# CHAPTER 25. P The following data are furnished by the Hypothetical Leasing Ltd (HLL):

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1 CHAPTER 25 Solved Problems P The following data are furnished by the Hypothetical Leasing Ltd (HLL): Investment cost Rs 500 lakh Primary lease term 5 years Estimated residual value after the primary period Nil Pre-tax required rate of return 24 per cent The HLL seeks your help in determining the annual lease rentals under the following rental structures: (a) Equated, (b) Stepped (an annual increase of 15 per cent), (c) Ballooned (annual rental of Rs 80 lakh for years 1 4) and (d) Deferred (2 years deferment period). You are required to compute the relevant annual rentals. (a) Equated annual lease rentals, Y: Y = Investment cost/pvifa (24, 5 years) = Rs 500 lakh/2.745 = Rs lakh (b) Stepped lease rental (assuming annual increase of 15 per cent annually), Y: Y PVIF(24, 1) + (1.15)Y PVIF(24, 2) + (1.15) 2 Y PVIF(24, 3) + (1.15) 3 Y PVIF(24, 4) + (1.15) 4 Y PVIF(24, 5) = Rs 500 lakh. Or 0.806Y Y Y Y Y = Rs 500 lakh Or Y = Rs 500 lakh or Y = Rs 500 lakh/ = Rs lakh Lease rentals (year-wise) (in lakh of rupees) Year Lease rent (c) Ballooned lease rental (Rs 80 lakh for years, 1 4) Rs 80 lakh PVIFA(24, 4), + Y PVIF (24, 5) = Rs 500 lakh Rs 80 lakh Y = Rs 500 lakh 0.341Y = Rs 500 lakh Rs lakh = Rs lakh or Y = Rs /0.341 = Rs lakh (ballooned payment) (d) Deferred lease rental (deferment of 2 years) Denoting Y as the equated annual rental to be charged between years 3 5, Y PVIF (24, 3) + Y PVIF (24, 4) + Y PVIF (24,5) = Rs 500 lakh Y Y Y = Rs 500 lakh Y = Rs 500 lakh/1.288 = Rs lakh. P Mr X, the Finance Manager of ABC Ltd, had almost decided to finance the purchase of Rs 20 lakh in new computer equipment with 16 % long-term debt when he was contacted by First Leasing Company Ltd. The manager of the leasing company tried to convince Mr X that leasing the equipment would be more beneficial to ABC Ltd. If ABC borrowed, the firm would be required to pay 16 per cent interest on the borrowed funds plus an annual sinking fund payment of Rs 2,00,000. The equipment has an expected life of 10 years, with an anticipated salvage value of Rs 4,00,000. The firm uses the straight line method of depreciation, and is in the 50 per cent tax bracket. The leasing company is willing to lease the equipment for Rs 3,80,000 per year. Further, it was stressed that the lease payments were fully tax deductible, while debt repayment was not. Mr X seeks your advice before committing to lease the computer equipment. What advise would you, as a financial consultant, give to the finance manager of ABC Ltd? PV of cash outflows under leasing alternative Year end Lease payment after PV factor Total PV taxes (L) (1 0.5) (0.08) 1 10 Rs 1,90, Rs 12,74,900

3 on interest depreciation (Col 2 tax cost alternative payment (Col 3 + 4) of debt (0.07) Rs 1,00,000 Rs 24,031 Rs 34,330 Rs 41, Rs 38, ,00,000 20,395 34,330 45, , ,00,000 16,250 34,330 49, , ,00,000 11,526 34,330 54, , ,00,000 6,147 34,330 59, ,440 m Total 2,02,536 Recommendation Since the PV of cash outflows for buying/borrowing (Rs 2,02,536) is lower than that of leasing (Rs 2,46,000), the buying alternative is preferred. (b) PV of cash outflows under leasing alternative, when lease rental is paid in advance Year-end Lease payment Tax shield Cash outflows PV factor Total PV after taxes (0.07) Rs 1,20,000 Rs 1,20, Rs 1,20, ,20,000 Rs 60,000 60, ,03, ,000 (60,000) (42,780) 2,80,440 Recommendation Buying alternative is better. P For the Hypothetical Ltd in P.25.3 assume, (i) The company follows written down value method of depreciation, the depreciation rate being 25 per cent. There is no other asset in this asset block; (ii) The corporate tax rate is 35 per cent; (iii) Post-tax marginal cost of capital is 10 per cent; (iv) Salvage value, Rs 40,000 at the end of 5th year. Compute the NAL to the lessee if lease rentals are paid (a) at the end of the year (b) in advance. (a) Computation of NAL (lease rentals are paid in arrear, that is, at the year-end) Benefits from leasing: Cost of the machine Rs 3,43,300 PV of tax shield on lease rentals (working note 2) 1,59,222 Total 5,02,522 Cost of leasing: PV of lease rentals (1) 4,11,960 PV of tax shield foregone on depreciation (3) 67,259 PV of interest tax shield foregone on debt (4) 43,810 PV of salvage proceeds (Rs 40, ) 24,840 PV of tax shield on short-term capital loss (5) 24,018 Total 5,71,887 NAL (69,365) Recommendation Leasing is not financially viable. (1) PV of lease rentals: Lease rentals PVIFA (14,5) = Rs 1,20, = Rs 4,11,960 (2) PV of tax shield on lease rentals: Rs 1,20, = Rs 1,59,222 (3) PV of shield foregone on depreciation Year Depreciation* Tax shield PV factor (at 0.10) Total PV 1 Rs 85,825 Rs 30, Rs 27, ,369 22, , ,277 16, , ,207 12, ,655 67,259 *No depreciation is to be charged in 5 th year as the block of assets ceases to exist.

