As a reminder, we covered in class re: the mechanics and implications of mortgag
ID: 2816256 • Letter: A
Question
As a reminder, we covered in class re: the mechanics and implications of mortgage lending. Specifically, a scenario where an individual buys a house for $100,000, hold it for three years and sells it. Over that three year period, the owner must pay the bank interest, and there may be a tax implication. To keep things simple, the mortgage payment is interest only. ie, if you borrow 100,000, and interest is 10%, you end up paying 30k in interest, but have to pay back the full 100,000 loan and 30k in interest at the end of the 3 year loan. While this is an example around an individual’s decision to purchase a house, we are using this as a way to understand a CFO’s decision to capital investments. Put another way, you are the CFO of a household making a capital decision on how to fund your home investment. I will refer to this as the CFO of the household making a housing investment decision.
The table directly below is the base case for illustration. To explain in particular, the row in yellow. CFO of house buys house for 100k. Using 20k in equity, plus an 80k loan. Over the three year period, CFO of house pays 24k in interest (10% times 80k=8k per year, times three years), but at a 50% tax bracket, the net outlay is 12k. In this scenario, house increases to 140k in value over three years. Therefore the CFO of the house’s return is 28k. 40 k on the increase in value of the house less the 12k interest payments. Since the CFO of the household put 20k down, the ROE is 140%.
Please answer the following questions by filling in the grids, and answering the questions. The information and answers within each grid should help with each question.
House Value – Year 1 (Purchase)
Money Put down by purchaser (Down Payment)
Bank Loan (Mortgage)
Net Interest Paid to Bank (10% loan – 50% tax bracket)
House Value at point of sale (after 3 years)
Net Return on house investment (increase in house value – payments to bank)
Return on Equity = Net Return / Money put down
$100,000
$100,000
0
0
$140,000
$40,000
40%=40,000/100,000
$100,000
$50,000
$50,000
$7,5000
$140,000
$32,500
65%=32,500/50,000
What happens if the expected house value is not that big? Rather than growing to 140k, we know the house will only increase in value to 110k. What is the ROE under different financing options? And how would you recommend the CFO finance this deal?
House Value – Year 1 (Purchase)
Money Put down by purchaser (Down Payment)
Bank Loan (Mortgage)
Interest Paid to Bank (10% loan – 50% tax bracket)
House Value at point of sale (after 3 years)
Net Return on house investment (increase in house value – payments to bank)
Return on Equity = Net Return / Money put down
$100,000
$100,000
0
0
$110,000
$100,000
$50,000
$50,000
$7,5000
$110,000
$100,000
$20,000
$80,000
$12,000
$110,000
House Value – Year 1 (Purchase)
Money Put down by purchaser (Down Payment)
Bank Loan (Mortgage)
Net Interest Paid to Bank (10% loan – 50% tax bracket)
House Value at point of sale (after 3 years)
Net Return on house investment (increase in house value – payments to bank)
Return on Equity = Net Return / Money put down
$100,000
$100,000
0
0
$140,000
$40,000
40%=40,000/100,000
$100,000
$50,000
$50,000
$7,5000
$140,000
$32,500
65%=32,500/50,000
Explanation / Answer
Case 1/Row 1 (Money Put down on the house = $100,000, Bank Loan = $0)
Net return on house investment = increase in the house value - Payments to the bank
Net return on house investment = (110,000 - 100,000) - 0
Net return on house investment = 10,000
Return on Equity = Net Return on House Investment/ Money put down on house
= 10,000/100,000
= 10%
Case 2/Row 2 (Money Put down on the house = $50,000, Bank Loan = $50,000)
Payments to the bank = 10%(which is the rate of interest)*$50,000(which is the Bank Loan)*3(which is the no of years for which the loan is taken)
= 10%*$50,000*3
= $15,000
But the investor lies in 50% tax bracket and he gets a 50% reduction on the bank payments. This reduction amounts to 50%*$15,000 = $7,500. So the net payments to the Bank is equal to $7,500.
Net return on house investment = increase in the house value - Payments to the bank
Net return on house investment = (110,000 - 100,000) - $7,500(as calculated above)
Net return on house investment = $2,500
Return on Equity = Net Return on House Investment/ Money put down on house
= 2,500/50,000
= 5%
Case 3/Row 3 (Money Put down on the house = $20,000, Bank Loan = $80,000)
Payments to the bank = 10%(which is the rate of interest)*$80,000(which is the Bank Loan)*3(which is the no of years for which the loan is taken)
= 10%*$80,000*3
= $24,000
But the investor lies in 50% tax bracket and he gets a 50% reduction on the bank payments. This reduction amounts to 50%*$24,000 = $12,000. So the net payments to the Bank is equal to $12,000.
Net return on house investment = increase in the house value - Payments to the bank
Net return on house investment = (110,000 - 100,000) - $12,000(as calculated above)
Net return on house investment = -$2,000
Return on Equity = Net Return on House Investment/ Money put down on house
= -2,000/50,000
= -4%
Recommendations :- The recommendations should be based on the Return on Equity calculations. In this case, Maximum Return on Equity is obtained from Case 1, Money Put down on the house = $100,000, Bank Loan = $0
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