You are an incredibly individual and have just won best price in a beauty context.you have the following options a)$1000 received now
b)$180000 at the end of five years
C)$11400per year for ever
Prove to select the optimal price assuming discount rate is 12%
To determine the optimal prize, we need to calculate the present value of each of the given options using the discount rate of 12%. The present value allows us to compare the values of different amounts of money received at different points in time.
Let's calculate the present value of each option:
a) $1000 received now:
The present value of a lump sum payment received now is simply the same amount since there is no discounting.
Therefore, the present value of option a is $1000.
b) $180000 at the end of five years:
To calculate the present value of this option, we need to use the formula for the present value of a future lump sum:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Discount rate
n = Number of periods in the future
In this case, FV is $180,000, r is 12%, and n is 5 years. Plugging these values into the formula:
PV = $180,000 / (1 + 0.12)^5
PV = $180,000 / 1.7623
PV ≈ $102,194.43
Therefore, the present value of option b is approximately $102,194.43.
c) $11,400 per year forever:
To calculate the present value of an infinite series of cash flows, we use the formula for the present value of a perpetuity:
PV = CF / r
Where:
PV = Present Value
CF = Cash Flow per period
r = Discount rate
In this case, CF is $11,400, and r is 12%. Plugging these values into the formula:
PV = $11,400 / 0.12
PV = $95,000
Therefore, the present value of option c is $95,000.
To select the optimal prize, we choose the option with the highest present value. Comparing the present values we calculated:
Option a: $1000
Option b: $102,194.43
Option c: $95,000
In this case, option b, $180,000 at the end of five years, has the highest present value of $102,194.43. Therefore, selecting option b would be the optimal choice given the discount rate of 12%.