Chinese version exercises
| Good question |
Chinese 11. It is recommended to change it to all English basic questions 1-6, which combines NPV, zero-sum game and rent inequality. It is very worth doing. By the way, you can review project valuation and sort out the error-prone tax deduction and tax payment cash flow again. Chinese 12. This calculation question is very easy to make mistakes, and it is very similar to the photo studio and actor questions in Tsinghua University. English 15, concept questions, review project investment decisions, and added why the lessor also needs to discount the lessee's after-tax interest rate. |
| lightning protection |
Questions on US accounting standards 5 and 6 are not required. English question 10 is a continuation of the oil drilling platform (English question 9, Chinese question 12), so there is no need to do it. First, the U.S. tax laws are different from those in China. According to IRS regulations, the number of years and annual depreciation depends entirely on the type of equipment. Therefore, no matter what happens here, depreciation will always be calculated at 1.94 million per year. Second, there is a logical problem with question 10 - if there is really a residual value of 700,000, the previous depreciation rate must not be 1.94 million per year, otherwise there will be no net residual value at all. The teaching materials of the China Association of Insurance Regulators will inform you of the net residual value rate, thereby directly adjusting the depreciation value, which is more operable. |
Concept questions
1【English concept 1】
1. From the perspective of interest tax deduction, leasing expenses are regarded as liabilities and can be used as the basis for tax calculation; for borrowing money to purchase, only the interest portion can be tax deducted.
Second, from the perspective of expense tax deduction, during the lease period, the lessee only has the right to use it, so it cannot obtain the advantage of depreciation tax deduction; for borrowing money to purchase, the part other than the residual value can enjoy depreciation tax deduction.
Third, from the perspective of liquidation rights, if the lessee defaults, the lessor, as a creditor, has no right to request bankruptcy liquidation.
Fourth, from the perspective of ownership, if there are no other contractual requirements, the ownership at the end of the period is not transferred.
//The basic idea is correct. Learn more about the rigorous logic of the answers.
When purchasing equipment with a loan, the buyer can enjoy depreciation tax deductions; when leasing equipment, the tax shield effect cannot be enjoyed because there is no transfer of ownership at the beginning of the period.
2【English Concept 2】
Leasing is more likely with lower tax rates because the tax savings of purchasing the equipment are less obvious. Companies with high tax rates will leverage the tax shield effect to purchase equipment.
3【English Concept 3】
//Two perspectives: one is the discount rate, the same IRR can be interpreted as high or low; the other is cash flow.
Tax savings are not considered; the cash flows and discount rates at the beginning and end of the period are different; compared with the incremental cash flow from purchasing equipment, the risks are different.
//Q: Where did IRR come from?
//Answer: It’s not mentioned in the text, so it’s just a review of project decisions.
4【English Concept 4】
1) In terms of capital cost, the essence of financial lease is secured borrowing, which is treated as debt replacement. Whether capital costs can be reduced must be compared with the costs of other financing channels before the answer can be given. As for the risk, it has nothing to do with whether to raise funds. We only care about NAL, which is the net present value of renting versus buying.
2) Financial leasing may not be 100% financing. Generally, the agreement requires advance payment or security deposit at the beginning of the period, or other implicit guarantee conditions.
3) Leasing will not disappear because compared with the transaction costs and sunk costs incurred in purchasing equipment, the advantages of leasing are obvious. Reducing the tax advantage, and at most reducing leasing, will not make it go away.
1)Correct. Leasing eliminates the need for companies to leverage to purchase equipment, but it also allows companies to reduce available financial liabilities in the process of debt replacement.
2)Correct. In a debt swap, the lessee obtains financing of 100100%, secured by the right of use. Accounted for as a lease liability.
3)Correct. The NPVNPV of lessees and lessors is exactly the opposite. If there are no tax incentives to adjust, it is a zero-sum game.
7【English concept 7】
Off-balance-sheet financing is specifically targeted at operating leases. Only when the lease period does not exceed 80% of the economic life and the rent is evenly distributed can it be recognized as a finance lease, otherwise it is an operating lease. Operating leases are only reflected in footnotes, so the asset items on the balance sheet will be reduced.
8【English concept 8】
//Refer to the answers to issuing warrants and convertible bonds: cash flow model, risk coordination, agency problem, backdoor equity
On the one hand, the tax saving effect of purchasing equipment is not obvious. On the other hand, there is an urgent need for funds now and there is confidence that they can be claimed back in the form of leasing in the future.
9【English concept 9】
The cash flow statement can be prepared from the borrower and lender perspectives respectively, and the income and expenditure of the two are exactly the same. The borrower can enjoy interest tax deductions, and the lender must pay interest income tax, so the two are equivalent.
