St. Luke’s Convalescent Center has $200,000 in surplus funds that it wishes to invest in marketable securities. If transaction costs to buy and sell the securities are $2,200 and the securities will be held for three months, what required annual yield must be earned before the investment makes economic sense
206,600
202,200
To determine the required annual yield, you need to calculate the minimum rate of return that will compensate for the transaction costs over the three-month investment horizon.
Here are the steps to find the required annual yield:
1. Subtract the transaction costs from the surplus funds:
$200,000 - $2,200 = $197,800
2. Find the amount that needs to be earned over three months to recover the transaction costs:
$2,200 / 3 months = $733.33 (approx.)
3. Add the transaction recovery amount to the remaining funds:
$197,800 + $733.33 = $198,533.33 (approx.)
4. Calculate the required annual yield using the formula:
Required Annual Yield = (Final Amount - Initial Amount) / Initial Amount
Required Annual Yield = ($198,533.33 - $200,000) / $200,000
Required Annual Yield = -$1,466.67 / $200,000
Required Annual Yield = -0.00733 (approx.) or -0.733% (approx.)
Based on the calculations, the required annual yield to make economic sense is approximately -0.733% or a negative yield. Negative yields are not realistic in a typical investment situation. Therefore, it may not be economically viable to invest the surplus funds in marketable securities due to the high transaction costs involved.