REVISION to International Capital Budgeting Analysis - Phyllis Cooper

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International Capital Budgeting

Review of Domestic Capital Budgeting

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

The basic net present value equation is

Where:

T = economic life of the project in years.

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

TVT = expected after tax terminal value including return of net working capital,

C0 = initial investment at inception,

K = weighted average cost of capital.

K = (1 – )Kl + (1 – t)i

The NPV rule is to accept a project if NPV  0

and to reject a project if NPV  0

Review of Domestic Capital Budgeting

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

Rt = incremental revenue

OCt = incremental operating costs

Dt = incremental depreciation

It = incremental interest expense

 = the marginal tax rate

CFt = (Rt – OCt – Dt – It)(1 – t) + Dt + It (1 – t)

Review of Domestic Capital Budgeting

Alternative Formulations CFt

CFt = (Rt – OCt – Dt – It)(1 – t) + Dt + It (1 – t)

CFt = NIt + Dt + It(1 – t)

CFt = (Rt – OCt – Dt)(1 – t) + Dt

CFt = NOIt(1 – t) + Dt

CFt = (Rt – OCt)(1 – t) + t Dt

CFt = OCFt(1 – t) + t Dt

We can use CFt = (OCFt)(1 – t) + t Dt

to restate the NPV equation

as:

NPV =

t = 1

CFt

(1 + K)t

– C0

TVT

(1 + K)T

NPV =

t = 1

(OCFt)(1 – t) + t Dt

(1 + K)t

– C0

TVT

(1 + K)T

Review of Domestic Capital Budgeting

The Adjusted Present Value Model

Can be converted to adjusted present value (APV)

NPV =

t = 1

(OCFt)(1 – t)

(1 + K)t

TVT

(1 + K)T

t Dt

(1 + K)t

–

t = 1

APV =

t = 1

(OCFt)(1 – t)

(1 + Ku)t

TVT

(1 + Ku)T

t Dt

(1 + i)t

–

t It

(1 + i)t

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.

APV =

t = 1

(OCFt)(1 – t)

(1 + Ku)t

TVT

(1 + Ku)T

t Dt

(1 + i)t

–

t It

(1 + i)t

The Adjusted Present Value Model

Domestic APV Example

Consider this project, the timing and size of the incremental after-tax cash flows for an all-equity firm are:

0 1 2 3 4

-$1,000 $125 $250 $375 $500

The unlevered cost of equity is r0 = 10%:

= –$1000

= $125

= $250

= $375

= 10

NPV

APV =

t = 1

(OCFt)(1 – t)

(1 + Ku)t

TVT

(1 + Ku)T

t Dt

(1 + i)t

–

t It

(1 + i)t

CF0

CF1

CF2

CF3

CF4

= $500

Domestic APV Example

Now, imagine that the firm finances the project with $600 of debt at r = 8%.

The tax rate is 40%, so they have an interest tax shield worth t×I = .40×$600×.08 = $19.20 each year.

APV =

$125

1.10

0 1 2 3 4

-$1,000 $125 $250 $375 $500

$250

(1.10)2

$375

(1.10)3

$500

(1.10)4

$19.20

(1.08)2

$19.20

(1.08)3

$19.20

(1.08)4

$19.20

1.08

– $1,000

The APV of the project under leverage is:

APV =

t = 1

(OCFt)(1 – t)

(1 + Ku)t

TVT

(1 + Ku)T

t Dt

(1 + i)t

–

t It

(1 + i)t

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

Capital Budgeting from the Parent Firm’s Perspective

The APV model is useful for a domestic firm analyzing a domestic capital expenditure or for a foreign subsidiary of a MNC analyzing a proposed capital expenditure from the subsidiary’s viewpoint.

The APV model is NOT useful for a MNC in analyzing a foreign capital expenditure from the parent firm’s perspective.

Blocked cash flows

Extra taxes

Marginal tax rates

Interest rates

Exchange rates

APV =

t = 1

(OCFt)(1 – t)

(1 + Ku)t

TVT

(1 + Ku)T

t Dt

(1 + i)t

–

t It

(1 + i)t

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.

Capital Budgeting from the Parent Firm’s Perspective

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

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

APV =

t = 1

(1 + Kud)t

TVT

(1 + Kud)T

t Dt

(1 + id)t

–

StOCFt(1 – t)

S0C0 + S0RF0 + S0CL0 -

t = 1

t It

(1 + id)t

t = 1

LPt

(1 + id)t

t = 1

Capital Budgeting from the Parent Firm’s Perspective

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

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

APV =

t = 1

(1 + Kud)t

TVT

(1 + Kud)T

t Dt

(1 + id)t

–

StOCFt(1 – t)

S0C0 + S0RF0 + S0CL0 -

t = 1

t It

(1 + id)t

t = 1

LPt

(1 + id)t

t = 1

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

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

APV =

t = 1

(1 + Kud)t

TVT

(1 + Kud)T

t Dt

(1 + id)t

–

StOCFt(1 – t)

S0C0 + S0RF0 + S0CL0 -

t = 1

t It

(1 + id)t

t = 1

LPt

(1 + id)t

t = 1

Capital Budgeting from the Parent Firm’s Perspective

One alternative for international decision makers:

1. Estimate future cash flows in foreign currency.

2. Convert to the home currency at the predicted exchange rate.

Use PPP, IRP et cetera for the predictions or actual rates arranged via hedges.