10【English concepts 10-12】
1) Direct purchase requires extremely high one-time expenditure; if borrowing is required, leverage will be increased and may damage the capital structure. Large amounts of borrowing can also lower a company's credit rating.
2)//In addition to returns, risks must also be considered
On the one hand, the lessor has ownership. If the lessee defaults, the lessor can take back the right to use and re-lease it. On the other hand, the total present value of the cash flow from renting out exceeds the initial purchase cost. When purchasing equipment and renting it out, the lessor can enjoy tax deductions on depreciation and maintenance costs; if the equipment is directly loaned to the lessee, the interest earned will be subject to tax.
3) Either the ownership transfer occurs, and the lessee purchases the aircraft at the agreed price; or the ownership transfer does not occur, and the lessor takes back the aircraft and cashes it in at an appropriate opportunity; or it continues to lease.
Calculation problems
11【English Basics 1-6】
//The same material runs through six questions to be considered complete.
1) According to the meaning of the question, the after-tax guaranteed borrowing interest rate is 0.08*(1-0.35)=0.052
Four years of depreciation, annual tax deduction 580/4*0.35=507,500
The four-year after-tax lease cost is 1.69*(1-0.35)=1.0985 million
Net present value of lease:
| project |
0 |
1 |
2 |
3 |
4 |
| abandon purchase |
+5.8 million |
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| Give up depreciation tax deduction |
|
-507,500 |
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-507,500 |
|
| Rent expense |
-1.0985 million |
-1.0985 million |
-1.0985 million |
-1.0985 million |
NAL=580-160.6*(1-1.052^(-4))/0.052=-+131,500①
Therefore, you should choose leasing
//Error-prone tip: Rental expenses are also tax deductible! !
The principle of CPA is to use 169*4 as the tax calculation basis and depreciate within four years. The annual depreciation tax deduction is still calculated on the basis of 169. Tax benefits are inevitable.
Net present value of lease:
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NAL=580-219.75*(1-1.052^(-4))/0.052=-195.62million
Therefore, you should choose enough to buy.
2) The cash flow of the lessor’s investment is as follows:
//Error-prone tip: If you buy an asset, you can deduct tax on depreciation; in addition, rent is considered business income and taxes must be paid.
From 1), the annual after-tax income is 1.69*(1-0.35)=1.0985 million
From 1), the annual depreciation tax deduction is 507,500
| project |
0 |
1 |
2 |
3 |
4 |
| Purchase equipment |
-5.8 million |
||||
| depreciation tax deduction |
+50.75 |
50.75 |
50.75 |
50.75 |
|
| after-tax income |
109.85 |
109.85 |
109.85 |
109.85 |
The cash flow is exactly the opposite of that of the lessee, NPV=-131,500
3) According to the meaning of the question, there is no difference in tax levels between the lessor and the lessee, so leasing becomes a zero-sum game.
If and only if NAL=0, no party is damaged.
From the perspective of the lessor, we can get NAL=0=-580+OCF*(1-1.052^(-4))/0.052
The solution is OCF=580*0.052/(1-1.052^(-4))(10,000)=1,643,274
Based on the cash flow model of 2), it is assumed that the rent collected by the lessor is L per year
L*(1-0.35)+507,500=1,643,274
The solution is L=(1,643,274-507,500)/0.65=1,747,344.62 yuan
4) In terms of cash flow, under no-tax conditions, the lessor cannot obtain depreciation tax deductions and does not need to EBIT< /span>The lessee cannot obtain the advantage of rent tax deduction through tax basis. Rent will not be reduced due to taxes. Pay taxes.
As far as the discount rate is concerned, under no-tax conditions, the after-tax debt capital cost is equal to the pre-tax debt capital cost, which can be directly used for discounting.
//Under the no-tax condition, there is still no tax policy difference between the two parties, so the absolute value of NAL is equal and the sign is opposite. But this question is for lessees.
Rearrange the equation in 1) to get
NAL=580-169*(1-1.08^(-4))/0.08=202,500 yuan
Therefore, for the lessee, the leasing option is still better than purchasing the equipment.
5)
//Tip: The key is not whether there is tax or not, but the lessee has no tax and the lessor has tax!
According to the meaning of the question, the lessor’s tax bracket remains unchanged. To be able to accept the leasing option, you must have:
NPV=-580+OCF*(1-1.052^(-4))/0.052>=0→OCF>=1,643,274
And ∵OCF=L*(1-0.35)+507,500>=1,643,274
When ∴L>=1,747,344.62, the lessor can accept the lease contract
When the lessee has no taxes, the cash flow model becomes:
| project |
0 |
1 |
2 |
3 |
4 |
| abandon purchase |
+5.8 million |
||||
| Give up depreciation tax deduction |
0 |
0 |
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0 |
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| Rent expense |
-Lwan |
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-L |
-L |
If the lessee chooses to purchase equipment, he will not be able to enjoy depreciation tax deductions; if he has rental expenses, he will not be able to enjoy the tax deduction advantage through the tax calculation basis. Therefore, no after-tax cash flow reduction is required.
