Exposure of two companies in a transaction involving an FX option

Question

An American company $A$ has sold a manufactured product to a German company $B$, and they agree for the payment of 100,000 EUR in 1 year.

1. What type of exposure does $B$ have?
2. What type of exposure does $A$ have?
3. What is the potential problem for $A$ if it decides not to hedge (i.e. not to cover)?
4. Repeat the exercise in case the payment is performed in USD.

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Let $K_T$ be the exchange rate (EUR/USD) at time $t=T$ (1 year from now), and let $K_0$ be the exchange rate at time $t=0$ (i.e. now).

1. Since EUR is the domestic currency of $B$, it will take no risk in the transaction.
2. If $A$ buys a Forward contract (at time $T$ the firm $A$ will sell 100.000 EUR at a fixed rate $K_F$) but $K_f < K_T$, then it will face an indirect loss of 100,000*($K_T - K_F$) USD. If $A$ buys a Put option which gives it the right to sell 100.000 EUR at the rate $K_P$, it will exercise the option only if $K_P > K_T$, otherwise it will not exercise and will sell 100.000 EUR at the rate $K_T$.
3. If $A$ decides not to hedge, the potential problem is in the case $K_T < K_0$, because in this case $A$ will face an indirect loss of 100,000*($K_0 - K_T$) USD.
4. Since USD is the domestic currency of $A$, it will take no risk in the transaction. On the other hand, $B$ should buy a Call option, because it gives $B$ the right to buy 100,000 USD at time $T$ at a fixed rate $K_C$: $B$ will exercise the option if $K_C > K_T$, otherwise it will not exercise and will buy 100,000 USD at the rate $K_T$.

Is the reasoning correct?