 C1 C2 C3 IRR NPV@7%

H -350 400 14.29% 24,000$ I -350 16 16 466 12.96% 59,000$

Fin351: lecture 4

Internal Rate of Return

%29.14

0)1(

400350

1

IRR

IRRNPV

%96.12

0)1(

466

)1(

16

)1(

16350

321

IRR

IRRIRRIRRNPV

Fin351: lecture 4

What’s wrong with IRR (2)?

Pitfall 2 - Lending or Borrowing?

Example

project C0 C1 IRR (%) NPV at 10%

J

K

-100 +150 +50 +$36.4

+100 -150 +50 -$36.4

Fin351: lecture 4

What’s wrong with IRR (3)?

Pitfall 3 - Multiple Rates of Return Certain cash flows can generate NPV=0 at two

different discount rates. The following cash flow generates NPV=0 at both (-

50%) and 15.2%. Example

• A project costs $1000 and produces a cash flow of $800 in year 1, a cash flow of $150 every year from year 2 to year 5, and a cash flow of -150 in year 6.

Fin351: lecture 4

Payback period rule

Payback period is the number of periods such that cash flows recover the initial investment of the project.

The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period. The following example will demonstrate the absurdity of this rule.

Fin351: lecture 4

Payback period rule

The following example shows that all the three projects have a payback period of 2. If the payback period used by the firm is 2, the firm can take project C and lose money.

Cash Flows

Prj. C0 C1 C2 C3 Payback NPV@10%

A -2000 +1000 +1000 +10000 2 7,429

B -2000 +1000 +1000 0 2 -264C -2000 0 +2000 0 2 - 347

Fin351: lecture 4

Some points to remember in calculating cash flows

Depreciation and accounting profit Incremental cash flows Change in working capital requirements Sunk costs Opportunity costs Forget about financing

Fin351: lecture 4

Cash flows, accounting profit and depreciation

Discount actual cash flows Using accounting income, rather than

cash flows, could lead to wrong investment decisions

Don’t treat depreciation as real cash flows

Fin351: lecture 4

Example

A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flow to the NPV using accounting income.

Fin351: lecture 4

Solution (using accounting profit)

Accounting NPV =500

1.10

500

11032

2( . )$41.

Year 1 Year 2

Cash Income $1500 $ 500

Depreciation -$1000 -$1000

Accounting Income + 500 - 500

Fin351: lecture 4

Solution (using cash flows)

Today Year 1 Year 2

Cash Income $1500 $ 500

Project Cost - 2000

Free Cash Flow - 2000 +1500 + 500

14.223$)10.1(

500

)10.1(

1500-2000=NPVCash

21

Fin351: lecture 4

Forget about financing

When valuing a project, ignore how the project is financed.

You can assume that the firm is financed by issuing only stocks; or the firm has no debt but just equity

Fin351: lecture 4

Incremental cash flows

Incremental cash flows are the increased cash flows due to investment

Do not get confused about the average cost or total cost?

Do you have examples about incremental costs?

Incremental Cash Flow

cash flow with project

cash flow without project= -

Fin351: lecture 4

Working capital Working capital is the difference between a

firm’s short-term assets and liabilities. The principal short-term assets are cash,

accounts receivable, and inventories of raw materials and finished goods.

The principal short-term liabilities are accounts payable.

The change in working capital represents real cash flows and must be considered in the cash flow calculation

Fin351: lecture 4

Example

We know that inventory is working capital. Suppose that inventory at year 1 is $10 m, and inventory at year 2 is $15. What is the change in working capital? Why does this change represent real cash flows?

Fin351: lecture 4

Sunk costs

The sunk cost is past cost and has nothing to do with your investment decision

Is your education cost so far at SFSU is sunk cost?

Fin351: lecture 4

Opportunity cost

The cost of a resource may be relevant to the investment decision even when no cash changes hands.

Give me an example about the opportunity cost of studying at SFSU?

