PLEASE SHOW WORK An investment property has a quoted overall capitalization rate

Question

PLEASE SHOW WORK

An investment property has a quoted overall capitalization rate of 8%. You can obtain a 25-year, fully amortizing loan at a stated interest rate of 4.5% to purchase this property, and the maximum loan-to-value that the lender will allow is 80% (and you will want to use as much debt as possible to buy this property). The property’s asking price is $5,000,000 and you deem this a reasonable price to pay. There are many ways to answer these next two questions, and all give you the same answers.

What is the loan constant (the lender’s rate of return)? PLEASE SHOW WORK

What is the equity dividend rate (your investment rate of return, or dividend yield)?PLEASE SHOW WORK

Explanation / Answer

Loan constant = Interest rate per month/ (1- (1/(1+interest rate per month)number of months))

= 4.5%/12 / (1- (1/(1+4.5%/12)300))

=0.00375/(1- (1/1.00375300) = 5.55832 * 10-3 per month = 0.0666998 = 0.0667 = 6.67%

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Capitalization rate = Net Opearating income /Asset value = Net operating income/ $5000000 = 8%

Net Opearating income = 8% of $5000000 = $400000

Mortgage payment per month = [Principal * interest rate per month *( 1+ interest rate per month)number of payments]/ [( 1+ interest rate per month)number of payments- 1]

= $4000000 * 0.045/12 * (1+0.045/12)300/ (1+.045/12)300-1

= 46106.13792/2.0737425 = $22233.3

Pretax cashflow = Net Opearating income - Mortgage payments = $400000 - $22233.3 = $377766.7  

Equity Dividend rate = Pretax cashflow/Initial Investment

= $377766.7 /$5000000 = 0.07555 = 7.555%

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