# International Capital Budgeting

There are two approaches to evaluate a foreign project: home currency approach and foreign currency approach. The first involves converting the foreign project cash flows to local currency based on expected forward exchange rates and discounting them based on home country cost of capital. The second requires calculating NPV based on foreign country cost of capital and then converting the foreign-currency NPV to local currency at the spot exchange rate.

Evaluating a foreign project is more complex than evaluating a local project due to multiple factors. First, foreign projects are subject to foreign exchange risk. It is because foreign project cash flows are in foreign currencies which must be converted to local currency. Even though there are different approaches such as relative purchasing power parity and relative interest rate parity, it is hard to accurately forecast exchange rates. Second, multiple tax jurisdictions are involved potentially subjecting the cash flows to double-taxation. Further, foreign governments may place restrictions on repatriation of earnings back to the home country.

## Foreign project cash flows

Foreign projects must be evaluated from the perspective of the parent company. A project might make sense in the foreign country when executed by a company based in that country but might not be feasible after considering the foreign exchange risk, taxation and restriction of repatriation of income back to the home country.

Foreign currency cash flows should be projected based on the foreign currency inflation rate.

Foreign tax laws are relevant in determining the depreciation that can be charged and the ultimate tax outflows. Both the corporate tax outflows and the tax outflows if any associated with repatriation of income back to the home country must be considered.

Following is a general equation that can be used to work out the after-tax repatriable cash flows of a project:

$$ {\rm CF}_i=\left[(CI-VC\ -\ FC\ -\ D)\times(1-t_c)+D\right]\times(1-t_r) $$

Where CI is the project cash inflows, VC is the variable cost outflows, FC is the fixed cost outflows, D is depreciation expense determined based on foreign country tax laws, t_{c} is the foreign corporate tax rate and t_{d} is the tax rate applicable to repatriation such as dividends.

Let’s you work for a US company that wants to set up a telecommunication company in Pakistan. The project costs PKR 6 billion to set up. A local business conglomerate has agreed to buy the business for PKR 10 billion in 5 years. In the meanwhile, the project will generate cash inflows of PKR 2 billion in first year, thereby growing at 10% per annum. Variable cash outflows are 30% of the cash inflows and fixed costs are PKR 200 million per annum. Initial investment of PKR 6 billion is required, including PKR 1 billion working capital. The difference is depreciable based on 5-year straight-line method. Corporate tax rate is 33% and a 10% tax rate applies to any dividends paid.

The following schedule shows cash flows of the project for five years:

Year | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|

Cash inflows | CI | 2,000 | 2,200 | 2,420 | 2,662 | 2,928 |

Less: variable cash outflows | VC | 600 | 660 | 726 | 799 | 878 |

Less:: fixed cash outflows | FC | 200 | 200 | 200 | 200 | 200 |

Less: depreciation | D | 1000 | 1000 | 1000 | 1000 | 1000 |

Cash flows before corporate tax | 200 | 340 | 494 | 663 | 850 | |

Less: corporate tax | Tc | 66 | 112 | 163 | 219 | 280 |

Add: depreciation | D | 1,000 | 1,000 | 1,000 | 1,000 | 1,000 |

After-tax corporate tax flows | 1,134 | 1,228 | 1,331 | 1,444 | 1,569 | |

Less: dividend tax | Td | 113 | 123 | 133 | 144 | 157 |

Net repatriable cash flows | 1,021 | 1,105 | 1,198 | 1,300 | 1,412 |

Now, that we have determined the project cash flows in foreign-currency, we need to work out the relevant net present value. There are two approaches: (a) home currency approach and (b) foreign currency approach.

## Home currency approach

In the home currency approach, the net present value of a foreign project is determined by (a) converting the foreign-currency cash flows of the project to the domestic currency based on the expected forward exchange rates, and (b) discounting the cash flows based on the domestic currency cost of capital.

In the above example, the PKR cash flows will be converted to USD based on the forward exchange rate forecasted based on either relative purchasing power parity or relative interest rate parity. USD equivalent cash flows can be discounted using USD cost of capital. Forward exchange rates can be determined based on the difference in interest rates between the domestic currency:

$$ F_t=S_0\times\left(\frac{1+r_d}{1+r_f}\right)^t $$

Where F_{i} and S_{0} are the forward exchange rate t years in future and spot exchange rate time 0 respectively expressed as domestic currency per unit of foreign currency (i.e. USD per PKR in this case), r_{d} is the nominal interest rate in domestic currency i.e. USD and r_{f} is the nominal interest rate in foreign currency i.e. PKR

If the current USD/PKR exchange rate is 0.0086 and the expected interest rate for PKR and USD are 6% and 4% respectively, we can work out the following forward rates and convert the cash flows to USD:

Net repatriable cash flows | C | 1,021 | 1,105 | 1,198 | 1,300 | 1,412 |
---|---|---|---|---|---|---|

Forward exchange rate | f | 0.0084 | 0.0083 | 0.0081 | 0.0080 | 0.0078 |

Net reptriable cash flows in USD | C×f | $8.61 | $9.15 | $9.73 | $10.36 | $11.04 |

The initial investment of PKR 6 billion equals USD 51.60 million. The terminal value of the project is PKR 9 billion (=PKR 10 billion multiplied by (1 – dividend tax rate of 10%)). It equals USD 70.37 million (=PKR 9 billion multiplied by 5-year forward rate of 0.0095).

Under the home currency approach, you will discount the cash flows based on the USD cost of capital which is 10%. You can adjust the discount rate up by 5% reflecting the additional risk.

Discounting the cash flows at 15%, the project NPV works out to $15.60 million:

Year | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Net reptriable cash flows in USD | $8.61 | $9.15 | $9.73 | $10.36 | $11.04 | |

Add: terminal cash flows | $70.37 | |||||

Initial investment | (51.60) | |||||

Total cash flows | (51.60) | 8.61 | 9.15 | 9.73 | 10.36 | 81.41 |

Discount factor at 15% | 1.0000 | 0.8696 | 0.7561 | 0.6575 | 0.5718 | 0.4972 |

Present value of cash flows | (51.60) | 7.49 | 6.92 | 6.40 | 5.92 | 40.48 |

Net present value (USD) | 15.60 |

## Foreign currency approach

In the foreign-currency approach, the foreign-currency cash flows are discounted based on implied cost of capital that would apply to the foreign currency to arrive at the foreign-currency NPV. The NPV denominated in foreign currency (PKR) is then converted to domestic currency (USD) using the spot exchange rate.

Net present value under this second approach should be equal the NPV under the first approach i.e. domestic currency approach.

The implied cost of capital roughly equals the domestic currency cost of capital adjusted for the differences in inflation rates, i.e. 15% plus the nominal interest rate difference of 2%, i.e. 17.3%.

Year | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Net reptriable cash flows in USD | 1,021 | 1,105 | 1,198 | 1,300 | 1,412 | |

Add: terminal cash flows | 9,000 | |||||

Initial investment | (6,000) | |||||

Total cash flows | (6,000) | 1,021 | 1,105 | 1,198 | 1,300 | 10,412 |

Discount factor at 17% | 1.0000 | 0.8525 | 0.7268 | 0.6196 | 0.5282 | 0.4503 |

Present value of cash flows | (6,000) | 870 | 803 | 742 | 687 | 4,689 |

Net present value (PKR) | 1,790.86 | |||||

Spot exchange rate | 0.0086 | |||||

Net present value (USD) | 15.40 |

Please note that the net present value under both the approaches is (almost) the same. The difference is attributable to rounding error.