You have recently accepted a one-year employment term by a firm. The firm has given you the option of receiving your salary as a lump sum value of $30,000 at the end of the year or as 12 monthly payments of $2,400 starting one month after you start work. If your relevant discount rate is 2 percent per month, then which salary options would you prefer? (Ignore taxes, risk, and consumption needs.)
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A. B. C. D. E.B
Monthly option PV = $2,400(PVIFA(2%,12)) = $2,400(10.5753) = $25,380.72.
Annual option PV = $30,000(PVIF(2%,12)) = $30,000(0.7885) = $23,655.
To determine which salary option is preferable, we need to compare the present values of both options. The present value is the current value of future cash flows, discounted at a specified rate. In this case, the relevant discount rate is given as 2 percent per month.
Option 1: Lump Sum Payment of $30,000 at the End of the Year Since the lump sum payment is received at the end of the year, we need to discount it back to the present value. Using the formula for present value, we can calculate the present value of the lump sum payment:
PV = FV / (1 + r)^n
Where: PV = Present Value FV = Future Value r = Discount Rate n = Number of Periods
In this case, the future value (FV) is $30,000, the discount rate (r) is 2 percent per month, and the number of periods (n) is 12 months. Plugging these values into the formula:
PV = $30,000 / (1 + 0.02)^12 PV = $30,000 / (1.02)^12 PV = $30,000 / 1.2682427 PV ≈ $23,635.41
So, the present value of the lump sum payment is approximately $23,635.41.
Option 2: 12 Monthly Payments of $2,400 Starting One Month After You Start Work For the monthly payments, we need to calculate the present value of each individual payment and sum them up. The formula for calculating the present value of a series of cash flows is:
PV = C1 / (1 + r)^1 + C2 / (1 + r)^2 + ... + Cn / (1 + r)^n
Where: PV = Present Value C1, C2, ..., Cn = Cash flows in each period r = Discount Rate n = Number of Periods
In this case, the cash flow in each period (Ci) is $2,400, the discount rate (r) is 2 percent per month, and the number of periods (n) is 12 months. Plugging these values into the formula:
PV = $2,400 / (1 + 0.02)^1 + $2,400 / (1 + 0.02)^2 + ... + $2,400 / (1 + 0.02)^12 PV = $2,400 / 1.02 + $2,400 / (1.02)^2 + ... + $2,400 / (1.02)^12 PV ≈ $27,515.91
So, the present value of the monthly payments is approximately $27,515.91.
Comparing the Present Values Now that we have calculated the present values for both options, we can compare them to determine the preferable salary option.
The present value of the lump sum payment is approximately $23,635.41, and the present value of the monthly payments is approximately $27,515.91. Since the lump sum payment has a lower present value, we can conclude that the preferable salary option, in this case, would be the monthly payments of $2,400 starting one month after you start work.
Therefore, the correct answer is: B. Monthly payments, since it has the larger present value.