Vacant land has been zoned for either one 10,000- square-foot five-unit condomin
ID: 2780517 • Letter: V
Question
Vacant land has been zoned for either one 10,000- square-foot five-unit condominium or two single-family homes, each with 3,000 square feet. The cost of constructing the single-family homes is $100 per square foot and the cost of constructing the condominium is $120 per square foot. If the real estate market does well next year, the homes can be sold for $300 per square foot and the condominiums for $230 per square foot. If the market performs poorly, the homes can be sold for $200 per square foot and the condos for $140 per square foot. Today, comparable homes could be sold for $225 per square foot and comparable condos for $180 per square foot. First-year rental rates (paid at the end of the year) on the comparable condos and homes are 20 percent and 10 percent, respectively, of today’s sales prices.
a. What is the implied risk-free rate, assuming that short selling is allowed?
b. What is the value of the vacant land, assuming that building construction will take place immediately or one year from now? What is the best building alternative?
Explanation / Answer
Cost of constructing the condominium is 120*10000= 12,00,000
If market does well then 230 per sq feet, else 140 per sq feet in bad times. Comparable rates are 180 per square feet
1st year rental rates are 20% of today's comparable rates which implies 36 per square feet which implies that total rentals will be 36* 2000 *5 rental for a condominium which is equal to 360,000
Cost of constructing two single famiy homes = 100*6000= 6,00,000(Per unit cost will be 3,00,000)
If market is good then rate is 300 per square feet else 200 per square feet. Comparable homes are 225 per square feet
Rental value is 10% of comparable homes which is 22.5 per square feet. Therefore if someone were to rent it he would have to pay 22.5*3000 = 6,75,000
a. What is the implied risk-free rate, assuming that short selling is allowed?
For the condominium it is 2.77% for the single family house it is 11.1%.
The expected price for condominium is 185 based on average of the two scenarios. Hence risk free rate of return is (185/180-1)*100 for condominium
The expected price for single family house is 250 based on average of the two scenarios. Hence risk free rate of return is (250/225-1)*100 for condominium.
This is based on the assumption that one is selling the building short
b. What is the value of the vacant land, assuming that building construction will take place immediately or one year from now? What is the best building alternative?
Value of land can be taken to be either (185-120) *10000= 6,50,000. 65 is arrived at by deducting 120 from 185
Value of land 150*6000= 9,00,000 ... 150 is arrived at finding the difference beween expected profit - cost of construction(250-100)
The value of land therefore has to be at least 9,00,000 based on the profit
Building the single family lot will be more profitable since the margin (250-100) is highest.
The best building alternative is the single family home which has a higher payoff
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