Capital Budgeting: Advanced Topics

Overview

• What you’ll learn: How to incorporate inflation into DCF analysis, the impact of income taxes on capital budgeting (depreciation tax shields), real options in investment decisions, sensitivity and scenario analysis, and post-audit of capital investments.
• Prerequisites: Lesson 4 — Capital Budgeting Methods
• Estimated reading time: 18 minutes

Introduction

The Grand Historian records: The basic capital budgeting methods assume a world of clean cash flows, stable prices, and no taxes. The real world offers none of these courtesies. Inflation erodes future cash flows, the tax collector demands his share, and uncertainty lurks behind every forecast. Advanced capital budgeting equips the strategist to navigate these complications — transforming idealized models into battle-tested tools.

Horngren (Chapter 22) extends the basic DCF framework to address these real-world complexities, producing more accurate and useful investment analyses.

Inflation in Capital Budgeting

Nominal vs. Real Cash Flows

Two consistent approaches exist:

• Nominal approach: Use nominal (inflation-included) cash flows discounted at the nominal discount rate. The nominal rate includes an inflation premium.
• Real approach: Use real (inflation-adjusted) cash flows discounted at the real discount rate.

The relationship: (1 + Nominal rate) = (1 + Real rate) × (1 + Inflation rate)

Both methods yield the same NPV when applied consistently. The critical error is mixing approaches — using nominal cash flows with a real discount rate, or vice versa.

Income Taxes and Capital Budgeting

The Tax Shield of Depreciation

Depreciation is a non-cash expense that reduces taxable income, thereby reducing tax payments. The tax savings from depreciation is called the depreciation tax shield:

Tax Shield = Depreciation × Tax Rate

For a $1,000,000 asset depreciated straight-line over 5 years at a 30% tax rate: annual depreciation = $200,000, annual tax shield = $200,000 × 0.30 = $60,000.

Accelerated depreciation methods (MACRS in the US) front-load depreciation, creating larger tax shields in earlier years — worth more in present value terms.

After-Tax Cash Flows

For each period:

After-tax operating cash flow = Pre-tax cash flow × (1 − Tax rate) + Depreciation × Tax rate

The first term adjusts operating cash flows for taxes; the second adds back the depreciation tax shield.

Gain or Loss on Disposal

If an asset is sold for more than its book value, the gain is taxable. If sold for less, the loss provides a tax benefit. The after-tax cash flow from disposal:

After-tax disposal = Selling price − Tax rate × (Selling price − Book value)

Real Options

Traditional NPV analysis assumes a “now or never” decision. Real options recognize that managers have flexibility:

• Option to expand: If the project succeeds, invest more. A pilot project is an option to expand.
• Option to abandon: If the project fails, cut losses and redeploy assets. Salvage value is the exercise price.
• Option to delay: Wait for more information before committing. Delay has value when uncertainty is high.
• Option to switch: Flexible manufacturing that can switch between products has option value.

太史公曰：The general who builds a forward camp does not commit his entire army. He commits a scouting force — an option to advance if intelligence is favorable, or to retreat if not. This flexibility has value beyond the scouting mission itself. Traditional NPV, which ignores this flexibility, systematically undervalues projects with embedded options.

Sensitivity and Scenario Analysis

Sensitivity analysis tests how NPV changes when one variable changes while others remain constant. Key variables to test: sales volume, selling price, variable costs, discount rate, and project life.

Scenario analysis changes multiple variables simultaneously to model optimistic, base-case, and pessimistic scenarios. This provides a range of possible NPVs rather than a single point estimate.

Post-Audit of Capital Investments

After the investment is made, compare actual results to the projections used to justify the investment. Post-audits:

• Improve future forecasting accuracy
• Hold managers accountable for their projections
• Identify systematic biases (optimism bias is common)
• Provide learning for the organization

Key Takeaways

• Inflation requires consistency — nominal cash flows with nominal rates, or real with real. Never mix.
• The depreciation tax shield provides real cash savings — accelerated depreciation is more valuable in PV terms.
• After-tax cash flow = Pre-tax flow × (1 − t) + Depreciation × t.
• Real options (expand, abandon, delay, switch) add value that traditional NPV misses.
• Sensitivity and scenario analysis provide ranges rather than point estimates — more honest and more useful.

What’s Next

In Lesson 6, we confront the thorny issue of transfer pricing — how divisions within the same empire trade with each other and why it matters enormously.