Final answer:
The value at year 7 of a perpetual stream of $2,300 annual payments that begins at Year 15 with a 3.9 percent discount rate is calculated using the present value of a perpetuity formula and then discounting that value back to year 7.
Step-by-step explanation:
To calculate the value at year 7 of a perpetual stream of $2,300 annual payments that begins at Year 15, given a discount rate of 3.9 percent per year, we first need to identify the present value of the perpetuity at the time it starts (Year 15). A perpetuity is a type of annuity that goes on indefinitely. In this case, we use the formula for the present value of a perpetuity:
PV = P / r
Where PV is the present value, P is the payment per period, and r is the interest rate. For a $2,300 payment at a 3.9% discount rate:
PV = $2,300 / 0.039 = $58,974.36
This is the present value at Year 15. To find the value at year 7, we must then discount this amount back 8 more years (from Year 15 to Year 7) using the formula:
PV7 = PV / (1 + r)n
Where PV7 is the present value at Year 7, n is the number of periods (years) we are discounting back.
PV7 = $58,974.36 / (1 + 0.039)8
Therefore, the value of the perpetuity at Year 7 is found by calculating the present value $58,974.36, discounted back 8 years at 3.9%.