0 1. Identify the SIZE and TIMING of all relevant cash flows on a time line. 2.Identify the RISKINESS of the cash flows to determine the appropriate discount

1

1. Identify the SIZE and TIMING of all relevant cash flows on a time line.

2. Identify the RISKINESS of the cash flows to determine the appropriate discount rate.

3. Find NPV by discounting the cash flows at the appropriate discount rate.

4. Compare the value of competing cash flow streams at the same point in time.

Review of Domestic Capital Budgeting

2

Measuring Cash Flows

• The guiding principle is to measure incremental cash flows. That is, how much the project really adds to the cash flow of the parent

• But this is often easier said than done. They are often real problems in measuring incremental cash flows such as

• Cross Relationship Between Parent and Subsidiary– Cannibalization– Cross Fertilization

• Accounting for cash flows– Transfer pricing (especially when market prices aren’t available)– Fees royalties and other charges for overhead

• Intangibles– Good will– Experience

3


The basic net present value equation is

01 )1()1(

CK

TV

K

CFNPV

TT

T

tt

t

Where:

CFt = expected incremental after-tax cash flow in year t,

TVT = expected after tax cash flow in year T, including return of net working capital,

C0 = initial investment at inception,

K = weighted average cost of capital.

T = economic life of the project in years.

4


The NPV rule is to accept a project if NPV 0

0)1()1( 0

1

CK

TV

K

CFNPV

TT

T

tt

t

and to reject a project if NPV 0

.0)1()1( 0

1

CK

TV

K

CFNPV

TT

T

tt

t

5


For our purposes it is necessary to expand the NPV equation.

)1()1)(( τIDτIDOCRCF ttttttt

Rt is incremental revenue

Ct is incremental operating cash flow

Dt is incremental depreciation

It is incremental interest expense

is the marginal tax rate

6


For our purposes it is necessary to expand the NPV equation.

)1()1)(( τIDτIDOCRCF ttttttt )1( τIDNI ttt

ttt DτDτOCR )1)((

tt DτNOI )1(

ttt τDτOCR )1)((

tt τDτOCF )1(

7


We can usettt τDτOCFCF )1(

01 )1()1(

CK

TV

K

CFNPV

TT

T

tt

t

to restate the NPV equation

01 )1()1(

)1(C

K

TV

K

τDτOCFNPV

TT

T

tt

tt

as:

8

The Adjusted Present Value Model

Can be converted to adjusted present value (APV)

01 )1()1()1(

)1(C

K

TV

K

τD

K

τOCFNPV

TT

tt

T

tt

t

By appealing to Modigliani and Miller’s results.

01 )1()1()1()1(

)1(C

K

TV

i

τI

i

τD

K

τOCFAPV

Tu

Tt

tt

tT

tt

u

t

9

The Adjusted Present Value Model

The APV model is a value additivity approach to capital budgeting. Each cash flow that is a source of value to the firm is considered individually.

Note that with the APV model, each cash flow is discounted at a rate that is appropriate to the riskiness of the cash flow.

01 )1()1()1()1(

)1(C

K

TV

i

τI

i

τD

K

τOCFAPV

Tu

Tt

tt

tT

tt

u

t

10

Capital Budgeting from the Parent Firm’s Perspective

• Donald Lessard developed an APV model for a MNC analyzing a foreign capital expenditure. The model recognizes many of the particulars peculiar to foreign direct investment.

T

tt

d

ttT

ud

TT

T

tt

d

ttT

tt

d

ttT

tt

ud

tt

i

LPSCLSRFSCS

K

TVS

i

τIS

i

τDS

K

τOCFSAPV

1000000

111

)1()1(

)1()1()1(

)1(

11


The operating cash flows must be translated back into the parent firm’s currency at the spot rate expected to prevail in each period.

T

tt

d

ttT

ud

TT

T

tt

d

ttT

tt

d

ttT

tt

ud

tt

i

LPSCLSRFSCS

K

TVS

i

τIS

i

τDS

K

τOCFSAPV

1000000

111

)1()1(

)1()1()1(

)1(

The operating cash flows must be discounted at the unlevered domestic rate

12


OCFt represents only the portion of operating cash flows available for remittance that can be legally remitted to the parent firm.

T

tt

d

ttT

ud

TT

T

tt

d

ttT

tt

d

ttT

tt

ud

tt

i

LPSCLSRFSCS

K

TVS

i

τIS

i

τDS

K

τOCFSAPV

1000000

111

)1()1(

)1()1()1(

)1(

The marginal corporate tax rate, , is the larger of the parent’s or foreign subsidiary’s.

13


S0RF0 represents the value of accumulated restricted funds (in the amount of RF0) that are freed up by the project.

