Question

Consider a 100,000 sq. ft. building that will be acquired (at price $0) and demolished by local government at the end of 15 years.  Assume the building is fully leased building under an absolute net lease structure (all expenses paid by tenant); Consider 2 leases:

      15 year lease at $15/ft./yr.

      5 year lease at $15/ft./yr.

Suppose that $15 is the market rate and that the forecasted rent growth rate is 0% . Also suppose that the discount rate for contractual lease cash flows (corporate bonds) is 7%, regardless of maturity, and that there is no TI at the end of each lease.

a) Under which lease is the building worth more?  Why?

b) What is the value of the building under the first scenario? Suppose you know that the market will pay $11.8 mil.  for the building under the second scenario.  What is the discount rate for speculative lease cash flows? (Hint: year 1-5 cash flows in the second scenario should be discounted at the bond rate, since they are under contract. Find the PV of the speculative cash flows (years 6-15) and then find the discount rate consistent with that PV.)  

c) What are the respective cap rates under the two lease structures?

Answer 1

A.) Under which leasse building worth more as follows:-

First 5 years:-

Lease rent = 100000 * 15 sq. ft. = 1500000

= 1500000 *  Present value of 7% for 5 years

= 1500000 * 4.10 = 6150000

Second for 15 years:-  

Lease rent = 100000 * 15 sq. ft. = 1500000

= 1500000 *  Present value of 7% for 15 years

= 1500000 * 9.108 = 13662000

In case of 15 years building worth more as per above calculations.

B.) 1.) Value of building under first scenario is calculated as above you can see that.

2.) Discount rate for speculative cash flows as follows:-

We will assume here period for 15 years as per hint given under question.

For first 5 years = Discount rate is 7 % for 5 years * 1500000

= 4.1 * 1500000 = 6150000

Now remaining cashflow balance is 5.65 m (11.8 m - 6.15 m)

Now find out discounting rate for next 10 years (i.e. 6 to 15) so that we will get above cash flow i.e. 5.65m.

Hence we have to use trial & error method to find out discounting rate to get cashflow of 5.65 m in next 10 years as follows:-

We assume two rates for discounting = 1.) 9% and 2.) 11%

1.) Discounting rate 9% for 10 years (6-15) i.e. = 4.17

So amount of present value of cash flows = 1500000 * 4.17 = 6255000

( PV of cashflow is more than 5.65 m hence 9 % is not adequate rate)

2.) Now evaluate 11 % rate for 10 years (6-15) hence discounting rate is = 3.495

so amount of present value of cash flows = 1500000 * 3.495 = 5242500

( PV of cashflow is less than 5.65 m hence 11% is not adequate rate)

Now we use formula to find correct discounting rate is as follows :-

= 9% + { (6255000 - 5650000) / 1012500 } * (11-9)

= when we solve above equation we got 10.19% as correct discounting rate.

Note:- Above amount 1012500 came as follows ( add both the amounts) :-

9% = 6255000 - 5650000 = 605000

11% = 5650000 - 5242500 = 407500