Question

Subject : Corporate Finance

One question with part questions. solutions must delineate how you reach the final answer.

Q1.

Vacant land has been zoned for either a condominium (10,000 sqft) or a single-family home (6,000 sqft). The construction cost of the condominium is $100 per sqft while that of the family home is $120 per sqft. There are two possible market states next year which determine the sales prices of the condominium and the family homes as follows:

? Good state: the condominium and the family home are sold at $230 per sqft and $300 per sqft, respectively.

? Bad state: the condominium and the family home are sold at $140 per sqft and $200 per sqft, respectively.

The current price of a comparable condominium is $180 per sqft and that of a com- parable family home is $225 per sqft. First-year rental rates (paid at the end of the year) on the comparable condos and homes are 20% and 10% of the current sales prices, respectively. Answer the following questions.

Respond to (a) through (g).

1. (a) Calculate the cash flows that a condominium and a family firm generates (i.e., the sum of the sales price and the rental revenue) in each state next year, respectively.

2. (b) What is the implied risk-free rate? (Hint: Construct a mimicking portfolio of a risk free asset using the cash flows from a condominium and a family home.)

3. (c) Suppose that you can build a condominium or a family home immediately. What is the value of the lot if you decide to build a condominium now?

4. (d) What is the value of the lot if you instead decide to build a family home now?

5. (e) Now suppose that you wait one year (i.e., until the realization of the states) before building a condominium or a family firm. Which building will you construct in each state?

6. (f) What is the value of the lot if you wait one year as above?

7. (g) Given all your answers (a)–(f), what is the best building alternative?

please help me with the part questions (a) thru (g)....need to prepare for the final next month so i need answers for practice questions for the final....

Answer 1

Ans cost of construction of condominium($100 per sqft)=$100x10000=$1000000

Cost of construction of single family home($120 per sqft)=$120x6000=$720000

In good state:

Sale price of condominium ($230 per sqft)=$230x10000=$2300000

Sale price of single family home($300 per sqft)=$300x6000=$1800000

In bad state:

Sale price of condominium ($140 per sqft)=$140x10000=$1400000

Sale price of single family home($200 per sqft)=$200x6000=$1200000

Current situation:

Sale price of condominium ($180 per sqft)=$180x10000=$1800000

Sale price single family home($225 per sqft)=$225x6000=$1350000

Year end rental price of condominium=20% of current value=0.2x1800000=$360000

Year end rental price of single family home=10% of current value=0.1x1350000=$135000

a, in good state:

Cash flows from condominium= sale price of condominium+ first year rental=$2300000+$460000=$2760000

Cashflow from single family home=sale price + first year rental=$1800000+$180000=$1980000

In bad state:

Cash flow from condominium=$1400000+$280000=$1680000

Cash flow from single family home=$1200000+$120000=$1320000

b, let us assume that our portfolio consist of condominium and single family home

So initial investment=cost of construction of condominium and single family home=$1000000+$720000=$1720000

Probability of good state=0.5

Probability of bad state=0.5

Cash flow of portfolio next year if state is good=sales of condominium and single family home+ rent on both properties=$2300000+($2300000x0.2)+1800000+(1800000x0.1)=$4740000

Cashflow of portfolio if state is bad=1400000+(1400000x0.2)+1200000+(1200000x0.1)=$3000000

Expected cashflow next year=probability of good statexcash flow in good state + probability of bad state x cashflow in bad state=(4740000x0.5)+(3000000x0.5)=$3870000

Let risk free return=r

Initial investmentx(1 + r)= expected cash flow

1720000(1+r)=3870000

So r=1.25=125%

c, if condominium is built now

Value of lot=current price of condominium-construction cost of condominium +(future sale of single fam house - construction cost of fam house + first year rent of condominium)/(1+r) +(first year rent of home/(1+r)(1+r) =1800000-1000000+((0.5x(1800000+1200000))/(1+1.25) -720000/(1+1.25)+(0.5x(460000+280000)/(1+1.25))+(0.5x(180000+120000)/(1+1.25)(1+1.25))=$1340740.71