Respuesta :
Answer:
$98,650 (lump sum) eight years from now yields the highest present value.
Explanation:
This can be determined as follows:
1. Calculation of the present value of $7,250 per year at the end of each of the next eight years.
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = present value of $7,250 per year at the end of each of the next eight years = ?
P = Annual payment = $7,250
r = discount rate = 8% or 0.08
n = number of years = 8
Substitute the values into equation (1), we have:
PV =$7,250 * ((1 - (1 / (1 + 0.08))^8) / 0.08)
PV = $41,663.13
2. Calculation of the present value of $49,650 (lump sum) now
Since now is the present time, the present value of $49,650 (lump sum) now is still equal to $49,650.
3. Calculation of the present value of $98,650 (lump sum) eight years from now
This can be calculated using the present value formula as follows:
PV = FV / (1 + r)^n ................... (2)
Where:
PV = present value of $98,650 (lump sum) eight years from now = ?
FV = future value or (lump sum) eight years from now = $98,650
r = discount rate = 8% or 0.08
n = number of years = 8
Substitute the values into equation (2), we have:
PV = $98,650 / (1 + 0.08)^8
PV = $53,297.53
Comparison of the present values
1. Present value of $7,250 per year at the end of each of the next eight years = $41,663.13
2. Present value of $49,650 (lump sum) now = $49,650
3. Present value of $98,650 (lump sum) eight years from now = $53,297.53
As can be seen from the above, $98,650 (lump sum) eight years from now yields the highest present value.