In addition, since the tax rate drops to 0, the after-tax interest rate is the pre-tax interest rate, which needs to be discounted to the lessee at an interest rate of 8%.
NAL=580-L*(1-1.08^(-4))/0.08>=0
The solution is L<=580*0.08/(1-1.08^(-4))=1,751,140.67, which is a condition acceptable to the lessee.
Taking the intersection of the above two intervals, the reasonable rent interval is
1,747,344.62<=L<=1,751,140.67
//This question is based on the same idea as calculating the capital cost inequality for warrants and convertible bonds, and calculating the conditions acceptable to both investors and the company.
6) Check the table and find that under the MACRS method, the depreciation result is
| Depreciation ratio |
0.3333 |
0.4445 |
0.1481 |
0.0741 |
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| years |
0 |
1 |
2 |
3 |
4 |
| depreciation |
193.314 |
257.81 |
85.898 |
42.978 |
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| depreciation tax deduction |
67.6599 |
90.2335 |
30.0643 |
15.0423 |
The cash flow model is as follows
| years |
0 |
1 |
2 |
3 |
4 |
| Give up buying equipment |
580 |
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| Give up depreciation tax deduction |
-67.6599 |
-90.2335 |
-30.0643 |
-15.0423 |
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| After-tax rental costs |
-109.85 |
-109.85 |
-109.85 |
-109.85 |
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| compound interest present value coefficient |
0.95057 |
0.903584 |
0.85892 |
0.816464 |
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| Present value |
580 |
-168.736 |
-180.792 |
-120.175 |
-101.97 |
| Project NPV |
8.326834 |
NAL=83,268.34 yuan>0
To sum up, whether it is no tax or accelerated depreciation, it is the same as the original plan, which is more supportive of leasing equipment.
12【English Intermediate 9-11】
1) First calculate the NAL based on the rental conditions given by Lambert Leasing Company.
The after-tax secured borrowing interest rate is 9%*(1-0.34)=5.94%
The annual depreciation tax deduction is 970/5*0.34=659,600
The after-tax rent at the beginning of each year is 215*(1-0.34)=1.419 million
The present value coefficient of the five-period ordinary annuity is (P/A,0.0594,5)=(1-1.0594^(-5))/0.0594=4.2192
The cash flow model is as follows. The period when the residual value reaches 0 is the economic cycle and the leasing cycle.
| period |
0 |
1 |
2 |
3 |
4 |
5 |
| Save on purchase costs |
9.7 million |
|||||
| Give up depreciation tax deduction |
-65.96 |
-65.96 |
-65.96 |
-65.96 |
-65.96 |
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| Pay rent after tax |
-141.9 |
-141.9 |
-141.9 |
-141.9 |
-141.9 |
To sum up, within the 5-year use period, the net present value of the leasing plan is
NAL=970-65.96*4.2192-141.9*4.2192*1.0594=574,340
Leasing options are better. If the leasing option is more favorable, the after-tax rent L, s.t.:
NAL=970-65.96*4.2192-L*4.2192*1.0594>0
The solution is L<(970-65.96*4.2192)/(4.2192*1.0594)=1.547494 million
//Summary: Error-prone points: First, there are many cash flow figures, and it is easy to copy them incorrectly; second, the present value coefficient is easy to miscalculate, and it is easy to confuse between ordinary compound interest and annuity models; third, L in the table is after-tax data, it’s easy to forget to strip out the tax effects…
Considering that pre-tax figures are required when pricing, the lessor should quote
1,547,494/0.66=2,344,687.88 yuan
//English No.10The question is a continuation of the oil drilling platform (English No. 9), you don’t need to do it. First, the U.S. tax law is different from that of China. According to the IRS regulations, the number of years and annual depreciation depends entirely on the type of equipment, so no matter what happens here , depreciation is always calculated at 194 million per year. Second, there is a logical problem with question 10 - if there really is 70 With a residual value of million, the previous depreciation rate must not be 194194 million per year, otherwise there will be no net residual value left at all.
