Question

Xian and Devi are each buying a house for $500,000. Xian puts $200,000 down and gets a mortgage for the other $300,000 at a 6% annual effective rate. Devi puts $100,00 down and gets a mortgage for the other $400,000 at the same annual rate. Both mortgages are interest only (i.e they pay 5% interest at the end of each year but do not repay any of the principal.)

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a) How much leverage does Xian have? How much leverage does Devi have?

b) After 1 year, if the house increases in value by 5%, what is Xian’s return on his investment (ROI) in the house? What is Devi’s?

c) What are their respective ROI’s if you include the interest they have to pay on their mortgages?

d) Devi invested only $100,000 in the house. She invests the other $100,000 (so her total investment is $200,000 matching Xian’s) in a savings account paying an effective annual rate of x%. What does x have to be so that her ROI on her total investment matches Xian’s?

Answer 1

Given:

	Xian	Devi
House Price	500,000	500,000
Own Money	200,000	100,000
Borrowed Money	300,000	400,000
Annual Interest @6% on the borrowed amount	18,000	24,000
Price of House after One year	525,000	525,000

(All amounts in Dollars)

a) leverage = Asset price/own money

Xian = $500,000/$200,000

= 2.5 times

Devi =  $500,000/$100,000

= 5 times

b) After one year, the house price increases by 5%.

Therefore, it becomes $500,000 *1.05 = $525,000

So, the return for both Xian and Devi is ($525,000-$500,000) = $25,000

So, Return on Investment for Xian = Return in Dollar terms/Own money invested

= 25,000/200,000

= 12.5%

This is the same as leverage multiplied by the increase in house price =2.5 times 5% = 12.5%

Return on Investment for Devi = Return in Dollar terms/Own money invested

= 25,000/100,000

= 25%

Again, we can get the same result by multiplying leverage with increase in house price = 5 times 5% =25%

c) If we include the interest @6%,  then

Return for Xian= Increase in house price - Interest paid

= $25,000 - $18,000

=$7,000

Return for Devi= Increase in house price - Interest paid

= $25,000 - $24,000

=$1,000

Xian = $7,000 / $200,000

= 3.5%

Devi = $1,000 / $100,000

= 1%

d) If Devi invests another $100,000 in a savings account earning x% , then for her total investments to earn same as that of Xian , her total return should also be $7,000 on a total investment of $200,000

So, Return from house + return from Savings account = $7,000

= $1000 + $100,000 * x% = $7000

=> x% of $1,00,000 = $6000

=> x = 6000/100,000 = 6%

So, x =6%

So, for the total return of Devi to be the same as that of Xian, the savings account must earn 6% p.a