A real estate developer has the opportunity to develop a parcel of land over the

Question

A real estate developer has the opportunity to develop a parcel of land over the next three years. Here is the relevant information:

Project today is valued at Ksh.216 million.

Development cost today is Ksh.200 million. These costs increase 5% per year.

It costs Ksh.10 million, payable at the beginning of each year, to maintain the land if not developed.

This cost is not incurred if the land is developed.

At any time the land can be sold for Ksh.20 million.

Project's value follows a binomial tree with U = 1.5 and D = 2/3.

Objective probability of the market going up is 0.70.

Risk-free rate is 2.5%.

Required

What is the value of this real estate development project? When should it be developed?

Explanation / Answer

Ans: This issue is like binomial pricing model

Note: all prices are in million

                                                                        1.5*216 -> [324 delta – 10]*p

Proj Today (216)

                                                                                               0.667*216 -> [144.07 delta*(1-p)

where, p=probability = 0.70 of lad not being developed

delta = case where fund is invested and land is not developed.

We can equate the two expressions:

(324*delta – 10)*0.7 = 144.07*delta*0.3

Hence, future value of project = U*Price*p + L*Price*(1-p) = 1.5*216*0.7+0.667*216*0.3

= 270.02

The same discounted at risk free rate of 2.5% for unit period say 1 year.

The real value of real estate project = e-rt* 270.02 where r=2.5% and t=1 yr

= 263.35

Since, delta is very low, portfolio of unprepared land and related project has very low value of 1.647 million. It also signals the delay in the start of project

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.