We are currently bidding on Treasury bills and have determined that we must have a 5% return for a $1,000 T-Bill that will mature in one year. How much would we be willing to bid on the Treasury bill? If we are bidding on a 13 weeks Treasury bill with a 1% return and a 26 weeks Treasury bill with a 2% return for a $1,000 T-bill, how much would we be willing to bid on the Treasury bills?
To determine how much you would be willing to bid on the Treasury bills, you need to calculate the present value of the expected return.
For the first scenario with a 5% return for a $1,000 T-Bill that will mature in one year:
1. Calculate the present value using the formula: Present Value = Future Value / (1 + Interest Rate)^Number of Periods.
In this case, the future value is $1,000, the interest rate is 5% (0.05), and the number of periods is 1.
Plug in these values into the formula to get: Present Value = $1,000 / (1 + 0.05)^1 = $952.38 (rounded to the nearest cent).
So, you would be willing to bid up to $952.38 on the Treasury bill in the first scenario.
For the second scenario with a 13-week Treasury bill with a 1% return and a 26-week Treasury bill with a 2% return:
1. Calculate the present value for the 13-week Treasury bill using the same formula.
The future value is $1,000, the interest rate is 1% (0.01), and the number of periods is 13/52 (as there are 52 weeks in a year and the bill matures in 13 weeks).
Plug in these values to get: Present Value = $1,000 / (1 + 0.01)^(13/52) = $990.25 (rounded to the nearest cent).
2. Calculate the present value for the 26-week Treasury bill using the same formula.
The future value is $1,000, the interest rate is 2% (0.02), and the number of periods is 26/52 (as there are 52 weeks in a year and the bill matures in 26 weeks).
Plug in these values to get: Present Value = $1,000 / (1 + 0.02)^(26/52) = $980.39 (rounded to the nearest cent).
So, you would be willing to bid up to $990.25 on the 13-week Treasury bill and up to $980.39 on the 26-week Treasury bill in the second scenario.