Discounting

Five flows, received through each year

The explicit free cash flows are produced throughout each financial year, not all on its last day. TANGE therefore uses a mid-year convention: year one is discounted for 0.5 years, year two for 1.5 years, and so on through 4.5 years for year five. This avoids systematically treating operating cash as if it arrived later than it does.

Discount factor, year t = 1 / (1 + WACC)^(t − 0.5)

Present value of FCFF, year t = FCFF(t) × discount factor(t)

The terminal value follows the same convention

The terminal value is the present value, at the end of year five, of the cash flows of year six onwards. Those flows arise throughout their years exactly as the explicit ones do, so they carry the same mid-year timing. Discounting the terminal for five full years while discounting the explicit flows to mid-year mixes two conventions and understates the result by roughly three to five per cent: the perpetuity is not a stock held on the last day of year five, it is the value of flows that behave like the five before them.

Terminal discount factor = 1 / (1 + WACC)^4.5

One rate for operating cash flows

All operating cash flows use the same WACC because they are unlevered flows available to debt and equity together. There is one rate and one valuation: the low and high cases that once moved the WACC half a point either way have been withdrawn, and how much the estimate depends on the cost of capital is now read from the sensitivity table on the result surface, where the leverage, the risk-free rate and the specific risk premium each move on their own.

The domain guard requires WACC to exceed perpetual growth by more than 0.5 percentage points. This is a validity condition, not a formatting choice.

Displayed numbers and calculation numbers

The engine calculates with full precision. Tables round only for presentation and preserve their visual bridges after rounding. Changing the display unit therefore never changes the valuation itself.