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 time period for which the securities will be held.
Step 1: Calculate the annualized transaction costs:
Annualized Transaction Costs = (Transaction costs / Holding period) x (12 months / 3 months)
= ($2,200 / 3) x (12/3)
= $2,200 x 4
= $8,800
Step 2: Subtract the transaction costs from the surplus funds:
Investment Amount = Surplus funds - Transaction costs
= $200,000 - $8,800
= $191,200
Step 3: Calculate the required yield:
Required Yield = (Transaction costs / Investment Amount) x 100%
= ($8,800 / $191,200) x 100%
≈ 4.60%
Therefore, the required annual yield that must be earned before the investment makes economic sense is approximately 4.60%.
To determine the required annual yield, we need to consider the transaction costs incurred and the time period for which the securities will be held. Here are the steps to calculate the required annual yield:
1. Subtract the transaction costs from the surplus funds:
Surplus funds - Transaction costs = Investable amount
$200,000 - $2,200 = $197,800
2. Determine the time period for which the securities will be held. In this case, it is three months.
3. Convert the time period to years:
3 months ÷ 12 months/year = 0.25 years
4. Calculate the required annual yield using the formula:
Required annual yield = (Transaction costs ÷ Investable amount) ÷ Time period
Required annual yield = ($2,200 ÷ $197,800) ÷ 0.25
Calculating the required annual yield:
Required annual yield = 0.0111 ÷ 0.25
Required annual yield = 0.0444 or 4.44%
Therefore, the required annual yield that must be earned before the investment makes economic sense is 4.44%.