Financial management: lecture 7

Free Cash Flows in Finance

Calculate future cash flows

Financial management: lecture 7

Today’s agenda

Review what we have learned in the last week

How to calculate the cash flows in the future

Financial management: lecture 7

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 7

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 7

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 7

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 7

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 7

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 7

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 7

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 7

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 7

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 7

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 7

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 7

Inflation

Example - nominal figures

99.429,26$

78.59708487.20=8000x1.034

56.63768240=8000x1.033

92.68098240=8000x1.032

73.727280001

10% @ PVCost FlowYear

4

3

2

10.182.87413

10.120.84872

10.18240

1.108000

Financial management: lecture 7

Inflation

Example - real figures

9942926

78.59707766.99=4

56.63767766.99=3

92.68097766.99=2

73.72727766.99=1

PV@6.7961%Cost FlowYear

44

33

22

068.199.7766

1.038741.82

068.199.7766

1.038487.20

068.199.7766

1.038240

1.0687766.99

1.038000

.,= $

Financial management: lecture 7

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 7

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 7

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 7

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 7

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 7

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 7

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 7

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