Discounted Cash Flow, explained.
Discounted cash flow, or DCF, values specified future payments in today's units. Its result depends on the amounts, timing, discount rate, and any included residual value.
Why it happens
A later payment receives more discounting than an earlier payment. Higher assumed cash-flow growth raises this project's value; a higher discount rate lowers it. Exact calculation does not make uncertain assumptions exact.
Discounted cash flow converts specified future cash payments into a present value using a discount rate. A valuation is conditional on the cash-flow and discount assumptions.
Read the result
Read each year's cash payment and present value before submitting a bid. Stress the assumptions after bidding to see how the same price can cross from below to above the calculated value. This project stops after five payments, with no terminal value.
A worked example
A finite project paying twenty each year
Set growth to zero, keeping all five annual cash payments at twenty teaching tokens.
At an 8% discount rate, their total present value is about 79.85, rather than the undiscounted total of 100.
A bid of 80 is close to that calculation. A changed discount rate or payment assumption changes the comparison without changing the submitted price.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The first year pays 20 tokens; subsequent payments grow at the selected rate for five years. Present value sums cash_t/(1+discount)^t. There is no terminal value. A bid from 20 to 160 is compared with that five-payment value; the stress button lowers growth and raises the discount rate.
Where this idea is useful
A practical use
A bid below an optimistic calculation can become above value when the underlying assumptions change.
A common misconception
“More decimal places make a valuation more certain.”
Precision in arithmetic does not remove uncertainty in future cash flows or the chosen discount rate. Sensitivity analysis can be more informative than extra decimal places.
What this explanation leaves out
- Payments are hypothetical and not guaranteed. This finite project has no residual sale value, taxes, or financing structure. The displayed number is not a stock target or a claim that Williams invented discounting.
Why does this project have no terminal value?
It is a deliberately finite payment stream. Continuing businesses often need a separate residual-value assumption, which can dominate a valuation and deserves explicit scrutiny.
Which assumption drives most of a value estimate you use, and what would make you revise it?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.