Fin351: lecture 4

Be consistent in how you handle inflation!! Use nominal interest rates to discount

nominal cash flows. Use real interest rates to discount real cash

flows. You will get the same results, whether you

use nominal or real figures

Inflation rule

Fin351: lecture 4

Example

You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

1 real interest rate = 1+nominal interest rate1+inflation rate

Fin351: lecture 4

Inflation

Example - nominal figures

99.429,26$

78.59708741.82=8000x1.034

56.63768487.2=8000x1.033

92.68098240=8000x1.032

73.727280001

10% @ PVFlowCash Year

4

3

2

10.182.87413

10.120.84872

10.18240

1.108000

Fin351: lecture 4

Inflation

Example - real figures

Year Cash Flow PV@6.7961%

1 = 7766.99

2 = 7766.99

= 7766.99

= 7766.99

80001.03

7766.991.068

82401.03

8487.201.03

8741.821.03

2

3

4

7272 73

6809 92

3 6376 56

4 5970 78

26 429 99

7766 991 068

7766 991 068

7766 991 068

2

3

4

.

.

.

.

..

..

..

= $ , .

Fin351: lecture 4

How to calculate free cash flows?

Free cash flows = cash flows from operations + cash flows from the change in working capital + cash flows from capital investment and disposal• We can have three methods to calculate cash

flows from operations, but they are the exactly same, although they have different forms.

Fin351: lecture 4

How to calculate cash flows from operations?

Method 1• Cash flows from operations =revenue –cost

(cash expenses) – tax payment Method 2

• Cash flows from operations = accounting profit + depreciation

Method 3• Cash flows from operations =(revenue –

cost)*(1-tax rate) + depreciation *tax rate

Fin351: lecture 4

Example

revenue 1,000- Cost 600- Depreciation 200- Profit before tax 200- Tax at 35% 70 - Net income 130

Given information above, please use three methods to calculate

Cash flows

Fin351: lecture 4

Solution:

Method 1• Cash flows=1000-600-70=330

Method 2• Cash flows =130+200=330

Method 3• Cash flows =(1000-600)*(1-0.35)+200*0.35

=330

Fin351: lecture 4

A summary example ( Blooper)

Now we can apply what we have learned about how to calculate cash flows to the Blooper example, whose information is given in the following slide.

Fin351: lecture 4

Blooper Industries

Year 0 1 2 3 4 5 6

Cap Invest

WC

Change in WC

Revenues

Expenses

Depreciation

Pretax Profit

.Tax (35%)

Profit

10 000

1 500 4 075 4 279 4 493 4 717 3 039 0

1 500 2 575 204 214 225 1 678 3 039

15 000 15 750 16 538 17 364 18 233

10 000 10 500 11 025 11 576 12 155

2 000 2 000 2 000 2 000 2 000

3 000 3 250 3 513 3 788 4 078

1 050 1137 1 230 1 326 1 427

1 950 2 113 2

,

, , , , , ,

, , , ,

, , , , ,

, , , , ,

, , , , ,

, , , , ,

, , , , ,

, ,

, , ,283 2 462 2 651

(,000s)

Fin351: lecture 4

Cash flows from operations for the first year

Revenues

- Expenses

Depreciation

= Profit before tax

.-Tax @ 35 %

= Net profit

+ Depreciation

= CF from operations

15 000

10 000

2 000

3 000

1 050

1 950

2 000

3 950

,

,

,

,

,

,

,

,

or $3,950,000

Fin351: lecture 4

Blooper Industries

Net Cash Flow (entire project) (,000s)

Year 0 1 2 3 4 5 6

Cap Invest -10,000

Change in WC -1,500 - 2,575 - 204 - 214 - 225 1,678 3,039

CF from Op 3,950 4,113 4,283 4,462 4,651

Net Cash Flow -11,500 1,375 3,909 4,069 4,237 6,329 3,039

NPV @ 12% = $3,564,000