4 (4) PV of interest tax shield Year Interest Tax shield PV factor (at 0.10) Total PV 1 Rs 48,062 Rs 16, Rs 15, ,791 14, , ,501 11, , ,052 8, , ,294 4, ,672 43,810 (5) PV of tax shield on short-term capital loss: (Cost of machine Accumulated depreciation Salvage value) t = (Rs 3,43,000 Rs 2,34,678 Rs 40,000) = Rs 68, = Rs 24,018. (b) Computation of NAL (lease rentals are paid in advance) Benefits from leasing: Cost of the machine Rs 3,43,300 PV of tax shield on lease rentals 1,59,222 Total 5,02,522 (Contd.) Cost of leasing: PV of lease rentals (1) 4,69,680 PV of tax shield foregone on depreciation 67,259 PV of interest tax shield foregone on debt 43,810 PV of salvage proceeds 24,840 PV of tax shield on short-term capital loss 24,018 Total 6,29,607 NAL (1,27,085) Recommendation Leasing is not financially viable. (1) PV of lease rentals Year Lease payment PV factor (at 0.14) Total PV 0 Rs 1,20, Rs 1,20, ,20, ,49,680 4,69,680 P For the facts in P.25.19, determine the break even lease rental (BELR) for the lessee in both the situations. (a) Computation of BELR (lease rents are paid at the end of the year) Benefits from leasing: Cost of the machine Rs 3,43,300 PV of tax shield on lease rentals (2) L Cost of leasing: PV of lease rentals (1) 3.433L PV of tax shield foregone on depreciation Rs 67,259 PV of interest tax shield foregone on debt 43,810 PV of salvage proceeds 24,840 PV of tax shield on short-term capital loss 24,018 1,59,927 BELR (L) = Rs 3,43, L = 3.433L + Rs 1,59, L = Rs 1,83,373 L = Rs 82,177 (1) PV of lease rentals: L PVIFA (14,5) = L = 3.433L (2) PV of tax shield on lease rentals: 3.433L tax rate = 3.433L 0.35 = L Benefits from leasing (b) BELR (lease rents paid in advance)

