Question

Steven is looking to purchase an investment property, and is interested in a particular apartment on London Street. This apartment costs $500,000. Steven has also estimated that the other upfront costs for purchasing the apartment will total $5,000. Steven has also spoken to his real estate agent Ray and his banker Jane, and gathered the following additional information:

• Strata for the apartment is estimated at $700 per quarter in arrears.

• Council rates are estimated at $500 per year payable in arrears.

• Steven can expect to receive $1,600 per month in rent, paid in advance. The apartment is currently tenanted, so he expects to receive the first rent payment immediately after he purchases the apartment.

• The bank will only lend a maximum of 80% of the apartment’s price.

• The bank is willing to lend to Steven at an interest rate of 3.5% p.a. compounding daily. The banking industry standard is to always assume there are 365 days in a year.

  Currently, Steven is considering the value of this investment over the next 10 years.

1. Calculate the equivalent effective quarterly rate.

2. Calculate the equivalent effective annual rate.

NOTE - please show working out using time value of money formulas on paper not excel

Answer 1

First, let us calculate the effective annual rate

ie. (1+3.5%/365)^365-1=

3.56180%

p.a.

Effective quarterly rate =

3.56180%/4=

0.89045%

Effective monthly rate =

3.56180%/12=

0.29682%

Initial cost	-500000
Upfront costs	-5000
PV of beg-of-qtr. Strata costs(700*(1-1.0089045^-40)/0.0089045*1.00089045)	23490.38	Beginning of qtr. For 10 yrs.*4=40 qtrs.
PV of big-of- yr. council rates(500*(1-1.035618^-10)/0.035618*(1.035618)=	4293.03	10 yrs.
PV of mthly.rental income(1600*12*(1-1.0029682^-120)/0.0029682*1.0029682)	-161808.51	Beginning of mth.. For 10 yrs.*4=120 mths.
Interest lost on down pmt.(500000*20%*(1+3.5%/365)^(365*10))=	141904.37
NPV of this investment	-497120.73
Value of this investment at end of 10 yrs.
497121*(1+3.56180)^10=	705436.64