# pnl calculation of FX forward

i am trying to clarify the correct method of computing pnl (in base ccy) on an FX forward. let's assume the following notation:

S(t) = spot rate at time t

df(base,t) = base ccy discount factor (USD in this case) at time t

df(foreign,t) = foreign ccy discount factor (JPY in this case) at time t

FXfwd(t) = FX forward at time t = S(t)*[df(base,t) / df(foreign,t)]

assuming, at time t=0, we buy 100 USDJPY, 1y forward, i would compute the pnl from t=0 to t=1 to be \\$100 * [(FXfwd(1) - FXfwd(0)) / FXfwd(1)]

however, an alternate approach seems to be to compute the present value of each of the future cashflows using each ccy's discount factor, sum in USD according to the spot for time t=0 and do the same at time t=1, and taking the difference.

it seems like the first approach i mention is more commonly referenced, but the 2 methods do not produce the same result and there is surprisingly little information found online for more practical matters like this