Lecture 5 Buy or Lease課程重點• 再看一個投資方案的評估• Buy or lease

– The financing decision– A lease is a debt– with tax– using a risk-adjusted discount rate– Risk considerations– Lease with uncertain lives– The rate of discount– Leverage lease

The Baldwin Company: an example

The Worksheet for Cash Flows of the baldwin Company (in thousands)

0 1 2 3 4 5Investments(1) Bowling ball machine -100 21.76(2) Accumulated depreciation 20 52 71.2 82.72 94.24(3) Adjusted basis of machine 80 48 28.8 17.28 5.76 after depreciation(4) Opportunity cost (warehouse) -150 150(5) Net working capital 10 10 16.32 24.97 21.22 0(6) Change in net working capital -10 0 -6.32 -8.65 3.75 21.22(7) Total cash flow of investment -260 0 -6.32 -8.65 3.75 192.98 (1)+(4)+(6)

Income(8) Sales revenue 100 163.2 249.72 212.2 129.9(9) Operating costs 50 88 145.2 133.1 87.84(10) Depreciation 20 32 19.2 11.52 11.52(11) Income before taxes 30 43.2 85.32 67.58 30.54 (8)-(9)-(10)(12) Tax (34%) 10.20 14.69 29.01 22.98 10.38(13) Net income 19.80 28.51 56.31 44.60 20.16

Operating revenues and costs of Baldwin company

1 2 3 4 5production 5000 8000 12000 10000 6000price 20 20.4 20.81 21.22 21.65sales revenue 100000 163200 249720 212200 129900cost per unit 10 11 12.1 13.31 14.64operating costs 50000 88000 145200 133100 87840

Depreciation for Baldwin companyRecovery period class

year 3 years 5 years 7 years1 33340 20000 142802 44440 32000 244903 14810 19200 174904 7410 11520 125005 11520 89206 5760 89207 89208 4480

Total 100000 100000 100000

Incremental cash flows for Baldwin Company (in thousand)0 1 2 3 4 5

(1) Sales revenue 100 163.2 249.72 212.2 129.9(2) Operating costs -50 -88 -145.2 -133.1 -87.84(3) Taxes -10.2 -14.69 -29.01 -22.98 -10.38(4) Cash flow from operations 39.8 60.51 75.51 56.12 31.68 (1)-(2)-(3)(5) Total cash flow of investment -260 -6.32 -8.65 3.75 192.98(6) Total cash flow of the project -260 39.8 54.19 66.86 59.87 224.66 (4)+(5)NPV 4% 123.64

10% 51.5915% 5.4720% -31.35

Buy or lease: the financing decision

• An example:

The acquired equipment costs $100,000.

We can borrow the $100,000 at a cost of 5% per year, or

we can lease the equipment at a cost of $29,000 per year.

Assuming the equipment has an expected life of four years.

• Approach 1:

Buy: Annual payment = $28,201

Lease: $29,000

Lease is better???

• Approach 2:Buy: PV=$10,000

Lease: PV=29000*B(4,0.05)=29000*3.5460=102,834

Buy is better.

• Approach 3:Buy: cost=5%

Lease: the implicit interest cost of leasing

29000*B(4,k)=100,000, k=0.062

Buy is better.

• Conclusion:With annual lease payment of $29,000 per year, there is a financial disadvantage to leasing, because the present value of the lease payment at 5% is larger than the amount that would have to be borrowed to finance the purchase through borrowing.

If the lease payment required were less than $28,201, the lease would have a financial advantage.

A lease is a debt

• A question

Assuming the firm normally uses a 0.1 weighted average cost of capital to evaluate investments, and the asset will earn cash flow benefits of $31,000 per year.

Approach 1:

Buy: NPV=31000B(4,0.1)-100,000=-1,733

Lease: NPV=(31000-29000)B(4,0.1)=6340

Lease is better???

• Approach 2: debt is included in the cash flow.

Buy: NPV=(31000-28201)B(4,0.1)=8873

Lease: NPV=(31000-29000)B(4,0.1)=6340

• Approach 3:to compute the NPV using the cost of debt

Buy: NPV=31000B(4,0.05)-100000=9923

Lease: NPV=(31000-29000)B(4,0.05)=7092

With taxes• Condition 1: use the after-tax borrowing rate as

the discount rate tax rate=0.4Buy: NPV=0 A different repayment schedule would lead to a different pattern of after-tax cash flows. If we subtract the present value of the positive cash flows associated with borrowing (+100,000) from the present value of the after-tax cash payments (-100,000), NPV=0

Lease :NPV=((1-0.4)*29000)B(4, 0.05*(1-0.4))=

=17400*3.7171=64677

Lease is better???

• Condition 2: Considering depreciation

With a tax rate of 40%, each dollar of depreciation expense for tax purpose will save $40 of taxes.

Depreciation=$25,000, tax saving=0.4*25,000=10,000

Buy: 10000*B(4,0.3)=37171, 100,000-37171=62,829

Lease=64677

Buy is better.• If a more rapid method of depreciation were used,

there would be a more clearly defined advantage in favor of buying.