Question

A store has 5 years remaining on its lease in a mall. Rent is $2,100 per month, 60 payments remain, and the next payment is due in 1 month. The mall's owner plans to sell the property in a year and wants rent at that time to be high so that the property will appear more valuable. Therefore, the store has been offered a "great deal" (owner's words) on a new 5-year lease. The new lease calls for no rent for 9 months, then payments of $2,500 per month for the next 51 months. The lease cannot be broken, and the store's WACC is 12% (or 1% per month).

a. Should the new lease be accepted? (Hint: Be sure to use 1% per month.)

b. If the store owner decided to bargain with the mall's owner over the new lease payment, what new lease payment would make the store owner indifferent between the new and old leases? (Hint: Find FV of the old lease's original cost at t = 9; then treat this as the PV of a 51-period annuity whose payments represent the rent during months 10 to 60.) Round your answer to the nearest cent. Do not round your intermediate calculations

c. The store owner is not sure of the 12% WACC—it could be higher or lower. At what nominal WACC would the store owner be indifferent between the two leases? (Hint: Calculate the differences between the two payment streams; then find its IRR.) Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

a) If new lease accepted, then there will be savings of Rent or $ 2100 for first nine months, but there will be incremental rent of $ 400 for month 10 to 60

It is assumed that 1% WACC is compounded monthly

PV of savings in rent at t = 0

= 2100 (PVAF 1%, 9) = 2100 x 8.56602 = $ 17988.64

Value of Incremental rent at t = 9 = $ 400 for next 51 months

= 400 x PVAF(1%, 51) = 400 x 39.79813 = $ 15919.25

This value is arrived at t = 9, this is further pulled to t = 0 for comparison with savings

Therefore, $ 15919.25 x PVIF (1%, 9) = $ 15919.25 x 0.914339 = $ 14555.61

Now, net savings if the new lease is accepted - $ 17988.64 - $ 14555.61 = $ 3433.03

So, there will be a net benefit of $ 3433.03 if the new lease is accepted, so it should be accepted.

b) For lease to be indifferent for store owner, the PV of savings of rent of 9 months should be equal to PV of incremental rent of $ 400 for the next 51 months

So, $ 17988.64 = Incremental Lease amount x PVAF(1%, 51) x PVIF (1%,9)

$ 17988.64 = Incremental Lease amount x 39.79813 x 0.914339

Solving above, we get Inncremental Lease amount = $ 494.34

Therefore, new Lease amount should be $ 2594.34 for the store owner to be indifferent between old and new lease

c) Using trial and error method, let us calculate NPV @ 0.2% per month  

Taking the differences between 2 payment streams we get -

Savings in rent for first 9 months -

2100 (PVAF 0.2%, 9) = 2100 x 8.910656 = $ 18712.38

Value of Incremental rent at t = 9 = $ 400 for next 51 months

= 400 x PVAF(0.2%, 51) = 400 x 48.4392286 = $ 19375.69

This value is arrived at t = 9, this is further pulled to t = 0 for comparison with savings

Therefore, $ 19375.69 x PVIF (0.2%, 9) = $ 19375.69 x 0.9821786 = $ 19030.39

Net Benefit = $ 18712.38 - $ 19030.39 = $ - 318.01

Doing the same excercise with 0.3 %, we get a positive NPV at $ 232.22

using interpolation we get -

0 - (-318.01)/232.22 - (-318.01) = 0.58

So, the IRR comes out to 0.0258% per month or 0.31 % per annum compounded monthly , at this WACC, the store owner will be indifferent between the two leases.