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GMBA8022 Know Your Numbers 2

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Task:

Assignment 1 - How required returns affect prices: a commercial property funded by a loan.
 

Question 1 :

Find a competitive interest rate on a P&I loan in your country. Interest rates that include all fees are best. In Australia this is called the comparison rate. In other countries, feel free to choose from loans with no or low fees and ignore loans with high fees. State the current interest rate per annum and the term (maturity) of the loan in years. Include a screenshot of these details and provide a link to the source.  

Question 2 :

Find the inflation rate in your country using the central bank or bureau of statistics. Include a screenshot of the inflation rate and provide a link to the source. 

Question 3 :

Find a commercial property for sale such as an office or warehouse. Include a screenshot of the price and provide a link to the source. 

Question 4 :

Make a spreadsheet showing the value of the loan liability and the property asset every month. Show the total loan payment and its principal and interest components every month. Also show the property asset’s net rental payments every month. These 6 items are best entered as columns in a spreadsheet with the months as rows. Continue the months rows until the end of the loan term. Use the following assumptions:

  • The loan can be valued using the annuity formula. 
  • The loan interest rate is variable but the interest rate is expected to remain constant throughout the life of the loan.
  • The property can be valued as a growing perpetuity of monthly rents. 
  • The property’s current price is that found in the previous question. 
  • The property’s expected capital return is equal to the inflation rate found in the previous question. For example, if the inflation rate was 3.6% pa then the monthly inflation rate would be 0.3% per month. This rate would be the property’s capital return (price increase) per month and also the increase in net rent per month. Therefore, if the property price this month was $500,000 and the rent was $1000/month, then the next month the price will be $501,500 (=500,000*(1+0.003)^1) and the rent will be $1,003/month (=1,000*(1+0.003)^1).
  • The property’s net rental yield (gross rent less costs of renting this month divided by property price last period) is equal to the loan interest rate per month less the inflation rate per month plus a 0.1 percentage point risk premium per month. For example, say the loan interest rate was 4.8% pa and the inflation rate was 3.6% pa, then the monthly net rental yield would be 0.2% (=4.8%/12 - 3.6%/12 + 0.1%) per month. So if the property price found in the previous question was initially $500,000 then the net rent in the first month would be $1,000 (=500,000*0.002).
  • The total required return of the property per month (the ‘r’ in the perpetuity with growth formula) is the sum of the capital return and the net rental yield per month. The growth rate of rents (the ‘g’ in the perpetuity with growth formula) will be inflation rate per month. 
  • The loan’s initial loan to valuation ratio (LVR) is initially 80% but it changes afterwards as the loan is paid down and the property price rises by the capital return. 
  • Ignore taxes.

State any other assumptions that you use in your model as necessary. 

GMBA8022 Know Your Numbers 2

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