Inflation and tax in appraisal

A money cash flow is the number of kwacha that will actually change hands on the day — inflation included. A real cash flow is the same amount expressed in today’s purchasing power, with inflation stripped out. Both are legitimate ways to describe the same project, and each has a discount rate that belongs to it.

• The money method: inflate the cash flows to what they will really be, then discount at the money (nominal) cost of capital.
• The real method: leave the cash flows in today’s prices, then discount at the real cost of capital.

Both give the same NPV. What you must never do is mix them — discounting today’s prices at a money rate deducts inflation twice and will tell you to reject a project that is worth doing.

With a real cost of capital of 10% and general inflation of 5%, the money rate is 1.10 × 1.05 − 1 = 15.5%. Turn it around and the same relationship converts a money rate the treasury actually quotes into the real rate: 1.155 ÷ 1.05 − 1 = 10%.

The real method only works when every cash flow in the project is inflating at the general rate. The moment one of them moves at its own rate — and in Zambia they almost always do — the real method breaks down and you must use money cash flows.

Think about a maize-milling project. The general rate might be 12%, but the maize price follows the harvest, the ZESCO tariff follows the regulator, and wages follow whatever the union settled. Three cash flows, three inflation rates. There is no single real rate that can describe all of them at once.

So you inflate each line at its own rate and build the money cash flow year by year.

Notice what the table shows that a real-terms working would have hidden completely: costs are outrunning prices, and the project is quietly getting worse each year. That is the reason the money method is the one the exam rewards.

Tax bites an investment project twice, and the two bites work in opposite directions. The first is a cost: the project generates taxable operating cash flows, and the company pays tax on them. The second is a relief, and it is the subject of the next section.

The cost side is straightforward arithmetic — the operating cash flow multiplied by the tax rate — but the timing is where marks are lost.

• Tax payable in the same year as the profits: the outflow sits on the same line as the cash flow that caused it.
• Tax payable one year in arrears: the outflow moves down a year, so a four-year project has cash flows in years 1 to 4 and tax payments in years 2 to 5.

A question that says tax is paid one year in arrears is handing you a year of free credit, and the working has to show it. A project whose last operating cash flow is in year 4 still has a year 5 column, holding nothing but the tax on year 4 and any allowance still to be claimed.

Only cash matters. Depreciation charged in the accounts is not deducted before applying the tax rate, because it is not a payment — the tax authority gives its own relief for capital spending instead, on its own terms.

Capital allowances — also called tax-allowable depreciation or writing-down allowances — are the deduction the tax authority gives for money spent on assets. They are not a cash flow themselves. What is a cash flow is the tax they save.

The saving is an inflow, and it arrives on the same timing as the tax it reduces. Where tax is one year in arrears, so is the saving.

Two ways the allowance is spread

• Straight line — the cost less any scrap value, divided equally across the asset’s life. An asset costing ZMW120 million over four years gives ZMW30 million a year.
• Reducing balance — a fixed percentage of whatever is left unrelieved. At 20%, a ZMW530,000 asset gives ZMW106,000 in year 1, then 20% of the remaining ZMW424,000 in year 2, and so on. The allowance shrinks every year.

The balancing figure at the end

Reducing balance never reaches zero, so in the year the asset is sold the company claims whatever relief it has not yet had. Take the written-down value carried into that year, subtract what the asset actually fetched, and the difference is a balancing allowance.

Where the asset sells for more than its written-down value the sign flips: the company has over-claimed, and the excess is a balancing charge — extra taxable profit rather than extra relief.

ETM Co is buying equipment for ZMW530,000 to make a new product. It will last four years and then be sold for ZMW40,000. Tax is 30%, payable one year in arrears, and capital allowances are available at 20% on the reducing balance. The after-tax money cost of capital is 10%. Sales prices and costs below are already in money terms.

Take the allowances next, because their timing has to be settled before anything can be discounted. Three years of 20% on the reducing balance, then a balancing allowance in year 4 when the equipment is sold.

Now assemble the cash flows. Contribution lands in years 1 to 4; the tax on it and the relief from the allowances both land a year later; the scrap comes in with year 4.

The NPV is ZMW82,168, so the equipment should be bought. Worth seeing how much of that answer the tax lines are carrying: the allowances hand back ZMW147,000 of relief across the project, and pushing every tax payment a year later is worth several thousand more on its own. Get the timing wrong and a viable project can read as a rejection.