Discounting a Fixed Cash Payment Separately from Stock Value

Summary

The exchange explains how to value a future payoff equal to the stock price at time t minus a fixed cash amount. It separates the two components: the stock exposure is valued at its current market price, while the fixed payment due at time t is discounted to present value. Under the stated setup, this gives the current stock price less the discounted value of 100, rather than discounting the entire difference as though both components were fixed cash payable in the future.

The intuition is that the stock component already has a market value today, whereas the fixed amount has a known future payment date and is converted to present value using the interest rate. The exchange gives a brief conceptual answer, not a full derivation or discussion of financing, dividends, risk-neutral valuation, or alternative contract terms. Those details can matter in other settings, so the result should be read in the simple payoff context posed.

Key ideas

• A payoff consisting of stock value less a fixed future payment has two distinct components.
• The stock component is represented by its current market price.
• The fixed cash payment is discounted from its payment date to today.
• The explanation assumes the simple contract described and does not cover additional financing or dividend features.

Tags

# Can someone explain to me the intuition behind the discount factor for this simple payoff?


# Can someone explain to me the intuition behind the discount factor for this simple payoff?












Let's say you enter into a contract today in which in time t, you receive the difference between the underlying stock price and 100. Denote the stock price as S. Why is today's value of such a contract equal to:

> S - 100 * exp(-rt)

As opposed to:

> (S - 100) * exp(-rt)

I see the former in texts a lot.

Thanks!

## Answer by Magic is in the chain (score 1, accepted)

https://quant.stackexchange.com/a/46796

Keeping it simple, your payoff at time t is:

$S_t-100$

The present value of the stock is $S_0$, it’s current price; and the present value of 100 is its discounted value as you correctly explained in your question.

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