Published On:Friday 23 December 2011
Posted by Muhammad Atif Saeed
Net Preset Value
NPV and IRR are two methods for making capital-budget decisions, or choosing between alternate projects and investments when the goal is to increase the value of the enterprise and maximize shareholder wealth. Defining the NPV method is simple: the present value of cash inflows minus the present value of cash outflows, which arrives at a dollar amount that is the net benefit to the organization.
To compute NPV and apply the NPV rule, the authors of the reference textbook define a five-step process to be used in solving problems:
1.Identify all cash inflows and cash outflows.2.Determine an appropriate discount rate (r). 3.Use the discount rate to find the present value of all cash inflows and outflows. 4.Add together all present values. (From the section on cash flow additivity, we know that this action is appropriate since the cash flows have been indexed to t = 0.)5.Make a decision on the project or investment using the NPV rule: Say yes to a project if the NPV is positive; say no if NPV is negative. As a tool for choosing among alternates, the NPV rule would prefer the investment with the higher positive NPV.
Companies often use the weighted average cost of capital, or WACC, as the appropriate discount rate for capital projects. The WACC is a function of a firm's capital structure (common and preferred stock and long-term debt) and the required rates of return for these securities. CFA exam problems will either give the discount rate, or they may give a WACC.
To compute NPV and apply the NPV rule, the authors of the reference textbook define a five-step process to be used in solving problems:
1.Identify all cash inflows and cash outflows.2.Determine an appropriate discount rate (r). 3.Use the discount rate to find the present value of all cash inflows and outflows. 4.Add together all present values. (From the section on cash flow additivity, we know that this action is appropriate since the cash flows have been indexed to t = 0.)5.Make a decision on the project or investment using the NPV rule: Say yes to a project if the NPV is positive; say no if NPV is negative. As a tool for choosing among alternates, the NPV rule would prefer the investment with the higher positive NPV.
Companies often use the weighted average cost of capital, or WACC, as the appropriate discount rate for capital projects. The WACC is a function of a firm's capital structure (common and preferred stock and long-term debt) and the required rates of return for these securities. CFA exam problems will either give the discount rate, or they may give a WACC.
Example:To illustrate, assume we are asked to use the NPV approach to choose between two projects, and our company's weighted average cost of capital (WACC) is 8%. Project A costs $7 million in upfront costs, and will generate $3 million in annual income starting three years from now and continuing for a five-year period (i.e. years 3 to 7). Project B costs $2.5 million upfront and $2 million in each of the next three years (years 1 to 3). It generates no annual income but will be sold six years from now for a sales price of $16 million.Applying the NPV rule, we choose Project A, which has the larger NPV: $3.269 million versus $2.429 million.
For each project, find NPV = (PV inflows) - (PV outflows).
Project A: The present value of the outflows is equal to the current cost of $7 million. The inflows can be viewed as an annuity with the first payment in three years, or an ordinary annuity at t = 2 since ordinary annuities always start the first cash flow one period away.
PV annuity factor for r = .08, N = 5: (1 - (1/(1 + r)N)/r = (1 - (1/(1.08)5)/.08 = (1 - (1/(1.469328)/.08 = (1 - (1/(1.469328)/.08 = (0.319417)/.08 = 3.99271
Multiplying by the annuity payment of $3 million, the value of the inflows at t = 2 is ($3 million)*(3.99271) = $11.978 million.
Discounting back two periods, PV inflows = ($11.978)/(1.08)2 = $10.269 million.
NPV (Project A) = ($10.269 million) - ($7 million) = $3.269 million.
Project B: The inflow is the present value of a lump sum, the sales price in six years discounted to the present: $16 million/(1.08)6 = $10.083 million.
Cash outflow is the sum of the upfront cost and the discounted costs from years 1 to 3. We first solve for the costs in years 1 to 3, which fit the definition of an annuity.
PV annuity factor for r = .08, N = 3: (1 - (1/(1.08)3)/.08 = (1 - (1/(1.259712)/.08 = (0.206168)/.08 = 2.577097. PV of the annuity = ($2 million)*(2.577097) = $5.154 million.
PV of outflows = ($2.5 million) + ($5.154 million) = $7.654 million.
NPV of Project B = ($10.083 million) - ($7.654 million) = $2.429 million.
| Exam Tips and Tricks Problems on the CFA exam are frequently set up so that it is tempting to pick a choice that seems intuitively better (i.e. by people who are guessing), but this is wrong by NPV rules. In the case we used, Project B had lower costs upfront ($2.5 million versus $7 million) with a payoff of $16 million, which is more than the combined $15 million payoff of Project A. Don't rely on what feels better; use the process to make the decision! |