3. Calculate NPV using the home currency cost of capital.

Capital Budgeting from the Parent Firm’s Perspective: Alternative 1

Capital Budgeting from the Parent Firm’s Perspective: Example

A U.S.-based MNC is considering a European opportunity.

It’s a simple example

There is no incremental debt

There is no incremental depreciation

There are no concessionary loans

There are no restricted funds

Capital Budgeting from the Parent Firm’s Perspective: Example

We can use a simplified APV:

APV =

t = 1

StOCFt(1 – t)

(1 + Kud)t

– S0C0

APV =

t = 1

(1 + Kud)t

TVT

(1 + Kud)T

t Dt

(1 + id)t

–

StOCFt(1 – t)

S0C0 + S0RF0 + S0CL0 -

t = 1

t It

(1 + id)t

t = 1

LPt

(1 + id)t

t = 1

Capital Budgeting from the Parent Firm’s Perspective: Example

The inflation rate in the euro zone is € = 3%, the inflation rate in dollars is p$ = 6%, and the business risk of the investment would lead an unlevered U.S. based firm to demand a return of Kud = i$ = 15%.

–€600

€200

€500

€300

A U.S. MNC is considering a European opportunity. The size and timing of the after-tax cash flows are:

Capital Budgeting from the Parent Firm’s Perspective: Example

$408.73

$661.94

–$750

$257.28

Find the NPV using the cash flow menu of your financial calculator and and interest rate i$ = 15%:

CF0

CF1

CF2

CF3

= 15

NPV

= ?

Capital Budgeting from the Parent Firm’s Perspective: Example

$408.73

$661.94

–$750

$257.28

Without a financial calculator, the NPV can be found as:

Another recipe for international decision makers:

1. Estimate future cash flows in foreign currency.

2. Estimate the foreign currency discount rate.

3. Calculate the foreign currency NPV using the foreign cost of capital.

4. Translate the foreign currency NPV into dollars using the spot exchange rate

Capital Budgeting from the Parent Firm’s Perspective: Alternative 2

Foreign Currency Cost of Capital Method

Let’s find i€ and use that on the euro cash flows to find the NPV in euros.

Then translate the NPV into dollars at the spot rate.

– €600

€200

€500

€300

€ = 3%

i$ = 15%

p$ = 6%

€

$1.25

S0($/€) =

The current exchange rate is

Before we find i€ let’s use our intuition.

Since the euro-zone inflation rate is 3% lower than the dollar inflation rate, our euro denominated discount rate should be lower than our dollar denominated discount rate.

Foreign Currency Cost of Capital Method

Finding the Foreign Currency Cost of Capital: i€

Recall that the Fisher Effect holds that

(1 + e) × (1 + $) = (1 + i$)

real rate

inflation rate

nominal rate

So for example the real rate in the U.S. must be 8.49%

(1 + e) =

(1 + i$)

(1 + $)

e =

1.15

1.06

– 1 = 0.0849

Finding the Foreign Currency Cost of Capital: i€

If Fisher Effect holds here and abroad then

If the real rates are the same in dollars and euros (e€ = e$)

(1 + e$) =

(1 + i$)

(1 + $)

(1 + e€) =

(1 + i€)

(1 + €)

and

(1 + i$)

(1 + $)

(1 + i€)

(1 + €)

we have a very useful parity condition:

Finding the Foreign Currency Cost of Capital: i€

If we have any three of these variables, we can find the fourth:

(1 + i€) =

(1 + i$) × (1 + €)

(1 + $)

In our example, we want to find i€

(1 + i$)

(1 + $)

(1 + i€)

(1 + €)

i€ =

(1.15) × (1.03)

(1.06)

– 1

i€ = 0.1175

International Capital Budgeting: Example

Find the NPV using the cash flow menu and i€ = 11.75%:

CF0

= –€600

CF1

= €200

CF2

= €500

CF3

= €300

= 11.75

NPV

= €194.39

– €600

€200

€500

€300

$1.25

= $242.99

€194.39 ×

€

Capital Budgeting from the Parent Firm’s Perspective: Example

NPV = –€600 +

(1.1175)3

€300

1.1175

€200

= €194.39

(1.1175)2

€500

Without a financial calculator, the NPV can be found as:

– €600

€200

€500

€300

$1.25

= $242.99

€194.39 ×

€

International Capital Budgeting

You have two equally valid approaches:

Change the foreign cash flows into dollars at the exchange rates expected to prevail. Find the $NPV using the dollar cost of capital.

Find the foreign currency NPV using the foreign currency cost of capital. Translate that into dollars at the spot exchange rate.

If you watch your rounding, you will get exactly the same answer either way.

Which method you use is your choice.

Back to the full APV

Using the intuition just developed, we can modify Lessard’s APV model as shown above, if we find it convenient.

APV =

t = 1

(1 + Kud)t

TVT

(1 + Kud)T

t Dt

(1 + id)t

–

StOCFt(1 – t)

S0C0 + S0RF0 + S0CL0 +

t = 1

t It

(1 + id)t

t = 1

LPt

(1 + id)t

t = 1

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NPV

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NPV

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NPV

τI

τD

OCF

APV

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