Sharon, who graduated from the local university 3 years ago with a degree in fin

Question

Sharon, who graduated from the local university 3 years ago with a degree in finance, is manager of Ann Naylor’s store in the mall. Sharon’s store has 5 years remaining on its lease. Rent is $2000 per month, 60 payments remain, and the next payment is due in one month. The mall’s owner plans to sell the property in a year and wants rents at that time to be high so that the property will appear more valuable. Therefore, Sharon has been offered a “great deal” (owner’s words) on a new 5 year lease. The new lease calls for zero rent for 9 months, then payments of $2600 per month for the next 51 months. The lease cannot be broken and the store’s cost of capital is 12 percent (APR). Sharon must make a decision. A good one could help her career and move her up in management, but a bad one could hurt her prospects for promotion.

1) Sharon does not trust the owner. So she decides to bargain with the owner over the new lease payment. What new lease payment would make Sharon indifferent between the new and old leases?

2) Sharon is not sure of the 12 percent cost of capital. It could be higher or lower. At what cost of capital (APR) would Sharon be indifferent between the two leases?

Explanation / Answer

APR =12% or 1% monthly

Present Value of Earlier Lease Payments =$2,000x{(1-(1+0.01)-60)/0.01} =$2,000 x 44.9550 =$89,910

1.) New lease payment which will make Sharon indifferent between the new and old leases

89,910 = P x {(1-(1+0.01)-51)/0.01} x (1+0.01)-9

89,910 = P x 39.7981 x 0.9143

P =$2,470.91

2.) Let r be the cost of capital at which Sharon is indifferent between the lease payments.

2,000x{(1-(1+r)-60)/r} = 2,600 x {(1-(1+r)-51)/r} x (1+r)-9

{(1-(1+r)-60)/r} = 1.3 x {(1-(1+r)-51)/r} x (1+r)-9

{(1-(1+r)-60)/r} - 1.3 x {(1-(1+r)-51)/r} x (1+r)-9 = 0

Using Trial and Error method to solve for r

For r=0.01, LHS= -2.35

For r=0.02, LHS= 0.18

For r=0.018, LHS= -0.239

For r=0.019, LHS= -0.023

For r=0.01911, LHS= 0

Hence, APR =12x1.9111 =22.93%

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