Aug 13

Value at Risk (VaR). 2007 FRM, Part 9: Project impact on CFaR

by David Harper, CFA, FRM, CIPM

FRM | Risk |

Learning Outcome

  • LO 8.4: Evaluate the impact of a project that is large relative to the firm's portfolio of projects on CFaR, and explain how the cost of additional CFaR impacts the capital budgeting decision.

For small project we used beta, for large project we recalculate cash flow volatility

Previously we looked at the cash flow at risk (CFaR) impact of small project; the key idea was to use the asset's beta to link its volatility to the firm's volatility. In the case of a large project, relative to the firm, we instead recalculate the CFaR.

Here is the key formula. Just like VaR, CFaR is cash flow volatility multiplied by the critical value (e.g., 1.65 at 95% confidence). But the cash flow volatility is the volatility of the cash flow plus the large project:

cfar_largeproject

...and the cash flow of the large project relies on the familiar two-asset portfolio variance. So, the volatility of the firm plus the cash flow is the variance of the firm's cash flow plus the variance of the project's cash flow plus the two times the covariance between the two cash flows.

The EditGrid spreadsheet below contains an example. Note there are five sets of inputs/calculations:

  • Specify a significance; e.g., 5% corresponds roughly to a critical value of 1.65
  • Input CAPM assumptions. This is to estimate a cost of capital (COC); the COC is the discount rate used to present value (PV) the large project's future payoff
  • Assumptions about the firm's cash flow and cash flow volatility before the large project
  • Assumptions about the additional large project. Note we need a correlation between firm and project cash flows
  • The calculation of CFaR including the large project.

Note the project NPV is an "all in" cost/benefit calculation. The benefit of the additional project is it's NPV. But a cost must be subtracted: the incremental CFaR (created by the project) multiplied by the dollar cost of CFaR (i.e., it does not cost a full dollar to "support" an additional dollar of CFaR).

Here is the EditGrid spreadsheet.

EditGrid Spreadsheet by bt/frm2007.

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