# Solutions to Chapter 26 (Leasing)-Brealey Myers Corporate Finance

Topics: Net present value, Lease, Depreciation Pages: 13 (3334 words) Published: December 2, 2008
CHAPTER 26

Leasing

8.The present value of the costs and the present value of the lease payments are shown in the following table: | |t = 0 |t = 1 |t = 2 |t = 3 |t = 4 |t = 5 |t = 6 | |Initial Cost |-3000.00 | | | | | | | |Depreciation | | 600.00 | 960.00 | 576.00 | 345.60 | 345.60 | 172.80 | |Depreciation tax shield | | 210.00 | 336.00 | 201.60 | 120.96 | 120.96 | 60.48 | |After-tax admin. costs |-260.00 |-260.00 |-260.00 |-260.00 |-260.00 |-260.00 | | |Total |-3260.00 | -50.00 | 76.00 | -58.40 |-139.04 |-139.04 | 60.48 | |PV(at 9%) = -\$3,439.80 | | | | | | | | |Break-even rent |1082.29 |1082.29 |1082.29 |1082.29 |1082.29 |1082.29 | | |Tax |-378.80 |-378.80 |-378.80 |-378.80 |-378.80 |-378.80 | | |Break-even rent after tax | 703.49 | 703.49 | 703.49 | 703.49 | 703.49 | 703.49 | | |PV(at 9%) = -\$3,439.80 | | | | | | | | |Cash Flow |-2556.51 | 653.49 | 779.49 | 645.09 | 564.45 | 564.45 | 60.48 |

The break-even lease rate (after tax) is the payment for a six-year annuity due whose present value is \$3,439.80: [pic]
[pic]
The pre-tax lease rate is: \$703.49/0.65 = \$1,082.29

9.Administrative costs drop to \$200 per year, so that the after-tax administrative costs are \$130 per year and the present value of the costs is now: \$2,804.15 Moreover, the lease payments are a fixed commitment of the blue-chip company. The six lease payments are discounted at the after-tax rate at which Acme would lend money, which is computed as follows: 0.06 × (1 – 0.35) = 0.039 = 3.9%

The break-even lease rate is computed as follows:

[pic]
[pic]
The pre-tax lease rate is: \$513.17/0.65 = \$789.49
10.a.If the expected rate of inflation is 5% per year, then administrative costs increase by 5% per year. We further assume that the lease payments grow at the rate of inflation (i.e., the payments are indexed to inflation). However, the depreciation tax shield amounts do not change because depreciation is based on the initial cost of the desk. The appropriate nominal discount rate is now: (1.05 ( 1.09) – 1 = 0.1445 = 14.45%

These changes yield the following, indicating that the initial lease payment has increased from \$1,082 to about \$1,113:

| |t = 0 |t = 1 |t = 2 |t = 3 |t = 4 |t = 5 |t = 6 | |Initial Cost |-3000.00 | | | | | | | |Depreciation | | 600.00 | 960.00 | 576.00 | 345.60 | 345.60 | 172.80 | |Depreciation tax shield | | 210.00 | 336.00 | 201.60 | 120.96 | 120.96 | 60.48 | |After-tax admin. costs |-260.00 |-273.00 |-286.65 |-300.98 |-316.03 |-331.83 | | |Total |-3260.00 | -63.00 | 49.35 | -99.38 |-195.07 |-210.87 |...