After this page you can
Calculate a weighted average cost of capital including the tax relief on debt, use it as a discount rate, and show why appraising a project against the cost of the cheapest source of finance accepts projects that destroy value
The number every appraisal needs
Capital is not free. Shareholders could have put their money somewhere else and expect to be compensated for not doing so; lenders charge an explicit rate. Add the two together, weighted by how much of each the company uses, and you have the return the company must earn simply to leave everybody no worse off.
where E and D are the equity and debt, V is E + D, ke and kd are what each demands, and t is the rate of tax relief on interest.
Three features of that expression carry the whole topic.
The cost of equity is higher than the cost of debt. Always, for the same company. Shareholders rank behind lenders and have no promised payment, so they require more. A WACC that comes out below the cost of debt has an arithmetic error in it.
Only the debt cost is reduced for tax. Interest is deductible against profit; dividends are not. So a rupee of interest costs the company less than a rupee, and the (1 − t) is where the tax advantage of borrowing enters the appraisal.
The weights are the company's target structure, not the funding of this project. This is the point of the page, and it is worth its own section.
The mechanism: why "this project is debt-funded" is not a reason
A finance director with a loan offer at 9% and a project returning 10% has an argument that sounds airtight: the project earns more than the money costs, so it adds value.
It does not, and here is why. A company that keeps a settled mix of debt and equity does not fund projects one at a time from one source; it keeps the mix. Borrow for this project and the company is now more geared than it intends to be, so the next project is funded with equity to bring the mix back. Average over a few years and every project has been financed with the mix, whatever the paperwork for any single one said.
So the cheap source is not a property of the project. It is a queue position, and the project that happens to be at the front of the queue has no better claim on the cheap money than the one behind it. Charge every project the blended rate and the ranking is consistent; charge each project the cost of whatever was raised that month and the same project is accepted in March and rejected in September.
There is a second reason, and it is the sharper one. Borrowing more raises the gearing, which raises the risk borne by the shareholders, which raises the return they demand. The cheap debt is not free even in the moment: part of its price is charged to the equity. The worked example below shows the shortfall in money, and arrives at the same figure three ways.
Using it, and knowing when not to
The WACC is the discount rate for a project of average risk for this company, financed in its usual mix. Both conditions matter, and a question that breaks one of them is testing whether you noticed.
A company moving into an unfamiliar business should not discount at its own WACC, because the new activity does not carry the old risk. The honest approach is to take the rate from companies already in that business and adjust it for the difference in gearing — and to say plainly that this is an approximation.
Two mechanical points cause most of the lost marks. The weights should be market values, because that is what the capital is worth now, not what it was issued for. And the cost of equity is a forward-looking required return, not last year's dividend divided by this year's price — a growing company's dividend yield and its cost of equity are very different numbers.
Questions students ask
If debt is cheaper and tax-relieved, why is the WACC not minimised by borrowing everything?
Because ke and kd are not constants. Both rise with gearing, for the reasons on the gearing page: the shareholders' claim gets more volatile and the lenders' queue gets longer. The weighted average falls at first, as cheap relieved debt displaces dear equity, then turns and rises as both components climb. The lowest point is the target structure the weights are supposed to represent.
Which comes first, the WACC or the capital structure?
The structure. The WACC is computed from a chosen mix, so using it to choose the mix is circular. In practice a company sets a target structure for the reasons on the gearing page and then uses the resulting WACC to appraise projects.
Does a project that exactly earns the WACC add anything?
Nothing, and that is the correct answer rather than a trick one. It pays the lenders their interest and the shareholders exactly the return they required, and leaves nothing over. Its net present value is zero. Value is created only above the line, which is why the line has to be in the right place.
A worked example
An invented example, built for this page. A manufacturer in Nashik with a settled capital structure, considering a machine. Every figure is made up and chosen so the arithmetic is exact.
| Amount | Required return | |
|---|---|---|
| Equity (market value) | ₹600 lakh | 15% |
| Debt | ₹400 lakh | 9% before tax |
| Total capital | ₹1,000 lakh |
Tax relief on interest is at 25%, so the after-tax cost of the debt is 9% × (1 − 0.25) = 6.75%.