3)
The cash flow model is as follows. The period when the residual value reaches 0 is the economic cycle and the leasing cycle.
| period |
0 |
1 |
2 |
3 |
4 |
5 |
| Save on purchase costs |
9.7 million |
|||||
| Give up depreciation tax deduction |
-65.96 |
-65.96 |
-65.96 |
-65.96 |
-65.96 |
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| Pay rent after tax |
-141.9 |
-141.9 |
-141.9 |
-141.9 |
-141.9 |
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| deposit |
-150 |
+150 |
To sum up, within the 5-year use period, the net present value of the leasing plan is
NAL=970-65.96*4.2192-141.9*4.2192*1.0594-150+150/1.0594^5=19.84
Still better to rent
13【English Intermediate 14】
1) The cash flow of the leasing plan is as follows:
Annual depreciation 280/4*0.35=24.5
| Purchase plan |
0 |
1 |
2 |
3 |
4 |
| Save on purchase costs |
2.8 million |
||||
| Give up depreciation tax deduction |
-24.5 |
-24.5 |
-24.5 |
-24.5 |
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| After-tax rental expense |
-53.95 |
-53.95 |
-53.95 |
-53.95 |
The after-tax discount rate is 0.09*0.65=0.0585
Ordinary annuity present value coefficient (1-1.0585^(-4))/0.0585=3.4770
NAL=280-24.5*3.4770-53.95*3.4770*1.0585=-3.74
//Q: Logically speaking, financial decisions should have nothing to do with project investment decisions. Should the after-tax interest expense be included in the cash flow model?
//Answer: Irrelevance is paramount, and it is right not to consider interest.
//Q: It doesn’t seem like the coupon rate here is...the model is weird. Is it a difference equation?
//Answer: It’s just a test question. You can see that it’s impossible to test differential equations, so just boldly follow the conventional problem-solving methods. This is not writing a paper, why are you so serious?
2) Let NAL=280-24.5*3.4770-L*0.65*3.4770*1.0585=0
The solution is L=(280-24.5*3.4770)/(0.65*3.4770*1.0585)=814,300
Supplement【English Intermediate 15】
1) The lessor’s borrowing interest rate has nothing to do with it. Just look at the lessee’s borrowing rate (risk).
//Principle: For the lessor, this is an investment project. The project discount rate is based on the project risk. If the risk remains unchanged, WACC is enough; if the risk difference is large, it needs to be recalculated.
A lease is a secured bond issued by the lessee. From the equivalence of the cash flow model, it can be proved that discounting with the after-tax lessee interest rate is most appropriate.
//The lessor’s interest rate is lower, and the lessee’s interest rate is higher, which means that the lessee’s risk is higher. If you purchase the equipment yourself, you will pay higher costs. ;The rate of return required by the lessor is also lower. Therefore, the willingness to cooperate in leasing is stronger.
2) Let the pre-tax rent be L. Since there is no tax difference between the two parties, the calculation of NPV only has a positive or negative sign.
Calculate NAL from the lessee's perspective.
Annual depreciation 590000/3=196666.67
Depreciation tax deduction 196666.67*0.34=66866.67
The cash flow distribution is as follows
| period |
0 |
1 |
2 |
3 |
| Save money on purchases |
590000 |
|||
| Give up depreciation tax deduction |
-66866.67 |
-66866.67 |
-66866.67 |
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| After-tax rental expense |
-L*0.66 |
-L*0.66 |
-L*0.66 |
The discount rate is the after-tax secured borrowing interest rate 0.09*0.66=0.0594
The present value coefficient of ordinary annuity is (1-1.0594^(-3))/0.0594=2.6760
Calculated NAL=590000-66866.67*2.6760-L*0.66*2.6760>=0
The solution is L<=(590000-66866.67*2.6760)/(0.66*2.6760)=232,744.93
3) Consider the tenant first. Under no-tax conditions, the foregone depreciation tax deduction is 0, the annual expenditure is the book rent, and the discount rate is the pre-tax depreciation rate.
| period |
0 |
1 |
2 |
3 |
| Save money on purchases |
590000 |
|||
| Give up depreciation tax deduction |
0 |
0 |
0 |
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| After-tax rental expense |
-L |
-L |
-L |
The annuity present value coefficient is now (1-1.09^(-3))/0.09=2.5313
590000-L*2.5313>=0
解得L<=590000/2.5313=233081.82
其次考虑出租人。
| 时期 |
0 |
1 |
2 |
3 |
| 设备支出 |
-590000 |
|||
| 折旧抵税 |
66866.67 |
66866.67 |
66866.67 |
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| 税后租金收入 |
L*0.66 |
L*0.66 |
L*0.66 |
现金流和折现率都不变，由2)，L需大于等于232,744.93
//错解：用出租人公司风险代替投资项目风险。
税后利率为0.07*0.66=0.0462
年金现值系数现为(1-1.0462^(-3))/0.0462=2.7428
590000-(66866.67+L*0.66)*2.7428>=0
解得L<=(590000/2.7428-66866.67)/0.66=224609.06
//问：出租人的折现率要不要扣税？
//答：问题不是扣不扣税，而是出租人的折现率就是个干扰项。一切以承租人税后利率折现。