A present value (PV) expresses a future cash flow in today's dollars by discounting for its timing and required return. Net present value (NPV) combines the present values of every incremental receipt and payment, including the initial investment.
A company can compare investment alternatives only after defining the objective, feasible choices, investment horizon and common valuation date. The highest accounting profit, fastest recovery and highest percentage return can identify different investments because these measures answer different questions.
Investment decision rules
HIGH-FREQUENCY: A positive undiscounted surplus does not establish positive net present value. Record when the cash arrives before deciding whether the investment earns its required return.
To calculate present value, the analyst first places every cash flow on a timeline measured from the valuation date. A time-zero payment has a factor of one; subsequent cash flows receive factors reflecting their actual distance from that date.
Cash-flow timing patterns
- A single sum occurs once, such as equipment disposal proceeds at the end of Year 4.
- An ordinary annuity contains equal payments at each period-end, such as annual savings received at Years 1 through 4.
Common mistakes
- Wrong cash sign. Subtracting eligible cash in the $102,000,000 enterprise bridge produces $67,000,000; the supported common-equity value is $77,000,000.
- Terminal value discounted too early. Applying 0.8116 instead of 0.7312 to $37,080,000 adds $37,080,000 x (0.8116 − 0.7312) = $2,981,232 to Example 4's value.
- Unsupported distractor explanation. No supported single-error derivation establishes $22,700,000 from Example 4's model; an explanation cannot invent arithmetic to justify that amount.
Bottom line
- Net present value discounts all incremental after-tax cash flows, including working capital, later spending, disposal taxes and terminal recovery.
- Independent positive-NPV investments add value; mutually exclusive choices require the highest feasible NPV under comparable assumptions.
- IRR requires inspection of cash-flow signs and can conflict with NPV because of scale, timing or multiple zero-value rates.
- Payback measures recovery, while constrained budgets and unequal lives require feasible combinations or supported annual comparisons.
Exam shortcut
Mark time zero, every later payment and terminal dates before selecting a factor. “Beginning of each year” signals an annuity due; unequal receipts require separate factors. Build the incremental cash-flow column before discounting. Cross out sunk costs, identify opportunity costs, and reconcile depreciation through either the earnings add-back or tax-shield path. Read the objective and constraints before ranking results.
The full lesson (about 10,118 words, 67 min read) adds 4 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- I.B3
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