The WACC
Weights are
600 ÷ 1,000 = 0.60and400 ÷ 1,000 = 0.40.WACC = 0.60 × 15% + 0.40 × 6.75% = 9.00% + 2.70% = 11.70%It sits between 6.75% and 15%, nearer the equity figure because equity is the larger share. If a WACC ever comes out outside the two component costs, it is wrong.
The project, and the tempting mistake
The machine costs ₹1,000 lakh and generates ₹100 lakh a year of after-tax operating cash, for ever. Its return is therefore
100 ÷ 1,000 = 10.00%A bank has offered to lend the whole ₹1,000 lakh at 9%, costing 6.75% after relief. Ten per cent beats 6.75%, so the project looks like a clear yes. Follow the money and it is not.
Route 1: who gets what, in rupees
Keep the company's usual mix, so the machine is funded with ₹600 lakh of equity and ₹400 lakh of debt.
Line Working Amount After-tax operating cash given ₹100.00 lakh Interest on the debt 9% × 400 ₹36.00 lakh Tax relief on that interest 25% × 36 ₹9.00 lakh Net cost of the debt 36 − 9 ₹27.00 lakh Left for the shareholders 100 − 27 ₹73.00 lakh What the shareholders required 15% × 600 ₹90.00 lakh Shortfall 90 − 73 ₹17.00 lakh The project pays the lenders in full and leaves the shareholders ₹17 lakh a year short of the return they required. It is a bad project, and the 6.75% comparison concealed it entirely.
Route 2: straight from the WACC
The capital costs
11.70% × 1,000 = ₹117.00 lakha year to service. The project produces ₹100.00 lakh.117 − 100 = ₹17.00 lakh shortThe same ₹17 lakh, from a calculation that never mentioned the project's funding.
Route 3: add the two demands up
The shareholders want ₹90.00 lakh and the net cost of the debt is ₹27.00 lakh, both printed in Route 1.
90 + 27 = ₹117.00 lakhwhich is Route 2's servicing cost exactly. So the WACC is not a separate idea from Route 1 — it is Route 1, divided by the capital. All three routes agree, and the agreement is the proof that the blended rate is the right test.
The same conclusion as a net present value
A perpetuity of ₹100.00 lakh discounted at 11.70% is worth
100 ÷ 0.1170 = ₹854.70 lakhagainst a cost of ₹1,000 lakh, so
NPV = 854.70 − 1,000 = −₹145.30 lakhCheck it against the shortfall: a perpetual shortfall of ₹17.00 lakh is worth
17 ÷ 0.1170 = ₹145.30 lakh. The two agree to the paisa, which they must, since the only difference between them is whether you subtract before or after discounting.Where the line actually falls
For this company, a perpetual project costing ₹1,000 lakh breaks even at an after-tax cash flow of
11.70% × 1,000 = ₹117.00 lakha year, whose NPV is117 ÷ 0.1170 − 1,000 = 1,000 − 1,000 = 0. Anything below ₹117 lakh destroys value and anything above it creates value — and the machine at ₹100 lakh is below it by the ₹17 lakh that all three routes found.
Where this fits in CB1
This page explains one idea from CB1 Business Finance. The full CB1 syllabus, with what each part is examined on, sits on the course page, and past-paper style mock exams with full solutions are where you find out whether the idea has stuck under time pressure.
Other CB1 topics explained
- Why financial reporting is regulated, and who it is regulated for
- Share capital and loan capital: why each source costs what it does
- Leasing against buying, and the only comparison that settles it
- Profit is not cash, and why a growing company can run out of money
- Return on capital employed, and the two things that drive it
- Gearing: why borrowing magnifies a shareholder return in both directions
- Modigliani-Miller: why gearing does not create value, and what does
- Dividend irrelevance, and the four reasons dividends still matter
- NPV against IRR, and the three times IRR gives the wrong answer
- Working capital: the days between paying out and being paid
- Valuing a company: discounted cash flow against comparable multiples
- Synergies and the takeover premium: who actually gets the gain
- Company tax in an appraisal, and the relief that reverses the answer
- Interest rate swaps: fixing a floating cost, and where the saving comes from
- Hedging currency risk: the forward contract and the money-market hedge
Stuck on a term rather than the idea? The actuarial glossary defines the notation used above. If something here is wrong or unclear, tell us — these pages get corrected.