5 Cost of the machine Rs 3,43,300 PV of tax shield on lease rentals (2) L Cost of leasing PV of lease rentals (1) 3.914L Other costs (already computed) 1,59,927 BELR(L) = Rs 3,43, L = 3.914L + Rs 1,59, L = Rs 1,83,373 L = Rs 1,83,373/ = Rs 72,078 (1) PV of lease rentals = L = 3.914L, PVIFA = (years, 1 4) + 1 (year 0) = (2) PV of tax shield on lease rentals: 3.914L 0.35 = L P Agrani Ltd. is in the business of manufacturing bearings. Some more product lines are being planned to be added to the existing system. The machinery required may be bought or may be taken on lease. The cost of machine is Rs 40,00,000 having a useful life of 5 years with the salvage value of Rs 8,00,000. The full purchase value of machine can be financed by 20 per cent loan repayable in five equal instalments falling due at the end of each year. Alternatively, the machine can be procured on a 5 years lease, year-end lease rentals being Rs 12,00,000 per annum. The Company follows the written down value method of depreciation at the rate of 25 per cent. Company s tax rate is 35 per cent and cost of capital is 16 per cent. (i) Advise the company which option it should choose lease or borrow. (ii) Assess the proposal from the lessor s point of view examining whether leasing the machine is financially viable at 14 per cent cost of capital (Detailed working notes should be given). (i) PV of cash outflows under leasing alternative Year-end Lease rent after taxes PVIFA at 13 per cent Total PV [LR (1-t)] [Rs 12,00,000 (1 0.35)] [20% (1 0.35)] 1-5 Rs 7,80, Rs 27,43,260 (ii) Borrowing/Buying option Equivalent annual loan instalment = Rs 40,00,000/2.991 (PVIFA for 5 years at 20 per cent) = Rs 13,37,345. PV of cash outflows under buying alternative Year- Loan Tax advantage on Net cash outflows PVIF Total PV end instalment on Interest Depreciation at 13% (I 0.35) (D 0.35) (Col. 2 Col ) Rs 13,37,345 Rs 2,80,000 Rs 3,50,000 Rs 7,07, Rs 6,26, ,37,345 2,42,386 2,62,500 8,32, ,51, ,37,345 1,97,249 1,96,875 9,43, ,53, ,37,345 1,43,084 1,47,656 10,46, ,41, ,37,345 77,635 1,10,742 11,48, ,23,890 Total PV of cash outflows 31,96,926 Less: PV of salvage value (Rs 8,00, ) 4,34,400 Less: PV of tax savings on short-term capital loss (9,49,279 8,00,000) 0.35 = (52, ) 28,358 NPV of cash outflows 27,34,168 Schedule of debt payment Year- Loan Loan at the Payments Loan outstanding end instalment beginning of Interest Principal at the year the year (Col. 3 20%) repayment (Col. 3 Col. 5) Rs 13,37,345 Rs 40,00,000 Rs 8,00,000 Rs 5,37,345 Rs 34,62, ,37,345 34,62,655 6,92,531 6,44,814 28,17, ,37,345 28,17,841 5,63,568 7,73,777 20,44,064

6 4 13,37,345 20,44,064 4,08,813 9,28,532 11,15, ,37,345 11,15,532 2,21,813* 11,15,532 *Difference between loan instalment and loan outstanding. Schedule of Depreciation Year Depreciation Balance at the end of the year 1 Rs 40,00, = Rs10,00,000 Rs 30,00, ,00, = 7,50,000 22,50, ,50, = 5,62,500 16,87, ,87, = 4,21,875 12,65, ,65, = 3,16,406 9,49,219 (ii) Recommendation The Company is advised to go for borrowing as the PV of cash outflows under borrowing option is lower than under leasing alternative. Assumption The machine is sold after the expiry of its useful of 5 years; for this reason, the depreciation is charged in 5th year and there is no other asset in this block. Determination of NPV of cash inflows Particulars Years Lease rent Rs 12,00,000 Rs 12,00,000 Rs 12,00,000 Rs 12,00,000 Rs 12,00,000 Less: Depreciation 10,00,000 7,50,000 5,62,500 4,21,875 3,16,406 Earnings before taxes 2,00,000 4,50,000 6,37,500 7,78,125 8,83,594 Less: Taxes (0.35) 70,000 1,57,500 2,23,125 2,72,344 3,09,258 Earnings after taxes 1,30,000 2,92,500 4,14,375 5,05,781 5,74,336 Cash inflows after taxes 11,30,000 10,42,500 9,76,875 9,27,656 8,90,742 (x) PV factor at (0.14) Present value 9,91,010 8,01,682 6,59,391 5,49,172 4,62,295 Total PV of operating CFAT 34,63,550 Add: PV of salvage value of machine (8,00, ) 4,15,200 Add: PV of tax savings on short-term capital loss (52, ) 27,105 Gross PV 39,05,855 Less: Cost of machine 40,00,000 NPV (94,145) Recommendation It is not financially profitable to let out the machine on lease by the leasing Company, as NPV is negative. Assumption The machine is to be sold after the expiry of 5 years. There is no other asset in the block of 25 per cent of the lessee. P The Hypothetical Equipments Ltd (HEL) has recently leased assets worth Rs 2,500 lakh from the Hypothetical Leasing Ltd (HLL). The following facts are available: (1) Lease period, 9 years, of which the first 6 years constitute the lease term; (2) Annual lease rates: First 6 years, Rs 360/Rs 1,000; Next 3 years, Rs 15/Rs 1,000; (3) Incremental borrowing rates for HEL, 22 per cent. (a) Assuming 14 years as the average economic life of the equipment, is the lease a finance lease or an operating lease (b) Assuming further (i) physical life of 14 years, (ii) technological life of 9 years and (iii) productmarket life of 11 years, how will you classify the lease? A lease is finance lease if one of the following two conditions is satisfied: (i) The lease term exceeds 75 per cent of the useful life of the equipment (the minimum of physical useful life, technological life and product market life). (ii) The PV of lease payments exceeds 90 per cent of the fair market value of the equipment (cost of equipment), the discount rate being incremental borrowing rate in the case of lessee and cost of capital in the case of lessor.

