NPV and IRR A store has 5 years remaining on its lease in a mall. Rent is $2,100

Question

NPV and IRR 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). 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 the 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. $__________ C.) The store owner is not sure of the 12% WACC

Explanation / Answer

a. 5 years remaining on lease; rent = $2,000/month; 60 payments left, payment at end of month. New lease terms: $0/month for 9 months; $2,600/month for 51 months. Cost of capital = 12% annual (1% per month). Old Lease New Lease Year Cash Flow PV at 1% PV of cash flow Cash Flow PV at 1% PV of cash flow 1 $2,000.00 0.990 $1,980.20 $0.00 0.990 $0.00 2 $2,000.00 0.980 $1,960.59 $0.00 0.980 $0.00 3 $2,000.00 0.971 $1,941.18 $0.00 0.971 $0.00 4 $2,000.00 0.961 $1,921.96 $0.00 0.961 $0.00 5 $2,000.00 0.951 $1,902.93 $0.00 0.951 $0.00 6 $2,000.00 0.942 $1,884.09 $0.00 0.942 $0.00 7 $2,000.00 0.933 $1,865.44 $0.00 0.933 $0.00 8 $2,000.00 0.923 $1,846.97 $0.00 0.923 $0.00 9 $2,000.00 0.914 $1,828.68 $0.00 0.914 $0.00 10 $2,000.00 0.905 $1,810.57 $2,600.00 0.905 $2,353.75 11 $2,000.00 0.896 $1,792.65 $2,600.00 0.896 $2,330.44 12 $2,000.00 0.887 $1,774.90 $2,600.00 0.887 $2,307.37 13 $2,000.00 0.879 $1,757.33 $2,600.00 0.879 $2,284.52 14 $2,000.00 0.870 $1,739.93 $2,600.00 0.870 $2,261.90 15 $2,000.00 0.861 $1,722.70 $2,600.00 0.861 $2,239.51 16 $2,000.00 0.853 $1,705.64 $2,600.00 0.853 $2,217.34 17 $2,000.00 0.844 $1,688.75 $2,600.00 0.844 $2,195.38 18 $2,000.00 0.836 $1,672.03 $2,600.00 0.836 $2,173.65 19 $2,000.00 0.828 $1,655.48 $2,600.00 0.828 $2,152.12 20 $2,000.00 0.820 $1,639.09 $2,600.00 0.820 $2,130.82 21 $2,000.00 0.811 $1,622.86 $2,600.00 0.811 $2,109.72 22 $2,000.00 0.803 $1,606.79 $2,600.00 0.803 $2,088.83 23 $2,000.00 0.795 $1,590.88 $2,600.00 0.795 $2,068.15 24 $2,000.00 0.788 $1,575.13 $2,600.00 0.788 $2,047.67 25 $2,000.00 0.780 $1,559.54 $2,600.00 0.780 $2,027.40 26 $2,000.00 0.772 $1,544.10 $2,600.00 0.772 $2,007.32 27 $2,000.00 0.764 $1,528.81 $2,600.00 0.764 $1,987.45 28 $2,000.00 0.757 $1,513.67 $2,600.00 0.757 $1,967.77 29 $2,000.00 0.749 $1,498.68 $2,600.00 0.749 $1,948.29 30 $2,000.00 0.742 $1,483.85 $2,600.00 0.742 $1,929.00 31 $2,000.00 0.735 $1,469.15 $2,600.00 0.735 $1,909.90 32 $2,000.00 0.727 $1,454.61 $2,600.00 0.727 $1,890.99 33 $2,000.00 0.720 $1,440.21 $2,600.00 0.720 $1,872.27 34 $2,000.00 0.713 $1,425.95 $2,600.00 0.713 $1,853.73 35 $2,000.00 0.706 $1,411.83 $2,600.00 0.706 $1,835.38 36 $2,000.00 0.699 $1,397.85 $2,600.00 0.699 $1,817.20 37 $2,000.00 0.692 $1,384.01 $2,600.00 0.692 $1,799.21 38 $2,000.00 0.685 $1,370.31 $2,600.00 0.685 $1,781.40 39 $2,000.00 0.678 $1,356.74 $2,600.00 0.678 $1,763.76 40 $2,000.00 0.672 $1,343.31 $2,600.00 0.672 $1,746.30 41 $2,000.00 0.665 $1,330.01 $2,600.00 0.665 $1,729.01 42 $2,000.00 0.658 $1,316.84 $2,600.00 0.658 $1,711.89 43 $2,000.00 0.652 $1,303.80 $2,600.00 0.652 $1,694.94 44 $2,000.00 0.645 $1,290.89 $2,600.00 0.645 $1,678.16 45 $2,000.00 0.639 $1,278.11 $2,600.00 0.639 $1,661.54 46 $2,000.00 0.633 $1,265.46 $2,600.00 0.633 $1,645.09 47 $2,000.00 0.626 $1,252.93 $2,600.00 0.626 $1,628.80 48 $2,000.00 0.620 $1,240.52 $2,600.00 0.620 $1,612.68 49 $2,000.00 0.614 $1,228.24 $2,600.00 0.614 $1,596.71 50 $2,000.00 0.608 $1,216.08 $2,600.00 0.608 $1,580.90 51 $2,000.00 0.602 $1,204.04 $2,600.00 0.602 $1,565.25 52 $2,000.00 0.596 $1,192.12 $2,600.00 0.596 $1,549.75 53 $2,000.00 0.590 $1,180.31 $2,600.00 0.590 $1,534.41 54 $2,000.00 0.584 $1,168.63 $2,600.00 0.584 $1,519.21 55 $2,000.00 0.579 $1,157.06 $2,600.00 0.579 $1,504.17 56 $2,000.00 0.573 $1,145.60 $2,600.00 0.573 $1,489.28 57 $2,000.00 0.567 $1,134.26 $2,600.00 0.567 $1,474.53 58 $2,000.00 0.562 $1,123.03 $2,600.00 0.562 $1,459.94 59 $2,000.00 0.556 $1,111.91 $2,600.00 0.556 $1,445.48 60 $2,000.00 0.550 $1,100.90 $2,600.00 0.550 $1,431.17 $89,910.08 $94,611.45 PV of old lease = $89,910.08 ; Pv of new lease = $94,611.45 Sharon should not accept the new lease because the present value of its cost is $94,611.45 - $89,910.08 = $4,701.37 greater than the old lease. b. FV of first 9 months’ rent under old lease: N = 9; I = 1; PV = 0; PMT = -2000; FV = ? FV = $18,737.05. Year Cash flow Fv at 1% F.V of Cash Flow 1 $2,000.00 1.00 $2,000.00 2 $2,000.00 1.01 $2,020.00 3 $2,000.00 1.02 $2,040.20 4 $2,000.00 1.03 $2,060.60 5 $2,000.00 1.04 $2,081.21 6 $2,000.00 1.05 $2,102.02 7 $2,000.00 1.06 $2,123.04 8 $2,000.00 1.07 $2,144.27 9 $2,000.00 1.08 $2,165.71 $18,737.05 The FV of the first 9 months’ rent is equivalent to the PV of the 51-period annuity whose payments represent the incremental rent during months 10-60. To find this value: N = 51; I = 1; PV = -18737.05; FV = 0; PMT = ? PV = PMT(PVIF1%,51) PMT = $470.80. Thus, the new lease payment that will make her indifferent is $2,000 + $470.80 = $2,470.80. Check: 1% 0 1 9 10 59 60 | | · · · | | · · · | | 0 0 -2,470.80 -2,470.80 -2,470.80 PV cost of new lease: CF0 = 0;CF1-9 = 0;CF10-60= -2470.80; I = 1. NPV = -$89,909.99. Except for rounding; the PV cost of this lease equals the PV cost of the old lease. c. Period Old Lease New Lease Difference Lease 0 0 0 0 1-9 -2,000 0 -2,000 10-60 -2,000 -2,600 600 CF0 = 0; CF1-9 = -2000; CF10-60 = 600; IRR = ? IRR = 1.9113%. This is the periodic rate. To obtain the nominal cost of capital, multiply by 12: 12(0.019113) = 22.94%. Check: Old lease terms: N = 60; I = 1.9113; PMT = -2000; FV = 0; PV = ? PV = -$71,039.17. New lease terms: CF0 = 0; CF1-9 = 0; CF10-60 = -2600; I = 1.9113; NPV = ? PV = -$71,038.98.

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