In: Finance
NPV AND IRR
A store has 5 years remaining on its lease in a mall. Rent is $1,900 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).
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.
%
Present value of both the payments need to be determined to compare the payments using the formula:
PV of an annuity = P * [(1-((1+r)^(-n))/r]
P is the amount due after one time period, r is rate of discounting, and n is total time period
i.e. For original lease: P = 1900, r = 1% & n = 60
PV (Original Lease) at time 0 = 1900 * [(1-((1+1%)^(-60))/1%] = $1900 * 44.95504
PV (Original Lease) at time 0 = $85414.58
For new lease P = 2500, r = 1% & n = 51, PV for new lease can be calculated at time 9 using above formula as first payment is due at time 10
PV (New Lease) at time 9 = 2500 * [(1-((1+1%)^(-51))/1%] = $2500 * 39.79814
PV (New Lease) at time 9 = $99495.35
To compare both the lease, we have to calculate the new lease PV by 9 months to get PV at time 0.
PV (New Lease) at time 0 = 99495.35/(1+1%)^9 = 99495.35/1.0936853 = $90972.56
Since Present Value of New Lease is more than Original lease, New lease should not be accepted.
Answer to first question is ‘NO’
To calculate the value of new lease payment to make the store owner indifferent, we have to calculate the FV of original lease at time 9 using the PV value as calculated above.
FV (Original Lease) at time 9 = 85414.58 * (1+1%)^9 = 85414 * 1.0936853 = $93416.67
Therefore to calculate the monthly payment amount of new lease, we use the above formula as
93416.67 = P * [(1-((1+1%)^(-51))/1%]
Hence, acceptable monthly payment amount to make the shop owner indifferent between two leases is $2347.26.
To calculate the store owner’s WACC so that store owner is indifferent between two payment, we find the difference in payments
Let IRR be 12i, then PV of this payment should be
1900 * [(1-((1+i)^(-9))/i] + (-600) * [(1-((1+i)^(-51))/i] * (1+i)^(-9)
Calculating PV of this payment at 12%
PV (12%) = -5557.98
Since, this series of payment have negative payments in the later duration, increasing the discount rate will lead to increase the PV. By trial and error
PV(20%) = -1912.64
PV(25%) = -117.3338
PV(26%) = 204.4676
By interpolation
IRR = 25% + (26% - 25%) * (0-(-117.3338)/(204.4676-(-117.3338) = 25% + .3646%
IRR = 25.365%