A.CRE

APY

APY (Annual Percentage Yield) is the true rate of return earned taking in compounding interest.
Also known as the Annual Effective Rate, the formula for APY is as follows:

APY = ( 1 + APR / n ) ^ n – 1
Periodic Rate = ( 1 + APY ) ^ ( 1 / n ) – 1
n = Frequency of compounding within a year

APY is used in the context of net returns expected by investors: i.e. equity return rate.

For any given APR, the corresponding APY will always be a little higher depending on how many times it is compounded within the year.

Putting ‘APY’ in Context

Scenario:

Texas Star Residential, a real estate private equity firm, is considering the acquisition of Greenview Apartments, a market-rate multifamily property in Austin, Texas. Greenview Apartments is a 200-unit complex that has demonstrated strong occupancy rates and stable cash flows. As part of their due diligence, the firm is evaluating the potential returns of the investment, particularly focusing on the Annual Percentage Yield (APY) to accurately gauge the true rate of return considering compounding interest.

Context and Calculation:

Texas Star Residential plans to finance the acquisition with a mix of equity and debt. They estimate an Annual Percentage Rate (APR) of 6% on their financing. Since they expect the compounding to occur monthly (n = 12), they need to calculate the APY to understand the actual annual return.

Using the APY formula:

  • APY = (1 + APR / n) ^ n – 1

Calculation:

  • APY = (1 + 0.06 / 12) ^ 12 - 1
  • APY = (1 + 0.005) ^ 12 - 1
  • APY = (1.005) ^ 12 - 1
  • APY ≈ 1.0617 - 1
  • APY ≈ 0.0617 or 6.17%

This calculation shows that with monthly compounding, the effective annual return (APY) on the financing is approximately 6.17%, slightly higher than the nominal APR of 6%.

Application:

Understanding the APY is crucial for Texas Star Residential as it provides a more accurate picture of the cost of their financing and the expected net returns from Greenview Apartments. If the property generates an annual net operating income (NOI) of $1,800,000 and they are financing 70% of the $30 million purchase price (i.e., $21 million in debt), they can better estimate their equity returns.

Given the APY of 6.17%, they can now calculate the annual interest cost:

  • Annual Interest Cost = Debt Amount × APY
  • Annual Interest Cost = 21,000,000 × 0.0617
  • Annual Interest Cost ≈ 1,295,700

Thus, their net income after debt service would be:

  • Net Income After Debt Service = NOI - Annual Interest Cost
  • Net Income After Debt Service = 1,800,000 - 1,295,700
  • Net Income After Debt Service = 504,300

This net income figure allows the firm to calculate their equity return and assess the investment’s viability.

By using APY instead of just APR, Texas Star Residential gains a more comprehensive understanding of their financing costs and potential returns, aiding them in making a well-informed investment decision.

Related Content:
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