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With respect to the investment because it says year 1 is immediately we discount it at 1.000 being year zero DF instead of 0.901 which is year 1 DF.
If the question did not say “immediately”then we would have discounted at 0.901?
Time 0 is the start of the first year.
Time 1 is the end of the first year/start of the second year
Time 2 is the end of the second year/start of the third year
We always assume that flows occur at the ends of years unless told differently.
So what you have written is correct 🙂