25400 · Financial Literacy
Cost of Capital & Capital Budgeting
Week 8 combines the cost of debt and the cost of equity into the Weighted Average Cost of Capital, WACC = (E/V)·Re + (D/V)·Rd·(1 − Tc) + (P/V)·Rp, using market-value weights, then appraises projects with NPV (accept if NPV > 0), IRR, payback period and ARR. It manages forecasting risk with scenario analysis (optimistic/base/pessimistic NPVs) and sensitivity analysis (how steeply NPV responds to one driver). WACC and NPV are the analytical heart of the group Excel financial model and prime Quiz 2 content.
What this chapter covers
- 01Cost of debt: YTM if bonds are traded, loan rate if a loan, Rf + CDS spread if untraded; after-tax Rd(1 − Tc)
- 02Cost of equity: DDM Re = D1/P0 + g, or CAPM Re = Rf + β(Rm − Rf); preference Rp = D1/P0
- 03WACC = (E/V)·Re + (D/V)·Rd·(1 − Tc) + (P/V)·Rp, with market-value weights and V = E + D + P
- 04NPV = −Initial Outlay + Σ CF_t/(1 + r)^t; accept if NPV > 0, using r = WACC
- 05IRR (rate that makes NPV = 0; accept if IRR > required return); payback period; ARR
- 06Forecasting risk: the danger of accepting a bad project (or rejecting a good one) from wrong forecasts
- 07Scenario analysis: recompute NPV under optimistic/base/pessimistic input sets
- 08Sensitivity analysis: freeze all inputs but one and measure the NPV slope
WACC, then an NPV accept/reject decision
- +1Weights: V = E + D = 6 + 4 = $10m, so E/V = 0.6 and D/V = 0.4.
- +1WACC = (E/V)·Re + (D/V)·Rd·(1 − Tc) = 0.6 × 12% + 0.4 × 6% × (1 − 0.30) = 7.2% + 0.4 × 4.2% = 7.2% + 1.68% = 8.88%. The debt cost is tax-shielded, which is why it enters after tax.
- +1Discount the project cash flows at ≈9%. The 5-year annuity factor is [1 − 1.09^−5]/0.09 = (1 − 0.64993)/0.09 = 3.8897.
- +1PV of inflows = 150,000 × 3.8897 = $583,448.
- +1NPV = −500,000 + 583,448 = +$83,448. Since NPV > 0, accept the project — it earns more than the 9% cost of capital and adds value.
Key terms
- Cost of debt
- The return lenders require, measured after tax as Rd(1 − Tc) because interest is tax-deductible. Use the bond YTM if the debt is traded, the loan rate if it is a loan, or the risk-free rate plus a credit spread if it is untraded.
- Cost of equity
- The return shareholders require, estimated from the dividend discount model (Re = D1/P0 + g) or CAPM (Re = Rf + β(Rm − Rf)). It is not tax-adjusted in the WACC.
- WACC
- The market-value-weighted, after-tax average cost of a firm's funding: WACC = (E/V)·Re + (D/V)·Rd·(1 − Tc) + (P/V)·Rp. It is the hurdle rate used to discount a project's cash flows.
- Net Present Value (NPV)
- The sum of a project's discounted cash flows less its initial outlay, NPV = −Outlay + Σ CF_t/(1 + r)^t, with r the WACC. Accept if NPV > 0, because the project then adds value.
- Scenario analysis
- A forecasting-risk tool that changes several inputs together to build optimistic, base and pessimistic cases and recomputes NPV for each. If plausible or pessimistic scenarios turn negative, forecasting risk is high.
- Sensitivity analysis
- A forecasting-risk tool that freezes all inputs but one, varies that single driver, and measures how steeply NPV responds. A steep NPV-versus-driver slope means the project is highly sensitive to that forecast.
Cost of Capital & Capital Budgeting FAQ
Why is the cost of debt taken after tax but not the cost of equity?
Because interest payments are tax-deductible, so each dollar of interest costs the firm only (1 − Tc) dollars after the tax saving — hence Rd(1 − Tc) in the WACC. Dividends and equity returns are not tax-deductible, so the cost of equity enters at its full value.
Should WACC weights be book or market values?
Market values. The WACC is meant to reflect the return investors currently require on the firm's funding at today's values, so use the market value of equity (market capitalisation) and of debt. Book weights can badly misstate the mix, especially for equity.
What is the difference between scenario and sensitivity analysis?
Scenario analysis flexes several inputs together into coherent optimistic/base/pessimistic worlds and reports an NPV for each. Sensitivity analysis isolates one input, varies it alone, and measures the NPV slope. Scenarios test plausible combinations; sensitivity pinpoints which single forecast the decision most depends on.
How do NPV and IRR relate?
IRR is the discount rate that makes NPV zero. The NPV rule accepts a project when NPV > 0 at the required return; the IRR rule accepts when IRR exceeds the required return. For a standard project they agree, but NPV is the more reliable rule when cash-flow patterns are unusual or projects are being ranked.
Assessment move
Build the WACC in a fixed order: find market-value weights, then the after-tax cost of debt Rd(1 − Tc), then the cost of equity (DDM or CAPM), then combine. Keep the tax adjustment on debt only. For appraisal, make NPV your primary rule (discount at the WACC, accept if positive) and be able to explain IRR, payback and ARR alongside it. Practise scenario analysis (recompute NPV across input sets) and sensitivity analysis (NPV slope against one driver), because both power the group financial model's what-if section. Rehearse a full WACC-then-NPV item under time pressure for Quiz 2, and ask Sia to set fresh cost-of-capital and NPV problems and check each step.
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