7 (a) (i) Term of lease is 9/14 years = 64 per cent. (ii) Determination of PV of lease payment (Rs in lakh) Year Lease payment Discount factor (0.22) Total PV Rs 2, * 23 2,873 *( ) The lease is finance lease as the PV of lease payment exceeds the cost of asset. (b) Finance lease as term of lease is 9/9 = 100 per cent. P From the given facts relating to the Hypothetical Leasing Ltd, calculate the annual rentals under the following rental structure for the 6-year period; (a) Equated, (b) Stepped (annual increase of 12 per cent), (c) Ballooned (annual rental of Rs 15 lakh for year 1 and 2) (d) Deferred (deferment period of 1 year). Investment cost Rs 96 lakh Primary lease term 3 years Residual value Nil Pre-tax required rate of annual return 22 per cent Assume that the lease can be renewed for an additional period of 3 years (secondary lease period). The lease rental for the secondary period will be 5 per cent of the rental charged during the primary period. (a) Equated annual lease rentals, Y Y PVIFA (22, 3) Y PVIFA (22, 4 6) = Rs 96 lakh 2.042Y Y = Rs 96 lakh Y = Rs 96 lakh/ = Rs lakh (primary lease period); Rs 2.29 lakh (secondary lease period). (b) Stepped lease rentals (annual increase of 12 per cent) Y PVIF (22, 1) Y PVIF (22, 2) + (1.12) 2 Y PVIF (22, 3) + (1.12) 3 Y PVIF (22, 4) + (1.12) 4 Y PVIF (22, 5) + (1.12) 5 Y PVIF (22, 6) = Rs 96 lakh Or 0.820Y Y Y Y Y Y = Rs 96 lakh Or Y = Rs 96 lakh/ = Rs lakh (c) Ballooned lease rentals (Rs 15 lakh for years 1 2) Rs 15 lakh PVIFA (22, 2) + Y PVIF (22, 3) Y PVIFA (22, 4 6) = Rs 96 lakh Rs lakh Y Y = Rs 96 lakh Y = Rs 96 lakh Rs lakh/ = Rs lakh (d) Deferred lease rentals (deferment of 1 year), Y Y PVIF (22, 2) + Y PVIF (22, 3) Y PVIF (22, 4 6) = Rs 96 lakh 0.672Y Y Y = Rs 96 lakh Y = Rs 96 lakh/ = Rs lakh P Hypothetical Ltd is expanding its facilities. In the coming year, the company will either purchase or lease equipment which it plans to use for 4 years and then replace it with a new one. Its current tax bracket is 50 per cent. The other data are as follows: Purchase: (i) The purchase price of the equipment is Rs 40,00,000, (ii) The expected salvage value after 4 years is Rs 10,00,000, (iii) The equipment is subject to the straight line method of depreciation, (iv) Funds to finance the equipment can be obtained at 16 per cent, (v) The loan is to be repaid in four equal annual instalments due at the end of each year, (vi) The equipment will increase the annual revenues by Rs 30,00,000, and increase annual cash operating costs by Rs 20,00,000. Leasing: (i) The annual lease is Rs 10,00,000, (ii) The lease rent is payable at the end of each year for 4 years, (iii) The equipment will increase annual revenues by Rs 30,00,000 and increase annual non-depreciation operating costs by Rs 19,00,000, as the lessor will pay Rs 1,00,000 for the maintenance costs associated with the equipment. Determine whether the company should purchase or lease the equipment. PV of cash outflows under leasing alternative

