Adjusted present value

Adjusted present value appraises a project in two separate pieces: what the project is worth if it were funded entirely by shareholders, and what the chosen financing adds or costs on top. Add the two and you have the APV.

An ordinary NPV cannot do this, because it buries the financing inside the discount rate. WACC is a blend of what the shareholders and the lenders demand at the company’s current mix of debt and equity — so the moment a project changes that mix, the WACC you discounted at describes a company that no longer exists.

That is exactly when APV earns its place. A cooperative that has always been equity-funded taking on a large loan for one expansion, or a mining subsidiary financed with far more debt than its parent carries, has changed its financial risk. Discounting at the old WACC would flatter or punish the project for reasons that have nothing to do with the project.

The base case NPV is the project appraised as though an all-equity company were undertaking it, with every financing effect ignored. No interest, no tax relief on interest, no issue costs — just the project’s own operating cash flows, discounted.

The rate you discount at has to match that fiction. It is the ungeared cost of equity: the return shareholders would demand for the project’s business risk alone, with no financial risk stacked on top.

• The business risk comes from what the project does — the volatility of its sales, the fixed costs it carries, the market it sells into.
• The financial risk comes from how it is paid for. Borrowing makes the shareholders’ returns more volatile, and they charge for that.

Those two risks are what the two betas separate. The equity beta measures both together, as the market sees them in a geared company’s shares. The asset beta — the ungeared beta — strips the borrowing out and measures the business risk on its own, which is the one the base case needs.

Where a question simply gives you the ungeared cost of equity, use it as stated. Where it gives you an asset beta instead, CAPM turns it into the rate — and where it gives you both an equity beta and an asset beta, the asset beta is the one the base case wants. The equity beta belongs to the geared company, and the base case is deliberately not that company.

Financing cash flows are the costs and benefits that exist only because of how the project is paid for. There are two of them.

• Issue costs — the fees paid to raise the money. An outflow, and normally at year 0.
• Tax relief on the interest — the tax the company does not pay because interest is deductible. An inflow, one per year for as long as the debt is outstanding.

These are discounted at a low rate, not at the cost of equity, because they are low-risk cash flows. The interest saving depends on a loan schedule and a tax rate, both known in advance. Use the pre-tax cost of debt or the risk-free rate — the question will tell you which.

Issue costs and the tax treatment

The two kinds of issue cost are not treated alike, and the difference is worth a mark on its own.

So gross debt issue costs of ZMW338.60 with tax at 30% enter the calculation at 338.60 × 0.70 = ZMW237.

Grossing up

Where the finance raised has to cover its own issue costs, the amount you need to raise is larger than the amount you want to spend. If a project needs ZMW2.4 million net and issue costs are 4%, then that ZMW2.4 million is 96% of the sum raised.

ZMW2.4m ÷ 0.96 = ZMW2,500,000 must be raised, and the issue cost is 4% × 2,500,000 = ZMW100,000. In one step, that is 2.4m × 4/96 = ZMW100,000. Taking 4% of the ZMW2.4 million instead gives ZMW96,000 and leaves the project ZMW4,000 short — the fee has to be charged on the whole amount raised, including the part that pays the fee.

The interest tax shield is the tax the company avoids because interest is deducted before profit is taxed. Borrow ZMW6,000 at 8% and the ZMW480 of interest reduces taxable profit by ZMW480 — which at a 30% tax rate is ZMW144 of tax the company never pays.

Four steps, in order, and the first is the one people skip: you need the loan balance at the start of each year, because that is what the interest is charged on.

• Lay out the loan year by year, opening balance and repayment, until it is cleared.
• Multiply each opening balance by the interest rate to get that year’s interest.
• Multiply the interest by the tax rate to get the shield.
• Discount each shield at the pre-tax cost of debt and add them up.

Where the loan is repaid in instalments the shield shrinks every year, because the balance it is calculated on is shrinking. Where the loan runs to the end and is repaid in one go — or is never repaid at all — the interest, and so the shield, stays flat.

Noble plc has a project costing ZMW10,000 with cash inflows of ZMW1,500, ZMW2,500, ZMW4,500 and ZMW5,000 over four years. The ungeared cost of equity is 10%. Start with the base case, ignoring the funding entirely.

ZMW224 positive, so the project is worth doing even before any financing benefit — though only just. On these numbers the financing is going to decide how comfortable the decision is.

Now the funding. ZMW6,000 of it is 8% debt, reduced by ZMW1,500 at the end of each year, with tax at 30%. Gross debt issue costs are ZMW338.60. Take the tax shield first, and note the opening balance stepping down as the loan is repaid.

The shields are discounted at 8% — the cost of the debt itself — because that is the risk of the cash flow. Then the issue costs: gross ZMW338.60, and debt issue costs are tax deductible, so ZMW338.60 × 0.70 = ZMW237. They are paid at the start, so no discounting is needed.

The APV is ZMW296 and the project is accepted. Read the three lines rather than just the answer. The project on its own is barely worth doing at ZMW224; the tax shield adds more value than the project’s own final year does; and the issue costs eat most of the shield. On a marginal project, the financing decision is doing as much work as the investment decision — which is the whole reason APV shows them separately.