FIN.5:5 - Archetypal Grounding

Combining supplied inputs. All numbers here are constructed. Suppose the supplying analysis has already qualified equity return 9% (3% + beta 1.2×premium 5%), debt return 6%, market equity 60, debt 40 and a usable 25% debt-tax adjustment for the receiving valuation. Their WACC is 0.6×9% + 0.4×6%×0.75 = 7.2%. Holding the returns and weights fixed, removing only that tax adjustment gives 7.8%. These computations combine supplied inputs; constructing them for another business or financing policy requires the following work.

Constructing a project rate. Take a peer with equity beta 1.15, debt beta 0.6 and market D/E of 0.5. Stipulate that it maintains a permanent fixed debt amount and that its constant 25% usable tax savings have debt risk. Its factor is therefore 0.75, giving βU = (1.15 + 0.6×0.75×0.5)/(1 + 0.75×0.5) = 1. Assume comparable operating exposure and no material excess cash.

The project instead resets debt each year to 40% of the remaining project’s market value, with final repayment at year 2. Assume no additional financing costs in either project policy. Use the annual model’s stated tax and loss-treatment assumptions, a flat 3% risk-free curve, market premium 5%, debt beta 0.6 and matched debt return kD = 3% + 0.6×5% = 6%. The factor becomes 1−0.25×0.06/1.06 = 0.985849. With D/E = 40/60, equity beta is 1 + (1−0.6)×0.985849×40/60 = 1.262893, equity return is 9.314465%, and WACC is 7.388679%.

Apply FIN.6 to an investment of 1,000 and expected after-tax operating cash flows of 556 at each of the next two year-ends, before financing payments. NPV at the constructed annual-policy rate is −1,000 + 556/1.07388679 + 556/1.07388679² = −0.13, rounded. The break-even rate is about 7.379143%. Using the earlier supplied 7.2% would give +2.48, but that earlier input does not establish the annual-policy rate for this business. Using the 6% debt return gives +19.37 and prices the wrong claim. The isolated 7.8% sensitivity gives −5.78.

Changing the financing policy. The annual-policy valuation implies initial debt of 0.4×999.868382 = 399.947353. Now hold that same amount until final repayment in year 2, instead of resetting it in year 1. Assume the expected tax savings are 0.25×0.06×399.947353 = 5.999210 each year, priced at the debt return under the stipulated tax/loss treatment. The unlevered required return is 3% + 1×5% = 8%. APV is 556/1.08 + 556/1.08² + 5.999210/1.06 + 5.999210/1.06² = 1,002.49. NPV is +2.49. This is a finite schedule calculation; the permanent-debt factor was used only to recover the stipulated peer’s business risk. If the project’s debt policy is unresolved, these differing signs require a conditional recommendation or resolution of that policy before choosing on value.

Changing business risk. Return to annual debt resetting, but use a supported unlevered beta of 1.4 for a more cyclical business. Hold the illustrative debt risk, financing share and other model assumptions fixed. Equity beta becomes 1.925786, equity return 12.628931%, WACC 9.377358%, and NPV −26.92. This adaptation requires the project’s operating-risk estimate. An actual leverage change would also reopen the debt estimate. The valuation does not establish funding access or authorize investment.