Match a protective put with call plus terminal cash

State the two compatible packages

Package A contains one underlying unit and one strike-100 put. Package B contains one strike-100 call and a certain cash amount 100 due at the same expiry. The table concerns terminal amounts, not present purchase costs.

Calculate each package

Below 100, A adds S and 100−S while B has zero call payoff plus 100. Above 100, A is S while B adds S−100 and 100. They match at every nonnegative terminal price.

Inspect the original scenarios

Discount the cash only when changing dates

To compare present costs under the selected European/no-income assumptions, the terminal cash amount becomes 100D today. Using undiscounted 100 as its present cost mixes dates unless D=1. The payoff identity itself needs no such discount calculation.