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?

To determine the required annual yield, we need to consider the transaction costs and the investment time frame.

Given:
- Surplus funds: $200,000
- Transaction costs: $2,200
- Investment time frame: 3 months

Step 1: Calculate the total transaction costs for buying and selling the securities.
Since there are transaction costs both for buying and selling, we multiply the transaction costs by 2:
Total transaction costs = $2,200 x 2 = $4,400

Step 2: Calculate the net investment amount.
The net investment amount is the surplus funds minus the transaction costs:
Net investment amount = $200,000 - $4,400 = $195,600

Step 3: Calculate the required annual yield.
The formula to calculate the required annual yield is:
Required annual yield = (Transaction costs / Net investment amount) * (12 / Investment time frame)

Required annual yield = ($4,400 / $195,600) * (12 / 3)

Step 4: Calculate the value of the required annual yield.
Required annual yield = (0.0225) * (4)

Required annual yield = 0.09 or 9%

Therefore, St. Luke’s Convalescent Center must earn a required annual yield of 9% before the investment makes economic sense.

To determine the required annual yield, we need to consider the transaction costs and the time period during which the securities will be held.

Step 1: Calculate the total transaction costs
The total transaction costs are given as $2,200.

Step 2: Determine the net investment amount
To find the net investment amount, we subtract the transaction costs from the surplus funds:
Net Investment Amount = Surplus Funds - Transaction Costs
Net Investment Amount = $200,000 - $2,200
Net Investment Amount = $197,800

Step 3: Determine the holding period
The holding period is three months. To calculate the annual yield, we need to convert this into a yearly value. Since there are 12 months in a year, we divide the holding period by 12:
Holding Period (in years) = 3 months / 12 months per year
Holding Period (in years) = 0.25 years

Step 4: Calculate the required annual yield
The required annual yield is the rate at which the investment must grow in order to cover the transaction costs and make economic sense.
Required Annual Yield = (Transaction Costs / Net Investment Amount) / Holding Period
Required Annual Yield = ($2,200 / $197,800) / 0.25
Required Annual Yield = 0.0111 / 0.25
Required Annual Yield = 0.0444 or 4.44%

Therefore, in order for the investment to make economic sense, St. Luke’s Convalescent Center must earn a required annual yield of 4.44%.