Question

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 $2,600 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: Make sure you use 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 old lease ? ( Hint: Find FV of the old lease's original cost at t=9 months; then treat this as the PV of a 51- period annuity whose payments represent the rent during months 10 to 60.)

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 lease ? ( HInt: Calculate the differences between the two payment stream; then find its IRR.)

The correct answer is (a) NO; PV_old= - $89,910.08 ; PV_new= -$94,611.45 ; (b) $2,470.80 ; (c) 22.94%

 

Answer 1

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;CF_1-9 = 0;CF_10-60= -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; CF_1-9 = -2000; CF_10-60 = 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; CF_1-9 = 0; CF_10-60 = -2600; I = 1.9113; NPV = ?

PV = -$71,038.98.

Except for rounding differences; the costs are the same.