T

tt

d

ttT

ud

TT

T

tt

d

ttT

tt

d

ttT

tt

ud

tt

i

LPSCLSRFSCS

K

TVS

i

τIS

i

τDS

K

τOCFSAPV

1000000

111

)1()1(

)1()1()1(

)1(

Denotes the present value (in the parent’s currency) of any concessionary loans, CL0, and loan payments, LPt , discounted at id .

14

Which Currency?

Time Period Free Cash Flow

0 -£56.00

1 £10.40

2 £8.90

3 £9.70

4 £9.90

5 £10.40

Terminal Value (Period 5) £78.00

15

Assume Subsidiary WACC=15%

Time Period Free Cash Flowpv (15%)

0 -£56.00-£56.00

1 £10.40 £9.04

2 £8.90 £6.73

3 £9.70 £6.38

4 £9.80 £5.60

5 £10.40 £5.17

5 £78.00 £38.78

Pound NPV £15.70

$ NPV (S=1.7) $26.70

16

Suppose R($)=6% R(pound)=10%

• Then Irp means S1=S0(1.06)/1.10

Time Period Free Cash Flow S FCF ($)

0 -£56.00 1.7 -$95.20

1 £10.401.638 $17.04

2 £8.90 1.579 $14.05

3 £9.70 1.521 $14.76

4 £9.80 1.466 $14.37

5 £10.401.413 $14.69

5 £78.001.413 $110.18

17

Estimating the Future Expected Exchange Rates

We can appeal to PPP:

tf

td

t π

πSS

)1(

)1(0

18

Suppose (1+WACC($))/(1+WACC(U.K))=(1+r($))/(1+r(U.K))

• WACC($)=(1.15)*(1.06)/(1.1)=10.8%

Time Period

Free Cash Flow

S FCF ($) PV

0 -£56.001.7 -$95.20 -$95.20

1 £10.40 1.638 $17.04 $15.37

2 £8.90 1.579 $14.05 $11.44

3 £9.70 1.521 $14.76 $10.84

4 £9.80 1.466 $14.37 $9.53

5 £10.40 1.413 $14.69 $8.79

5 £78.00 1.413 $110.18 $65.93

NPV $26.70

19

Moral

• If the assumptions are met, it doesn’t seen to matter what currency is used to evaluate the project

• But– What if IRP doesn’t hold– What if the Wacc’s are inconsistent with the

risk free rates

20

A recipe for international decision makers:

1. Estimate future cash flows in foreign currency.

2. Convert to U.S. dollars at the predicted exchange rate.

3. Calculate APV using the U.S. cost of capital.

International Capital Budgeting

Example

– 600 200 500 300

0 1 year 2 years 3 years

21

Facts

International Capital Budgeting

%6

%15

$

$

π

i Is this a good investment from the perspective of the U.S. shareholders?

– 600 200 500 300

0 1 year 2 years 3 years

= 3%

S0($/ ) = $.55265

22

E[St($/ )] can be found by appealing to the interest rate differential:

E[S1($/ )] = [(1.06/1.03)S0($/ )]

CF0 = ( 600) S0($/ ) =( 600)($.5526/ ) = $331.6

= [(1.06/1.03)($.5526/ ) ] = $.5687/ so CF1 = ( 200)($.5687/ ) = $113.7

CF2 = [(1.06)2/(1.03)2 ] S0($/ )( 500) = $292.6

APV = -$331.60 + $113.7/(1.15) + $292.6/(1.15)2 + $180.7/(1.15)3 = $107.3 > 0 so accept.

CF1 = ( 200)E[St($/ )]

Similarly,

Solution

CF3 = [(1.06)3/(1.03)3 ] S0($/ )( 300) = $180.7

23

Risk Adjustment in the Capital Budgeting Process

• Clearly risk and return are correlated.• Political risk may exist along side of

business risk, necessitating an adjustment in the discount rate.

24

Sensitivity Analysis

• In the APV model, each cash flow has a probability distribution associated with it.

• Hence, the realized value may be different from what was expected.

• In sensitivity analysis, different estimates are used for expected inflation rates, cost and pricing estimates, and other inputs for the APV to give the manager a more complete picture of the planned capital investment.

25

Real Options

• The application of options pricing theory to the evaluation of investment options in real projects is known as real options.– A timing option is an option on when to make the

investment.– A growth option is an option to increase the scale

of the investment.– A suspension option is an option to temporarily

cease production.– An abandonment option is an option to quit the

investment early.

Documents

0 1. Identify the SIZE and TIMING of all relevant cash flows on a time line. 2.Identify the RISKINESS of the cash flows to determine the appropriate discount