You are thinking of buying a craft emporium. It is expected to generate cash flows of $30,000 per year in years 1 through 5, and $40,000 per year in years 6 through 10. If the appropriate discount rate is 8%, what amount are you willing to pay for the emporium
To determine the amount you are willing to pay for the craft emporium, you need to calculate the present value of the expected cash flows. The present value is the current value of future cash flows, taking into account the time value of money.
First, let's calculate the present value of the cash flows for years 1-5 using the formula for the present value of an ordinary annuity:
PV = CF * (1 - (1 + r)^-n) / r
Where:
PV = Present Value
CF = Cash Flow per year
r = Discount Rate (8% or 0.08)
n = Number of years
So, for years 1-5 with a cash flow of $30,000 per year:
PV1-5 = $30,000 * (1 - (1 + 0.08)^-5) / 0.08
= $30,000 * (1 - 1.46933) / 0.08
= $30,000 * (-0.46933) / 0.08
= -$173,800.625
Next, let's calculate the present value of the cash flows for years 6-10 with a cash flow of $40,000 per year:
PV6-10 = $40,000 * (1 - (1 + 0.08)^-5) / 0.08
= $40,000 * (1 - 1.46933) / 0.08
= $40,000 * (-0.46933) / 0.08
= -$231,750.78125
Now, sum up the present values of both periods to find the total present value (amount willing to pay):
Total PV = PV1-5 + PV6-10
= -$173,800.625 + -$231,750.78125
= -$405,551.40625
Therefore, you would be willing to pay approximately -$405,551.41 for the craft emporium, which represents the present value of the expected cash flows given a discount rate of 8%. Keep in mind that this value is negative because it reflects the cost of the investment.