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.)

YES or NO

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

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 = 2100, r = 1% & n = 60

PV (Original Lease) at time 0 = 2100 * [(1-((1+1%)^(-60))/1%] = $2100 * 44.95504

PV (Original Lease) at time 0 = $94405.58

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 = $99495.34

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 = 99495.34/(1+1%)^9 = 99495.34/1.0936853 = $90972.55

Since Present Value of New Lease is more than Original lease, New lease should be accepted.

Answer to first question is ‘YES’

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 = 94405.58 * (1+1%)^9 = 94405.58 * 1.0936853 = $103250

Therefore to calculate the monthly payment amount of new lease, we use the above formula as

103250 = P * [(1-((1+1%)^(-51))/1%]

103250 = P * 39.78914

P = 103250/39.78914 = 2594.34

Hence, monthly payment amount to make the shop owner indifferent between two leases is $2594.34.

To calculate the store owner’s WACC so that store owner is indifferent between two payment, we find the difference in payments

1. Saving of 2100 for month 1 to 9 i.e. +2100 for month 1 to 9
2. Excess payment of $400 (2500-2100) for month 10 to 60 i.e. -400 for month 10 to 60

Let IRR be i, then PV of this payment should be

2100 * [(1-((1+(i/12))^(-9))/(i/12)] + (-400) * [(1-((1+(i/12))^(-51))/(i/12)] * (1+(i/12))^(-9)

Calculating PV of this payment at 12%

PV (12%) = 3433.03

Since, this series of payment have negative payments in the later duration, decreasing the discount rate will lead to reduce the PV. By trial and error

PV(6%) = 1257.44

PV(3%) = -39.63

PV (3.5%) = 187.36

By interpolation

IRR = 3% + (3.5% - 3%) * (0-(-39.63)/(187.36-(-39.63) = 3.09%

IRR = 3.09%

Hence, WACC of 3.09%