CAPITAL BUDGETING · FORMULA AND EXCEL
1. Match the discount rate to the cash flow
| Cash flow | Discount rate / approach | Typical use |
|---|---|---|
| Unlevered project FCFF | Project-risk-consistent WACC | Relatively stable target leverage |
| Equity cash flow after debt flows | Project cost of equity | Value to equity holders |
| Unlevered operating cash flow | Unlevered required return, then APV adjustments | Financing effects valued separately |
| Certainty-equivalent cash flow | Risk-free rate appropriate to timing/currency | Risk adjustment made in cash flows |
The corporate WACC is suitable only when the project has comparable operating risk and consistent financing assumptions. A firm moving into a very different industry should estimate that activity’s risk rather than apply its existing average hurdle blindly.
Continue with Cost of Capital for a broader treatment of financing components.
CAPITAL BUDGETING · FORMULA AND EXCEL
2. Weighted average cost of capital
Assume market-value weights E = 60%, D = 40%, cost of equity 14%, debt cost 8% and a usable marginal interest tax shield at 25%. WACC = 0.6 × 14% + 0.4 × 8% × 75% = 10.8%.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | 0.6 | Equity weight |
| B3 | 0.4 | Debt weight |
| B4 | 0.14 | Cost of equity |
| B5 | 0.08 | Pre-tax cost of debt |
| B6 | 0.25 | Applicable tax rate |
| B8 | =B2*B4+B3*B5*(1-B6) | WACC = 10.8% |
| B9 | =B2+B3 | Weight check = 1 |
Use target market-value financing weights and marginal costs, not simply historic book costs. Interest deductibility limits, losses, changing leverage and distress can require more detailed modelling. A WACC tax adjustment assumes the shield can actually be realised.
CAPITAL BUDGETING · FORMULA AND EXCEL
3. Pure play: estimate project operating risk
βL,target = βU[1 + (1−T)(D/E)target]
ke = rf + βL,target × ERP
A comparable focused business has levered equity beta 1.375, D/E = 0.5 and tax rate 25%. Unlevered beta = 1.375/1.375 = 1.00. For target D/E = 0.8, relevered beta = 1 × (1 + 0.75 × 0.8) = 1.60.
With risk-free 6% and equity risk premium 6%, cost of equity = 15.6%. Debt cost 8% and target weights E = 1/1.8, D = 0.8/1.8 give WACC = 11.33%.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | 1.375 | Comparable levered beta |
| B3 | 0.5 | Comparable D/E |
| B4 | 0.25 | Tax rate |
| B5 | 0.8 | Target D/E |
| B6 | 0.06 | Risk-free rate |
| B7 | 0.06 | Equity risk premium |
| B8 | 0.08 | Target debt cost |
| B10 | =B2/(1+(1-B4)*B3) | Unlevered beta |
| B11 | =B10*(1+(1-B4)*B5) | Relevered project beta |
| B12 | =B6+B11*B7 | Project equity cost |
| B13 | =(B12+B5*B8*(1-B4))/(1+B5) | Project WACC |
This simplified relevering assumes negligible debt beta and a standard treatment of tax shields. In practice examine several comparable businesses, remove surplus-cash effects where relevant, use consistent operating exposures and judge estimation noise. A comparable’s equity beta is not automatically a project asset beta.
CAPITAL BUDGETING · FORMULA AND EXCEL
4. Adjusted present value: separate operating and financing value
A separate project costs 100 and generates unlevered operating cash flows of 45 at the end of each of three years. Unlevered required return is 10%. Unlevered NPV = −100 + 45 × 2.486852 = 11.9083.
A fixed debt amount of 40 remains outstanding for three years at 6%, repaid at maturity. If interest is deductible at 25%, annual shield = 40 × 6% × 25% = 0.60. Assume its risk warrants a 6% discount rate and shields are fully usable. Shield PV = 1.6038. A net financing fee of 2 is paid today. APV = 11.9083 + 1.6038 − 2 = 11.5121.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | 100 | Initial investment |
| B3 | 45 | Annual unlevered cash flow |
| B4 | 3 | Years |
| B5 | 0.1 | Unlevered required return |
| B6 | 40 | Fixed debt outstanding |
| B7 | 0.06 | Debt cost |
| B8 | 0.25 | Tax rate |
| B9 | 0.06 | Assumed shield discount rate |
| B10 | 2 | Net financing fee at time zero |
| B12 | =-B2+B3*(1-(1+B5)^(-B4))/B5 | Unlevered NPV |
| B13 | =B6*B7*B8 | Annual interest shield |
| B14 | =B13*(1-(1+B9)^(-B4))/B9 | Shield PV |
| B15 | =B12+B14-B10 | APV |
Debt drawdown and repayment are financing cash flows; borrowing is not itself value creation. Value comes from net financing benefits or costs relative to fair financing. Shield discounting depends on the debt policy and risk. Discounting at debt cost here is a stated assumption, not a universal rule.