8 Year- Effective lease payment PV factor Total end Gross Savings Net Tax Cash (0.08) PV in main- (Col 2 shield outflows tenance costs Col 3) (Col ) after taxes Rs 10,00,000 Rs 1,00,000 Rs 9,00,000 Rs 4,50,000 Rs 4,50, Rs 14,90,400 Determination of interest and principal components of loan instalment Year- Loan Loan at Payment of Principal end instalment the beginning out-standing Interest Principal at the end (Col ) (Col 2 Col 4) of the year Rs 14,29,593* Rs 40,00,000 Rs 6,40,000 Rs 7,89,593 Rs 32,10, ,29,593 32,10,407 5,13,665 9,15,928 22,94, ,29,593 22,94,479 3,67,117 10,62,476 12,32, ,29,593 12,32,003 1,97,590 12,32,003 *Rs 40,00, that is, PV annuity factor of 4 years at 16 per cent. PV of cash outflows under buying alternative Year Loan Interest Depreciation Cash outflows PV factor Total PV instalment (I t) (D t) after taxes (0.08) [Col 2 (Col 3 + Col 4)] Rs 14,29,593 Rs 3,20,000 Rs 3,75,000 Rs 7,34, Rs 6,80, ,29,593 2,56,832 3,75,000 7,97, ,83, ,29,593 1,83,558 3,75,000 8,71, ,91, ,29,593 98,795 3,75,000 9,55, ,02,512 4 Salvage value (10,00,000) (7,35,000) 20,23,028 Recommendation The lease alternative is better, as it is a cheaper source of finance than debt in terms of the NPV of the cash outflows. Review Questions Beta Limited is considering the acquisition of a personal computer costing Rs 50,000. The effective life of the computer is expected to be 5 years. The company plans to acquire the same either by borrowing Rs 50,000 from its banker at 15 per cent interest per annum or by lease. The company wishes to know the lease rentals to be paid annually which will match the loan option. The following further information is provided to you. (a) The principal amount of the loan will be paid in 5 annual equal instalments. (b) Interest, lease rentals, principal repayments are to be paid on the last day of each year. (c) The full cost of the computer will be written off over the effective life of computer on a straight-line basis and the same will be allowed for tax purposes. (d) The company s effective tax rate is 40 per cent and the after-tax cost of capital is 9 per cent. (e) The computer will be sold for Rs 1,700 at the end of the fifth year. The commission on such sales is 9 per cent on the sale value and the same will be paid. You are required to compute the annual lease rentals payable by Beta Ltd. which will result in indifference to the loan option Welsh Limited is faced with a decision to purchase or acquire on lease a mini car. The cost of the mini car is Rs 1,26,965. It has a life of 5 years. The mini car can be obtained on lease by paying in advance equal lease rentals annually. The leasing company desires a return of 10 per cent on the gross value of the asset. Welsh Limited can also obtain 100 per cent finance from its regular banking channel. The annual

9 rate of interest will be 15 per cent and the loan will be paid in 5 annual equal instalments, inclusive of interest, each instalment becoming due at the beginning of the year. The effective tax rate of the company is 40 per cent. For the purpose of taxation, it is to be assumed that the asset will be written off over a period of 5 years on a straight line basis. (a) Advise Welsh Limited about the method of acquiring the car. (b) What should be the annual lease rental to be charged by the leasing company to match the loan option? Computeronics Ltd sells computer services to its clients. The company has recently completed a feasibility study and decided to acquire an additional computer the details of which are as follows: 1. The purchase price of the computer is Rs 2,30,000; maintenance, property taxes and insurance will be Rs 20,000 per year. The additional annual expenses to operate the computer are estimated at Rs 80,000. If the computer is rented, the annual rent will be Rs 85,000, plus 5 per cent of annual billings. The rent is due on the last day of each year. Maintenance expenses are to be borne by the lessor. 2. Due to competitive conditions, the company feels it will be necessary to replace the computer at the end of of 3 years with a more advanced model. The resale value is estimated at Rs 1,10, The appropriate income tax rate is 50 per cent, and the straight-line method of depreciation is used. 4. The estimated annual billing for the services of the new computer will be Rs 2,20,000 during the first year, and Rs 2,60,000 during the subsequent two years. 5. If the computer is purchased, the company will borrow to finance the purchase from a bank with interest at 16 per cent. The interest will be paid regularly, and the principal will be returned in one lumpsum at the end of year 3. Assuming cost of capital at 12 per cent, you are required to analyse the financial viability of the proposal from the viewpoint of the leasing company as well as the Lessor. Answers Rs 14, (a) Leasing option is better; PV of cash outflows under lease is Rs 81,719; PV of cash outflows under borrowing and buy option is Rs 87,442, (b) Rs 34, (a) Computeronics should buy the computer (PV of cash outflows under leasing alternative is Rs 1.25 lakh and under buying alternative is Rs 1.17 lakh) (b) Proposal is financially unsound from the point of leasing company ( NPV of Rs 0.11 lakh).

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