CHAPTER 24 Term Loans and Leases CHAPTER ORIENTATION The first section of this chapter provides an overview of the major sources of term loans and their characteristics The second section of the chapter provides an overview of lease financing, including a discussion of leasing arrangements, the accounting treatment of financial leases, the lease versus purchase decision, and the potential benefits from leasing CHAPTER OUTLINE I Term loans A In general, term loans have maturities from one to 10 years and are repaid in periodic installments over the life of the loan Term loans are usually secured by a chattel mortgage on equipment or a mortgage on real property The principal suppliers of term credit include commercial banks, insurance companies and, to a lesser extent, pension funds B The common attributes of term loans include the following: The maturities of term loans are usually as follows: a Commercial banks: to years b Insurance companies: to 15 years c Pension funds: to 15 years The collateral backing term loans: a Shorter maturity loans are usually secured with a chattel mortgage on machinery and equipment or securities such as stocks and bonds b Longer maturity loans are frequently secured by mortgages on real estate 65 II In addition to collateral, the lender on a term loan agreement will often require restrictive covenants that are designed to maintain the borrower's financial condition on a par with that which existed at the time the loan was made a Working capital restrictions involve maintaining a minimum current ratio that reflects the norm for the borrower's industry, as well as the lender's desires b Additional borrowing restrictions prevent the borrower from increasing the amount of debt financing outstanding without the lender's approval c A third covenant that is very popular requires that the borrower supply periodic financial statements to the lender d Term loan agreements often include a key-man provision that the borrower requires that the lender approve major personnel changes and insure the lives of "key" personnel with the lender named as the beneficiary Term loans are generally repaid in periodic installments in accordance with repayment schedules established by the lender Each installment includes both an interest and a principal component Frequently a bank will have demand for loans that exceeds its lending capacity In order to satisfy the demand, the bank will share the loan demand with other participating banks The participating banks receive a certificate of participation and a commitment from the lead bank to pay a portion of the loan cash flows as they are received Eurodollar loans are intermediate term loans made by major international banks to businesses based on foreign deposits denominated in dollars The rate of the loan is an amount greater than the London Interbank Offered Rate The Eurodollar loan market is governed by a limited number of regulations Leasing A There are three major lease agreements: direct leasing, sale and leaseback, and leveraged leasing In a direct lease the firm acquires the services of an asset it did not previously own Direct leasing is available through a number of financial institutions, including manufacturers, banks, finance companies, independent leasing companies, and special-purpose leasing companies Basically, direct leasing involves the purchase of the asset by the lessor from a vendor and leasing the asset to the lessee A sale and leaseback arrangement occurs when a firm sells land, buildings, or equipment that it already owns to a financial institution and simultaneously enters into an agreement to lease the property 66 back for a specified period under specific terms The lessee firm receives cash in the amount of the sales price of the asset sold and the use of the asset over the term of the lease In return, the firm must make periodic rental payments throughout the term of the lease to the lessor B C In a leveraged lease a third participant is added who finances the acquisition of the asset to be leased for the lessor From the lessee's standpoint, this lease is no different from the two lease arrangements discussed above But with a leveraged lease, specific consideration is given to the financing arrangement used by the lessor in acquiring the asset to be leased The accounting profession through Financial Accounting Statement No 13 requires the capitalization of any lease that meets one or more of the following criteria: The lease transfers ownership of the property to the lessee by the end of the lease term The lease contains a bargain repurchase option The lease term is equal to 75 percent or more of the estimated economic life of the leased property The present value of the minimum lease payments equals or exceeds 90% of the excess of the fair value of the property over any related investment tax credit retained by the lessor The lease–versus-purchase decision requires a standard capital budgeting type of analysis, as well as an analysis of two alternative "packages" of financing Two models are used to evaluate the lease versus purchase decision The first model computes the net present value of the purchase option which can be defined as follows: n NPV (P) = ACF t  t t  (1  K) - IO where ACFt = the annual after-tax cash flow resulting from the asset’s purchase in period t K = the firm's cost of capital applicable to the project being analyzed and the particular mix of financing used to acquire the project IO = the initial cash outlay required to purchase the asset in period zero (now) n = the productive life of the project 67 In the second model a net advantage to lease (NAL) over purchase equation is used that indicates the more favorable (least expensive) method of financing The equation used to arrive at NAL is as follows: n NAL = O t (1 - T) - R t (1 - T) - TI t - TD t (1  rb ) t  t - Vn (1  