L7 Default

L7 Default - Default in Real Estate Transactions HKU Real...

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Unformatted text preview: Default in Real Estate Transactions HKU Real Estate Finance K. S. Maurice Tse University of Hong Kong ktse@econ.hku.hk Content Introduction Real Estate Price Risk and Default in Real Estate Transactions Financial Implications of Default in Real Estate Transactions Introduction Example. A buyer would like to buy the following property from the seller. The agreed price is $5 million. The buyer will make a down payment equal to 10% of the agreed price. Time for closing the transaction is 3 months. What could happen between the buyer and the seller before the transaction is completed??? Example Contd. The transaction can be depicted by the following event line. Buyer applies for bank financing (Mortgage) Bank appraises the market value of the house 0 Buyer and seller sign a preliminary sale & purchase agreement Contracted price (Pc) = $5m Down = 10% of Pc Time t 3 mos Mortgage Policy: 70%*MIN{Contracted Price, Appraised Value} Default by Buyer If appraised market value = $6m Mortgage amount = 0.7 * ($5m) = $3.5 m If appraised market value = $4m Mortgage amount = 0.7 * ($4m) = $2.8 m If the appraised market value is substantially lower than the contracted price, the amount of bank financing may not be enough for the buyer to close the transaction. This is very likely when the property market is going deep south. In this case, the buyer may have to default. Another reason for the buyer to walk away is that he/she wants to stop loss. In this case, the buyer will give up the amount of down payment to the seller. Of course, the seller may sue the buyer for the price loss. Default by Seller Seller may also choose not to complete the transaction with the buyer, especially during periods of upswings in the property market. Seller may receive an offer from other buyers that is significantly higher than that of the original buyer, say $8m. Seller may be tempted to walk away from the first buyer and turn around to sell the property to another buyer with higher offer. In Hong Kong, the seller returns the down payment to the buyer, and The seller pays the buyer an additional amount equal to the down payment (compensation/penalty). Market Practices in Hong Kong When the buyer is interested in the property, he will enter into a preliminary sale and purchase agreement (PSPA) with the seller and make a deposit to the seller equal to 3 percent of the contracted price. Formal Sale and Purchase Agreement (SPA) to be signed at the end of 14 days At this time the buyer will pay another 7 percent of the contracted price to the seller. From SPA to the closing date, it may take between 2 to 6 months, or even longer. If buyer defaults during the two week period between PSPA and SPA, he will have to give up the 3 percent down payment to the seller. The seller usually will not sue the buyer. If buyer defaults after the formal agreement is signed by not paying the seller the remaining balance of the contracted price, the seller can sue the buyer for the price loss. The price loss = Difference between the contracted price and the lower price at which the seller sells the property. Relationship between Real Estate Price Risk and Default Consider a buyer who wants to buy a house from the seller with bank financing. Contracted price (pc) = $46.5m Down payment (δ) = 10% Bank appraises property value (pt) Mortgage policy = α min[pc, pt] = 70% min[pc, pt] Sign S&P Agreement Contracted Price pc = $46.5m Down = 10%pc Buyer applies for bank mortgage time 0 time t Closing Date T What is the financial position (cash outlay, equity, profit/loss) of the buyer? The amount of cash the buyer needs to have in order to complete the transaction?? Financial Position of Buyer Balance Sheet of Buyer = Pt Debt = 0.7 MIN{46.5m, Pt } Equity = Pt – Debt CASH OUTLAY = $46.5 – 0.7 MIN{46.5m, Pt } Equity = Pt – 0.7 MIN{46.5m, Pt } Profit/Loss = Pt – 46.5m (No Default by Buyer or Seller) Suppose the bank’s appraisal value = $46.5m Additional fund (F) that the buyer must have to close the transaction successfully is F = pc – δ pc – α min{pc, pt} = 46.5m – 0.1(46.5) – 0.7(46.5) = $9.3m Condition for Default to Occur Let F be the actual amount of money the buyer has. The condition for default is F < p c − δ * p c − α min p c , ~t p ( ) RHS = Contracted price minus down payment and mortgage. It represents the additional fund needed by the buyer to close the transaction. Assume the random price (Pt) follows a normal distribution with mean price = µ and price risk (standard deviation) = σ. Pt ~ N(µ, σ) Question: What can we say about the probability of default by the buyer? What are the factors underlying default? ~ F < p − δ * p − α min p , pt c c c ( ) Factors underlying Default Assume everything else remaining unchanged. The likelihood of default decreases (the likelihood the transaction will go through) with ↓ ↑ ↑ ↑ ↑ contracted price (p c) down payment (δ) buyer’s additional fund (F) mortgage lending policy (α) mean property price (µ) Example: Default in Real Estate Transaction Consider the following transaction information. Contracted Price = $46.5 m Down payment = 10% of contracted price Mortgageable amount = 70% of min(contracted price, appraised price) At the time the buyer enters the preliminary sale and purchase agreement with the property seller, the contracted price is $46.5m. Before the close of the transaction, property price will fluctuate, and hence the buyer may default by giving up the down payment to the seller. What are the financial payoffs to the buyer over different property prices?? Example Contd. Property P Investment Equity Profit/Loss Default 40.00 40.50 41.00 41.50 42.00 42.50 43.00 43.50 44.00 44.50 45.00 45.50 46.00 46.50 47.00 47.50 48.00 48.50 18.50 18.15 17.80 17.45 17.10 16.75 16.40 16.05 15.70 15.35 15.00 14.65 14.30 13.95 13.95 13.95 13.95 13.95 12.00 12.15 12.30 12.45 12.60 12.75 12.90 13.05 13.20 13.35 13.50 13.65 13.80 13.95 14.45 14.95 15.45 15.95 -6.50 -6.00 -5.50 -5.00 -4.50 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 -4.65 -4.65 -4.65 -4.65 -4.50 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 The table presents the financial payoff to the buyer over a wide range of property price. Investment = 46.5 – 0.7Min(46.5, pt) Equity = Price (pt) –0.7Min(46.5, pt) Profit/Loss = Pt – 46.5m (No Default by Buyer or Seller) Example Contd The following diagram depicts the payoff to the buyer at each possible property price. 