Financial management: lecture 6 Other Investment Criteria and Free Cash Flows in Finance Capital...

Financial management: lecture 6

Other Investment Criteria and Free Cash Flows in

Finance

Capital Budgeting Decisions

Financial management: lecture 6

Today’s agenda

Midterm exam Net Present Value (revisit) Other two investment rules Free cash flows calculation A specific example

Financial management: lecture 6

Mid-term exam

The midterm exam score and the solution were posted on my website last Friday: http://online.sfsu.edu/~li123456

Most students have done very well in the first midterm exam. If you don’t do very well, don’t worry about it and you can try your best to do much better in the second midterm and the final.

Remember the weight of 0.2 for the midterm with a lower score.

Financial management: lecture 6

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.

Financial management: lecture 6

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.

Financial management: lecture 6

Net Present Value

NPV = PV - required investment

NPV CC

r

C

r

C

rt

t

01

12

21 1 1( ) ( )...

( )

Financial management: lecture 6

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?

Financial management: lecture 6

Net Present Value

0 1 2 3

$16,000

$16,000$16,000

$450,000

$466,000Example - continued

Financial management: lecture 6

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

Financial management: lecture 6

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?

Financial management: lecture 6

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,

Financial management: lecture 6

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?

Financial management: lecture 6

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?

Financial management: lecture 6

Two other investment rules

IRR rule Payback period rule

Financial management: lecture 6

IRR rule

Internal Rate of Return (IRR) – Single 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.

Financial management: lecture 6

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?

Financial management: lecture 6

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

Financial management: lecture 6

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%

Financial management: lecture 6

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%

Financial management: lecture 6

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?

Financial management: lecture 6

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$

Financial management: lecture 6

Internal Rate of Return

%29.14

0)1(

400350

1

IRR

IRRNPV

%96.12

0)1(

466

)1(

16

)1(

16350

321

IRR

IRRIRRIRRNPV

Financial management: lecture 6

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

Financial management: lecture 6

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.

Financial management: lecture 6

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.

Financial management: lecture 6

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

Financial management: lecture 6

Some points to remember in calculating free cash flows

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

Financial management: lecture 6

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

Financial management: lecture 6

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.

Financial management: lecture 6

Solution (using accounting profit)

Year 1 Year 2

Cash Income $1500 $ 500

Depreciation -$1000 -$1000

Accounting Income + 500 - 500

Accounting NPV =500

1.10

500

11032

2( . )$41.

Financial management: lecture 6

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

Financial management: lecture 6

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

Financial management: lecture 6

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= -

Financial management: lecture 6

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

Financial management: lecture 6

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?

Financial management: lecture 6

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?

Financial management: lecture 6

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?

Financial management: lecture 6

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

Financial management: lecture 6

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

Financial management: lecture 6

Inflation

Example - nominal figures

Year Cash Flow PV @ 10%

1 8000

2 8000x1.03 = 8240

8000x1.03 = 8240

8000x1.03 = 8487.20

80001.10

2

3

7272 73

6809 92

3 6376 56

4 5970 78

429 99

82401 108487 20

1 108741 82

1 10

2

3

4

.

.

.

.

$26, .

..

..

.

Financial management: lecture 6

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

.

.

.

.

..

..

..

= $ , .

Financial management: lecture 6

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.

Financial management: lecture 6

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

Financial management: lecture 6

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

Financial management: lecture 6

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

Financial management: lecture 6

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.

Financial management: lecture 6

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)

Financial management: lecture 6

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

Financial management: lecture 6

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