The rate is the return the money could earn elsewhere at the same risk
◈ 9 cardsExplain the discount rate as the minimum required return, compute the after-tax cost of debt and the WACC with market-value weights, and say what WACC is doing inside an NPV.
Where the rate comes from
Every factor in lessons 13.2 and 13.3 needed a rate. The discount rate is the minimum return the project must earn — the return the company’s money could earn elsewhere at the same risk, which is why it is also called the opportunity cost of capital or the required return. A company’s money comes from its lenders and its shareholders, each of whom requires a return; the rate that keeps both satisfied is the weighted average of what they require — the weighted average cost of capital (WACC).
Juniper Health Clinics
Juniper Health Clinics Ltd., a private chain of physiotherapy clinics in the Fraser Valley, has debt with a market value of 4,000,000 on which it pays 6 % before tax, and shares with a market value of 6,000,000 on which its shareholders require an 11 % return. Its tax rate is 25 %.
Cost of debt. Interest is tax-deductible, so every dollar of interest saves 25 cents of tax; the lender receives 6 % but the company bears only
Cost of equity. Dividends are not deductible, and shareholders stand last in line, so equity costs more than debt: 11 %, with no tax relief.
Weights. By market value, debt is and equity 0.60.
Component Market value Weight Cost After tax Weighted
Debt 4,000,000 0.40 6.0 % 4.50 % 1.80 %
Equity 6,000,000 0.60 11.0 % 11.00 % 6.60 %
WACC 8.40 %With a 10 % pre-tax cost of debt and a 30 % tax rate, the same weights give .
The two slips
Both appear on every marker’s list. Using the pre-tax cost of debt: — too high by 0.6 points, because it ignores the tax shield. Using book-value weights: Juniper’s equity has a book value of only 2,000,000, so book weights are debt and 0.333 equity, giving — too low, because the cheap component is over-weighted. Market values are what the providers of capital actually have at stake today; book values are history.
What the 8.4 % is doing inside an NPV
Discounting a project at 8.4 % asks: after paying every provider of capital the return it requires, is there anything left? If the present value of the inflows at 8.4 % exceeds the investment — NPV ≥ 0 — the project has beaten what Juniper’s lenders and shareholders could earn elsewhere at the same risk, and the surplus is value created for the shareholders. If it falls short, the project earns less than the capital costs, even if it shows an accounting profit.
A riskier project deserves a higher rate
WACC is the required return on projects of the company’s average risk. A rate can be built up from a risk-free rate (a Government of Canada bond) plus premiums for the business, the leverage and the project. When Juniper proposes an imaging centre — a new line, heavier equipment, an uncertain referral base — its consultant raises the rate to 11 %. The higher rate lowers the present value of the same inflows, so more of the risky projects fail the test, which is exactly the intent: the extra risk must be paid for. Lowering the rate so that a favoured project passes is the reverse of the logic.