The discount rate goes up by a point. What happens to the DCF, and which hurts more: that, or terminal growth falling by a point?

Say value falls either way and the higher discount rate usually hurts more, because WACC discounts every cash flow while growth only touches the terminal value. Prove it with a quick DCF, and note that growth drops out with an exit multiple.

Updated

How a 90-point answer starts

Value falls either way, and the higher discount rate usually does more damage. WACC touches every cash flow in the model.

See the full answer, the 50 and 70 versions, and what moves each score up.

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The numbers, step by step

Five years of $100 of free cash flow, a 10% WACC, 2% perpetuity growth, with the terminal value at the end of year five.

Forecast years at 10%$100 a year for 5 years at 10%
about $379
Terminal value at year five$100 × 1.02 ÷ (10% − 2%)
$1,275
Enterprise value today$379 + $1,275 ÷ 1.1^5
about $1,171
Enterprise value at an 11% WACC$370 + $1,133 ÷ 1.11^5
about $1,042
Enterprise value at 1% growth$379 + $1,122 ÷ 1.1^5
about $1,076
Loss from the higher WACC$1,171 − $1,042
about $129
Loss from the lower growth$1,171 − $1,076
about $95

What the interviewer listens for

  • Do you say value falls and that WACC usually hurts more?
  • Do you explain that WACC hits every cash flow and growth only the terminal value?
  • Can you show it with numbers?
  • Do you know the role of the spread and the exit multiple case?

Common mistakes

  • Saying they are always equal because both widen the spread by a point.That holds only for a pure perpetuity with no forecast years.
  • Forgetting that WACC also discounts the forecast cash flows and the terminal value back to today.
  • Ignoring that growth doesn't appear at all when the terminal value uses an exit multiple.
  • Getting the direction wrong and saying a higher discount rate raises value.

Likely follow-ups

  • In a pure perpetuity with next year's cash flow at $100, which is bigger?They're the same. $100 over 11% minus 2% and $100 over 10% minus 1% both come to about $1,111.
  • Why does a narrow spread make the DCF so sensitive?The terminal value is cash flow divided by the spread. Halving the spread from 4% to 2% doubles the terminal value.

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