3 2 1 0 Profit/Loss Default 40 40.5 41 41.5 42 42.5 43 43.5 44 44.5 45 45.5 46 46.5 47 47.5 48 -1 -2 -3 -4 -5 -6 -7 Question for Class Discussion: What does the payoff with default to the buyer resemble? What is the financial meaning of the down payment? What should be the fair amount of down payment??? 48.5 III. Financial Implications of Default in Real Estate Transactions Default by Buyer: The condition for default is that the property price during the transaction period falls below the contracted price net of the down payment; i.e., Profit/Loss Payoff to Buyer pt < p c − δ . p c pc -δ pc 0 -δ pc pc Property Price Price Range Default Price Range NO default What about the financial implication of default by the seller? The seller may choose not to complete the transaction with the buyer by returning the down payment to the buyer plus an amount of compensation equal to the down payment. This is likely especially when the property market is on the rise, and the seller is tempted to sell the property to another buyer who is willing to make a significantly higher offer. Default by Seller Default by Seller: Profit/Loss pt > p c + δ . p c Payoff to Seller Property Price -δ pc pc +δ pc 0 pc Seller commits to the original buyer Seller pays δ pc to the buyer in order to sell the property to someone else for higher price Advanced Example 1 Suppose a buyer wants to enter into a preliminary sale and purchase agreement with the seller to buy a property. The relevant market information is as follows: Contracted Price = $5m Time between preliminary and formal sale and purchase agreement= 3 months Risk-free interest rate = 3% Volatility of property price = 25% per year. Down payment = 3 percent of contracted price What is the value of this 2-week call option?? Advanced Example 1 Contd The Black-Scholes formula for calculating the value of a call option is as follows: C = S * N (d 1 ) − Xe − rT N (d 2 ) d1 = ln(S / X ) + (r + 0.5σ 2 )T σT d 2 = d1 − σ T S = contracted price = $5 million X = exercise price = $5 m – 3%($5 m) = $4.85 m T = Transaction period (year) = 14 days/365 = 0.0384yr r = risk-free rate of interest = 3% σ = property price volatility = 25% (annualized) Using the Black-Scholes formula, the value of the implied call option to the buyer is $0.193 million. Is the down payment too high or too low, is it fair?? Advanced Example 2 Suppose a seller enters into a preliminary sale and purchase agreement with the buyer with the following market information. What is the value of this 2-week put option?? Contracted Price = $5m Time between preliminary and formal sale and purchase agreement= 3 months Risk-free interest rate = 3% Volatility of property price = 25% per year. Down payment by buyer = 3 percent of contracted price In case of default by the seller, the seller will pay 3% + 3% of the contracted price to the buyer. Advanced Example 2 Contd The Black-Scholes formula for calculating the value of a put option is as follows P = C − S + Xe − rT ; C = S * N (d 1 ) − Xe − rT N (d 2 ) d1 = ln(S / X ) + (r + 0.5σ 2 )T σT d 2 = d1 − σ T S = contracted price = $5 million X = exercise price = $5 m + 3%($5 m) = $5.15 m T = Transaction period (year) = 14 days/365 = 0.0384 yr r = risk-free rate of interest = 3% s = property price volatility (annualized) = 25% Using the put formula above, the value of the implied put option to the seller is $0.187 million. Is this down payment too high or too low, is it fair?? Question for Discussion In a real estate transaction, the gain or loss to one party, either the buyer or the seller, is also the loss or gain to the other party. It is a zero sum game. Since either party may default in the transaction, what does the overall payoff to both parties look like, what is the price range within which the transaction has a good chance to complete, what is the price range beyond which the transaction is not going to go through??? Effect of Default to Buyer and Seller Profit/Loss Payoff to Buyer pc -δ pc 0 -δ pc pc Property Price Recall that buyer may default if c c p t < p − δp Payoff to Seller What is the net payoff to buyer and seller in case of buyer’s default ?? -δ p c Net Payoffs Profit/Loss Payoff to Seller pc -δ pc 0 -δ pc pc Property Price Net payoff to buyer and seller in case of buyer’s default Payoff to Buyer -δ p c Effect of Default to Buyer and Seller Profit/Loss Payoff to Seller pc pc +δ pc Property Price Recall that Seller may default if 0 -δ pc pt > p + δp c c Payoff to Buyer What is the net payoff to buyer and seller in case of seller’s default ?? +δ pc Net Payoffs Net payoff to buyer and seller in case of seller’s default Profit/Loss Net Payoff to Seller pc 0 pc +δ pc Property Price Net Payoff to Buyer +δ pc pc pc +δ pc Putting Things Together What is the price range within which the transaction has a good chance to complete? What is the price range beyond which the transaction is not going to go through??? Overall Net Payoff to Buyer Profit/Loss Net Payoff to Buyer +δ pc pc +δ pc Complete Transaction pc -δ pc 0 -δ pc Buyer Defaults pc Property Price Question: Net Payoff to Buyer + Net Payoff to Seller = ??? Seller Defaults Net Payoff to Seller +δ pc pc +δ pc pc -δ pc -δ pc End of Lecture ...
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This note was uploaded on 09/06/2010 for the course FINA FINA0805 taught by Professor Tse during the Spring '09 term at HKU.

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