Question

2. Suppose you bought a house for $200,000 financing it with a $40,000 down payment of your own funds and a $200,000 mortgage loan from a bank. (12 points)

a. Assume that the market value of your house has now risen to $230,000. Ignoring interest and other costs, and assuming the loan amount is still $160,000, calculate your rate of return on your asset (ROA) and your rate of return on equity (ROE).

b. Now assume that, instead of (a), you only put down $20,000 and borrowed $180,000 to buy the house. Assuming that the market value of your house has risen to $230,000 and ignoring interest and other costs, calculate your rate of return on your asset (ROA) and your rate of return on equity (ROE).

c. Now, instead of (a) or (b), suppose the value of the house fell from $200,000 to $170,000. Assuming you paid $200,000, financing it with $40,000 of your own money and $160,000 with a mortgage loan, and ignoring interest and other costs, calculate your rate of return on your asset (ROA) and your rate of return on equity (ROE).

d. Now assume that, instead of (c), you only put down $20,000 and borrowed $180,000 to buy the house. Assuming that the market value of your house has fallen to $170,000 and ignoring interest and other costs, calculate your rate of return on your asset (ROA) and your rate of return on equity (ROE).

All your answers should be expressed in percent.

Answer #1

The investment value or the cost of the house is $200000

Rate of Return = ((Final Value of the Asset / Initial Value of the)
- 1) * 100

Return on Equity = ( Net Gain / Total Equity ) * 100

a) The final value is $230000 and equity part is $40000.

RoR = (230000 / 200000) - 1 = 0.15 or 15%

RoE = 30000 / 40000 = 0.75or 75%

b) The final value is $230000 and equity part is $20000.

RoR = (230000 / 200000) - 1 = 0.15 or 15%

RoE = 30000 / 20000 = 1.5or 150%

c) The final value is $170000 and equity part is $40000.

RoR = (170000 / 200000) - 1 = -0.15 or -15%

RoE = -30000 / 40000 = -0.75 or -75%

d) The final value is $170000 and equity part is $20000.

RoR = (170000 / 200000) - 1 = -0.15 or -15%

RoE = -30000 / 20000 = -1.5or -150%

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