IFMP Capital Budgeting – Corporate Finance Certification (CBCFC), Pakistan cheat sheet

Net present value: NPV = Σ CFt/(1+r)^t − Initial Outlay, for t = 1 to n; accept an independent project when NPV > 0, reject when NPV < 0, and rank mutually exclusive projects by the highest positive NPV.

Internal rate of return: the discount rate r* at which NPV = 0; a single conventional project (one sign change in cash flows) is accepted when IRR > cost of capital. IRR can produce multiple roots or no root when cash flows change sign more than once.

Profitability index: PI = PV of future cash inflows ÷ Initial Outlay; accept when PI > 1. PI is used to rank projects under capital rationing because it measures NPV per unit of scarce capital.

Payback period: the time until cumulative cash inflows recover the initial outlay; accept if payback ≤ a preset cutoff. It ignores all cash flows after the cutoff and ignores the time value of money unless discounted payback is used.

Accounting rate of return: ARR = Average annual accounting profit ÷ Average investment, where average investment ≈ (Initial cost + Salvage value) ÷ 2. ARR uses accounting profit, not cash flow, and ignores the time value of money.

Incremental cash flow rule: include only cash flows that change because the project is accepted. Exclude sunk costs, ignore financing costs (interest is captured in the discount rate), and include opportunity costs and externalities such as lost sales of existing products.

Depreciation tax shield: annual shield = Depreciation × Tax rate. Under straight-line, Depreciation = (Cost − Salvage) ÷ Useful life. The shield is a real cash inflow because it reduces tax payable.

Working capital: an increase in net working capital at project start is a cash outflow, and its recovery at project end is a cash inflow. Ignore it only if the problem states working capital is unchanged.

Replacement decisions: compare the incremental cash flows of the new asset against keeping the old one, including the after-tax salvage value of the old asset now (proceeds − tax on gain) and the lost salvage value of the old asset at the end of its remaining life.

Weighted average cost of capital: WACC = (E/V) × Ke + (D/V) × Kd × (1 − T), where V = E + D. Use market values of debt and equity, and use the after-tax cost of debt because interest is tax-deductible.

Cost of equity by CAPM: Ke = Rf + β × (Rm − Rf), where Rf is the risk-free rate, β the equity beta, and (Rm − Rf) the market risk premium. The beta must reflect the project's business risk, not the firm's existing mix.

Cost of equity by the dividend growth model: Ke = (D1 ÷ P0) + g, where D1 = D0 × (1 + g). This model requires a constant growth rate below Ke and is unsuitable for firms paying no dividend.

Capital asset pricing and project discount rates: a project in a different risk class from the firm should be discounted at a rate built from a pure-play or unlevered beta for that industry, then relevered to the project's target gearing.

Levered and unlevered beta: βL = βU × [1 + (1 − T) × (D ÷ E)]. Unlever comparable-company betas, average them, then relever at the target debt-to-equity ratio to obtain the project beta.

Capital rationing: when capital is limited, rank divisible projects by profitability index and take the combination with the highest total NPV. With indivisible projects, use trial combinations or linear programming to maximise total NPV within the budget.

Sensitivity analysis: recalculate NPV for a percentage or absolute change in one input while holding others constant; the sensitivity margin = NPV ÷ PV of the input's cash flow effect, giving the percentage change that drives NPV to zero.

Scenario and simulation analysis: scenario analysis changes several inputs together for consistent states of the world; Monte Carlo simulation assigns probability distributions to inputs and yields a distribution of NPVs, so risk is measured by variance or standard deviation of NPV.

Real options: the option to delay, expand, contract, or abandon has value beyond static NPV. Abandonment value raises project value when salvage proceeds are certain; the option to delay is worth more when volatility of project cash flows is high.

Relevant cash flow timing: assume cash flows occur at the end of each year unless stated otherwise. If cash flows are received evenly through the year, mid-year discounting multiplies NPV by (1 + r)^0.5.

Tax on asset disposal: tax paid = (Sale proceeds − Tax written-down value) × Tax rate. A loss on disposal creates a tax credit (cash inflow) equal to the loss times the tax rate.

Tax depreciation and balancing allowances: when an asset is sold, the tax written-down value is reduced by the disposal proceeds, and any remaining balance continues to attract tax depreciation unless the pool is closed.

Nominal versus real discount rates: discount nominal cash flows at a nominal rate and real cash flows at a real rate. Real rate ≈ (1 + nominal) ÷ (1 + inflation) − 1; mixing nominal cash flows with a real rate overstates NPV.

Foreign project appraisal: discount foreign-currency cash flows at the foreign cost of capital and translate the NPV at the spot rate, or translate each cash flow at the forward rate implied by interest rate parity and discount at the home cost of capital. Both routes give the same NPV when parity holds.

Inflation and cash flows: selling prices and costs may inflate at different rates. Apply each rate to its own cash flow line rather than a single general inflation figure, and remember depreciation tax shields are fixed in nominal terms when based on historic cost.

Equivalent annual annuity: EAA = NPV ÷ Annuity factor for the project life. For mutually exclusive projects with unequal lives, choose the project with the higher EAA, which converts NPV into a level annual equivalent.

Capital budgeting under uncertainty: expected NPV = Σ (probability × NPV of scenario). Do not use the expected cash flows of mutually exclusive scenarios in place of the expected NPV when the projects are alternatives.

Post-completion audit: compares actual outcomes with the approved appraisal, feeds back into forecasting accuracy, and may reveal systematic bias such as over-optimistic promoters, but it cannot change the sunk decision.