NPV AND IRR A store has 5 years remaining on its lease in a mall. Rent is $2,000
ID: 2791109 • Letter: N
Question
NPV AND IRR
A store has 5 years remaining on its lease in a mall. Rent is $2,000 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 $2,750 per month for the next 51 months. The lease cannot be broken, and the store's WACC is 12% (or 1% per month).
Should the new lease be accepted? (Hint: Be sure to use 1% per month.)
-Select-YesNoItem 1
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.
$
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.
%
Explanation / Answer
Solution
A. The present value of the current lease of $2,000 pm for the next 60 months at the discount rate of 1% p.m is obtained by discounting the stream of $2,000 over the next 60 months
The current value of the lease = Lease rent * (1 - discount factor ^ 60) / ( 1- discount factor)
Discount factor (DF) = 1/ (1+ 0.01)= 1/1.01 = 0.990099
Plugging the DF, PV of the lease (at t=0) = $ 90,809.17 [t=month; t varies from 0 to 60]
The new proposed lease includes no lease rent for first 9 months and lease rent of $ 2,750 for the balance 51 months
The present value of the new lease = PV of the lease rent from 10th to 60th month = PV of the lease rent of $2,750 from 10th to 60th month to t=9
= 2,750 *(1-DF^51)/(1-DF) = 2750* (1-0.990099^51)/(1-0.990099) = $1,10,539.32 at t=9
PV of lease rent (at t=0) = $1,10,539.32/(1.01^9) = $1,01,070.50
Hence, the current lease is beneficial to the Store ownera and the new lease should not be accepted
B.
The PV of the original lease rent at t=9 = PV *1.01^9 = 90,809*1.01^9 = $99,316.66 (t=9)
Let's assume that the lease rental for the new lease be $X, accordingly the PV of the new lease rental at t=9 is as below: X*(1-0.990099^51)/(1-0.990099) = 40.196X
For the Store owner to be indifferent to the lease, the PV of the current lease (at t=9) = PV of the new lease from 10th to 60th month
40.196X = 99316 ; X = $2,470.8
At X= $2,470.8, the store owner shall be indifferent to the new lease system
C.
On solving the following equation for the discount rate (WACC), r:
0 = 2000*(1-r^9)/(1-r) - 750*(1-r^51)(r^9)/(1-r), we get r = 2.81% p.m ~ 33.80% p.a.
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