To determine the present value of receiving $1,128.00 per year forever starting 10 years from today, we need to use the formula for the present value of a perpetuity:
\[ PV = \frac{C}{r} \]
where:
- \( PV \) is the present value of the perpetuity,
- \( C \) is the cash flow per period (which is $1,128.00),
- \( r \) is the discount rate (which is 6.00% or 0.06).
First, we calculate the present value of the perpetuity at the time it begins (which is 10 years from now):
\[ PV_{10} = \frac{1,128}{0.06} = 18,800 \]
This means that the present value of receiving $1,128 forever, starting in year 10, is $18,800 at the end of year 10.
Next, we must discount this amount back to today (year 0). Since this amount is received 10 years from now, we discount it using the formula:
\[ PV = \frac{FV}{(1 + r)^n} \]
where:
- \( FV \) is the future value (which is $18,800),
- \( r \) is the discount rate (0.06),
- \( n \) is the number of years until cash flow is received (10).
\[ PV = \frac{18,800}{(1 + 0.06)^{10}} = \frac{18,800}{(1.7913)} \approx 10,482.42 \]
Therefore, the present value today of receiving $1,128 per year forever, starting 10 years from now, is approximately $10,482.42.
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