Question

A young family considers buying a property for an asking price of $210,000. The going rent for comparable properties in the same neighbourhood is currently $500 per month. The ownership option involves a deposit of 20% of property value. The remaining balance will be financed with an interest-only mortgage loan (with monthly repayments) with an interest rate of 2% for 10 years. The cost of homeownership also includes annual maintenance ($500 p.a.) and insurance ($140 p.a.).

1. Determine the monthly mortgage repayments of the family. The family believes that rents for this property type will remain unchanged in the next ten years. Calculate the net cash flows of the homeownership option for years 1 through 9. (25marks)

2. For the next ten years, the house price appreciation is expected to be 2% per annum. Assume that the family requires an annual return of 7% on its investment. Analyse whether it would be preferable for the family to buy the property, use it as a main residence, and resell it after ten years (rather than renting a similar property). For your calculations assume that the real estate agents’ commission is 4% of the transaction (resale) price in this local residential market.

Answer 1

1. Monthly Mortgage Payment Calculation

Total Price = $210000, out of that 20% is deposit

so the mortgage is for 80%, i.e. $168000

p= $168000

r= rate of interest = 2% for year, means for month , 2%/12 = 0.167 %

n= Number of installments = 12 months for 10 years = 12*10= 120

Monthly Mortgage Payment = p*r*((1+r)ⁿ/ ((1+r)ⁿ -1))

= 168000*0.167%*((1+0.167%)¹²⁰/ ((1+0.167%)¹²⁰-1)

=280.56*(1.22/0.22)

Monthly Mortgage Payment  =$1555.83

For year = $18670

2. Net cash flows of the home ownership option for years 1 through 9

year 1   2 3 4 5 6 7 8 9

Deposit   $42000   0 0     0 0 0 0 0 0

Mortgage Repayment $18670 $18670 $18670 $18670 $18670 $18670 $18670 $18670 $18670

Maintenance $500   $500    $500   $500    $500    $500   $500    $500   $500

Insurance $140 $140 $140     $140 $140 $140    $140 $140     $140

Total $61310    $19310 $19310  $19310  $19310   $19310   $19310 $19310  $19310

3. Buy or Rent

Rent

$500 per month, The family believes that rents for this property type will remain unchanged in the next ten years

Rent for 10 years = 500*12*10 = $60000

Buy

Value = $210000

2% pa appreciation

at the end of the 10 year its value will be = $255990 = selling price

commission = 4% of selling price = $10240

inflow at the end of year 10 = $245750

outflow for 10 years = $61310+$19310+$19310 +$19310+$19310 +$19310+ $19310+$19310+$19310+$19310

= $235100

Net Earning = $10650

So, It is preferable for the family to buy the property.