CAPITAL BUDGETING · FORMULA AND EXCEL
5. WACC versus APV: choose a coherent model
| Issue | WACC route | APV route |
|---|---|---|
| Operating cash flow | Before interest and debt repayment | Before financing effects |
| Interest tax benefit | Typically embedded in the after-tax rate | Added separately as shield PV |
| Financing policy | Often target leverage maintained | Can handle a specified debt schedule explicitly |
| Fees and subsidies | Must be included consistently | Explicit separate PV adjustments |
| Main danger | Using a rate inconsistent with project risk/leverage | Double-counting financing benefits or overstating shields |
Both approaches should reconcile when operating assumptions, financing policy, tax shields and risk treatment are consistent. Different answers from independent assumptions do not prove one method is wrong. A project with changing debt may require period-specific rates or a detailed APV.
CAPITAL BUDGETING · FORMULA AND EXCEL
6. A practical investment recommendation
A useful recommendation states the business alternative, incremental cash-flow basis, investment size, NPV, relevant return and recovery metrics, key assumptions, downside tests, financing assumptions and the management decisions that remain. Include ownership of implementation and a post-completion review date.
Before approval
- Reconcile initial, operating and terminal flows, including working-capital timing.
- Check units, dates, taxes, inflation, currency and financing consistency.
- Use NPV to assess value and the other metrics to explain the trade-offs.
- Test the main drivers and any constraints or options that change the choice.
- Record what evidence could trigger delay, redesign, expansion or abandonment.
Can interest be deducted from OCF while also using an after-tax WACC?
That generally mixes financing and operating valuations and can double-count financing effects. Match FCFF with WACC, FCFE with equity cost, or use APV consistently.
Should every division use the same hurdle rate?
Only when operating risk and financing assumptions justify it. A common rate can overinvest in risky projects and reject relatively safe ones.
Sources and further reading
Selected relevant sections of the supplied materials informed this series. Prasanna Chandra’s planning framework also informs the emphasis on estimation and strategic fit. These are original explanations and teaching cases, not reproduced textbook examples.
- Prasanna Chandra (2019), Projects: Planning, Analysis, Selection, Financing, Implementation, and Review, 9th edition, McGraw Hill. The uploaded 150-page scan was visually checked in selected opening sections: importance and difficulties of capital investment, project categories, planning–analysis–selection–financing–implementation–review, strategy and demand forecasting. It ends during Chapter 4; later detailed appraisal chapters appear in its contents but are not present in this extract.
- Dayananda, Irons, Harrison, Herbohn and Rowland (2002), Capital Budgeting: Financial Appraisal of Investment Projects, Cambridge University Press. Reviewed selected passages on relevant cash flows, appraisal methods, sensitivity, simulation and capital constraints. The chapter structure also guides further reading.
- Dr. Vijay Shankar Pandey, Capital Budgeting Techniques, uploaded as “Basics of Capital Budgetings”: process, payback, ARR, NPV, IRR and comparison. Rounded examples and conventions are checked independently rather than copied.
- Professor James P. Dow Jr., FIN 303, Part 8: Topics in Capital Budgeting: uncertainty, flexibility and unequal project lives.
- Capital Budgeting – Risk Analysis, uploaded five-page extract: probability, certainty equivalents and risk-adjusted approaches.
For continued study: Dayananda Chapters 1–2 for foundations; 5–6 for appraisal; 7–9 for risk; 11–12 for constrained selection; 16 for international appraisal. Review here is targeted, not a claim that the entire 343-page book was read.
Prasanna Chandra: further-reading map
The 9th-edition contents identifies Chapter 8 (Investment Criteria), Chapter 9 (Project Cash Flows), Chapter 10 (Cost of Capital), Chapter 11 (Project Risk Analysis), Chapter 12 (Project Rate of Return) and Chapter 13 (Special Decision Situations). These are reading directions, not claims that their absent pages were consulted.
Public reference links
All rates, taxes, exchange rates and business figures in the examples are teaching assumptions. Results use unrounded calculations and are rounded for display. Excel formulas use English function names and commas.