Capital Budgeting and Bond Valuation Formulas

Posted on Apr 24, 2026 in Finance

Capital Budgeting Metrics

  • NPV: NPV = -C₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + … + CFₙ/(1+r)ⁿ. Accept if NPV > 0.
  • IRR: The discount rate where NPV = 0. Accept if IRR > r.
  • Payback: Years to recover initial investment. Discounted Payback uses discounted cash flows.
  • PI: PI = PV(future CFs) / Initial Investment. Accept if PI > 1.
  • MIRR: Solves PV(outflows) × (1+MIRR)ⁿ = FV(inflows).

Decision Rules and Conflicts

  • NPV vs IRR: Use NPV for mutually exclusive projects or differences in scale/timing.
  • Scale Problem: Use incremental IRR.
  • Non-conventional CFs: Multiple IRRs may exist.
  • Advantages: NPV is the best measure of value; IRR assumes reinvestment at IRR; Payback ignores TVM.

Cash Flow Analysis

  • Incremental CFs: Only include additional cash flows. Ignore sunk costs; include opportunity costs.
  • Erosion: Subtract lost sales.
  • Synergies: Add extra benefits.
  • OCF Formula: OCF = (Sales – Costs)(1 – Tc) + (Depreciation × Tc).
  • Terminal Cash Flow: After-tax Salvage + NWC recovery.
  • After-tax Salvage: Salvage – Tc(Salvage – Book Value).
  • Net Capital Spending: Ending Net FA – Beginning Net FA + Depreciation.
  • NWC: Increase in NWC is an outflow at t=0; recovery is an inflow at the end.

Depreciation and Unequal Lives

  • Straight-line: (Cost – Salvage) / Life.
  • MACRS: Accelerated depreciation provides a better tax shield early.
  • Replacement Chain: Repeat projects to a common life to compare NPV.
  • EAC: EAC = NPV / Annuity Factor, where Annuity Factor = [1 – (1+r)⁻ⁿ] / r.

Bond Valuation

  • Price: Price = Σ [Coupon/(1+YTM)ᵗ] + Face/(1+YTM)ⁿ.
  • YTM Calculation: Use financial calculator (N = periods, PMT = coupon, FV = 1000, PV = -price).
  • Yield Relationships: Coupon > YTM (Premium); Coupon < YTM (Discount); Coupon = YTM (Par).
  • Current Yield: Annual Coupon / Current Price.
  • Price Behavior: Discount bonds rise to par; premium bonds fall to par over time.

Interest Rate Risk and Debt

  • Price Risk: Rising rates decrease price (worst for long maturity, low coupon).
  • Reinvestment Risk: Falling rates decrease reinvestment income (worst for short maturity, high coupon).
  • Fisher Effect: 1 + Nominal = (1 + Real) × (1 + Expected Inflation).
  • Debt vs Equity: Debt offers interest tax shields but fixed obligations; Equity has no tax shield and residual claims.
  • Bond Types: Munis (tax-exempt), Treasury (risk-free), Corporate (credit risk).