International project appraisal

A project abroad earns in a currency the company does not report in, so somewhere in the appraisal the money has to cross. There are two places you can put that crossing, and both are correct.

The first converts early and discounts late; the second discounts early and converts once, at today’s rate. They agree because the same relationship between inflation and exchange rates is doing the work in both — in the first it moves the exchange rate year by year, in the second it sits inside the foreign discount rate.

Which one to use is usually decided for you. A question giving inflation rates in both countries wants the first; a question giving a foreign cost of equity and a spot rate wants the second. Where a question asks for both, expect a small difference from rounding, and say so rather than forcing the two to match.

The exchange rate in five years’ time is forecast from the difference between the two countries’ inflation rates, or from the difference between their interest rates. The two ideas have names — purchasing power parity for inflation, interest rate parity for interest — and identical arithmetic.

The one thing to be careful about is which currency is which. In a rate quoted as ZMW16.25 = US$1, the dollar is the base — the currency there is one of — and the kwacha is the quoted currency, the one whose quantity varies.

So with Zambian inflation at 15% and US inflation at 6.5%, the kwacha rate is the numerator: 16.25 × 1.15 ÷ 1.065 = ZMW17.547 in a year. The kwacha buys less, which is what higher inflation at home means. Put the rates the wrong way round and the forecast has the kwacha strengthening against the dollar while Zambian prices rise faster than American ones — an answer the working itself tells you is wrong.

To discount dollar cash flows you need a dollar rate, and the same parity relationship converts the domestic one into it. A rate is a price for money over time, so it moves between currencies the same way an exchange rate does.

A Zambian company requiring 18% on kwacha cash flows, appraising a dollar project where US inflation is 6.5% against 15% at home, needs 1.18 × 1.065 ÷ 1.15 − 1 = 9.3% on the dollar flows.

Half of the 18% is not a required return at all — it is compensation for the kwacha losing value. Dollar cash flows do not need that compensation, so the dollar rate is far lower. Discounting dollars at 18% would reject good projects on the strength of an inflation rate that has nothing to do with them.

BC, a Zambian company, is considering a five-year project in the US. It needs capital expenditure of $1,250,000 with no scrap value, plus working capital of $500,000 recovered at the end. Pre-tax net cash inflows are $800,000 a year. US tax is 40%, with straight-line depreciation allowable, paid at the end of the year following the profits. A double taxation agreement means no Zambian tax is due. The spot rate is ZMW16.25 = $1, inflation is 15% in Zambia and 6.5% in the US, and BC requires 18% post-tax on projects of this risk.

Build the dollar cash flows first. Depreciation is $1,250,000 ÷ 5 = $250,000 a year, so taxable profit is $800,000 − $250,000 = $550,000 and the tax is $220,000, paid a year later.

Now forecast the rate for each year at 1.15 ÷ 1.065, convert, and discount the kwacha at 18%.

An NPV of about ZMW14.3 million, so the project is worth doing. Watch what the exchange rate column is doing to the answer: by year 6 a dollar is worth ZMW25.76 rather than ZMW16.25, so every dollar the project earns late is worth more kwacha than the same dollar earned today. The weakening kwacha is working in BC’s favour here, because the project is a dollar earner.

The same project, the other way round. Discount the dollar cash flows at the dollar cost of capital of 9.3%, then convert the answer once at today’s spot rate of ZMW16.25.

$881,500 × 16.25 = ZMW14,324,000, against ZMW14,343,000 the long way round. The gap is about a tenth of a percent and it is entirely rounding — three-decimal discount factors and a discount rate stated as 9.3% rather than 9.2783%. Two approaches landing within ZMW20,000 of each other on a ZMW28 million project is confirmation that both were done right.

This route is much shorter, and it is the one to reach for when a question gives you a foreign cost of capital directly. It hides something, though. There is no exchange rate column, so nothing on the page shows what the currency is doing to the project — and on a long project in a fast-depreciating currency, that column is often the most interesting thing in the answer.

Which way the currency helps

• A weakening kwacha raises the kwacha value of foreign-currency inflows, so the NPV of a project earning abroad rises.
• A strengthening kwacha does the reverse: the same dollars convert into fewer kwacha and the NPV falls.

That cuts both ways, and it is not a forecast anyone should rely on. BC’s ZMW14.3 million rests on the kwacha losing roughly 8% a year against the dollar for six years. If it holds steady instead, the late years convert at nothing like ZMW25.76 and a large part of the NPV disappears — which is why a foreign project is normally appraised alongside the question of how much of that exposure the company intends to hedge away.