K s ) n + IO where Ot = any operating cash flows incurred in period t that are incurred only when the asset is purchased Most often this consists of maintenance expenses and insurance that would be paid by the lessor Rt = the annual rental for period t T = the marginal tax rate on corporate income It = the tax deductible interest expense foregone in period t if the lease option is adopted This level of interest expense was set equal to that which would have been paid on a loan equal to the full purchase price of the asset Dt = depreciation expense in period t for the asset Vn = the after-tax salvage value of the asset expected in year n Ks = the discount rate used to find the present value of V n This rate should reflect the risk inherent in the estimated Vn For simplicity, the after-tax cost of capital is often used as a proxy for this rate IO = the purchase price of the asset which is not paid by the firm in the event the asset is leased rb = the after-tax rate of interest on borrowed funds This rate is used to discount the relatively certain after-tax cash flow savings accruing through leasing the asset If NAL is positive, there would be a positive cost advantage to lease financing If NAL is negative, then purchasing the asset and financing with a debt plus equity package would be the preferred alternative However, we would lease or purchase the asset in accordance with the value of NAL in only two circumstances: a If NPV(P) is positive, then the asset should be acquired through the preferred financing method as indicated by NAL 68 b D If NPV(P) is negative, then the asset's services should be acquired via the lease alternative only if NAL is positive and greater in absolute value than NPV(P) That is, the asset should be leased only if the cost advantage of leasing (NAL) is great enough to offset the negative NPV(P) In effect, if a positive NAL were to more than offset a negative NPV(P), then the net present value through lease would be positive Over the years a number of potential benefits have been offered for lease financing Some of the more frequently cited advantages are enumerated and commented upon here Flexibility and convenience It is often argued that lease financing is more convenient than other forms of financing because smaller amounts of funds can be raised at lower cost In addition, it is often argued that lease payment schedules can be made to coincide with cash flows generated by the asset These may or may not be real advantages It depends on the actual circumstances faced by the lessee firm Lack of restrictions It has been argued that leases require fewer restrictions on the lessee than debt agreements Avoiding the risk of obsolescence This argument is generally conceded to be fallacious because the lessor includes his or her estimated cost of obsolescence in the lease terms Conservation of working capital Here it is argued that leasing involves no down payment However, the borrower could obtain the same effect by borrowing the down payment 100-percent financing The lease involves 100% financing but purchasing the asset would surely involve some equity As we noted above, the down payment could be borrowed to produce 100% financing via a loan In addition, it is not clear that 100% lease financing is desirable because it represents 100% non-owner financing Finally the lease agreement does not entitle the lessee to the asset's salvage value Thus, the lease provides 100% financing for the "use value" of the asset but not its "salvage value." Tax savings The difference in tax shelters between leasing and other forms of financing can only be evaluated by using a net advantage of lease model as we discussed earlier Ease of obtaining credit Lease financing may be more or less difficult to obtain than other forms of financing This advantage (or disadvantage) can only be evaluated on a case-by-case basis 69 ANSWERS TO END-OF-CHAPTER QUESTIONS 24-1 Intermediate-term financing includes all those financing arrangements with final maturities longer than one year and with a maximum of ten years Short-term financing is for a period of less than one year and long-term financing generally involves a period of more than ten years 24-2 The major types of restrictions usually found in the covenants of term loan agreements include: (1) Working capital requirement This restriction involves maintaining a minimum amount of working capital Very often this restriction takes the form of a minimum current ratio such as to or 1/2 to 1, or a minimum level of net working capital such as $200,000 (2) Additional borrowing Generally, this type of restriction will require the approval of the lender before any additional debt is issued The restriction is often extended to long-term lease agreements (3) Periodic financial statements A standard covenant in most term-loan agreements involves supplying the lender with periodic financial statements These usually include annual or quarterly-income statements and balance sheets (4) Management Term-loan agreements will sometimes include a provision requiring prior approval by the lender of major personnel changes In addition, the borrower may be required to insure the lives of certain "key" personnel with the lender named as beneficiary 24-3 (1) In a direct leasing agreement the firm acquires the services of an asset it did not previously own The lease basically involves purchase of the asset by the lessor from a vendor and leasing it to the lessee (2) Sale and leaseback arrangements arise when a firm sells land, buildings, or equipment which it already owns to a financial institution and simultaneously enters into an agreement to lease the property back for a specified period under specific terms (3) A net-net lease requires that the lessee maintain the leased asset and return it to the lessor at the end of the lease term with a value equal to a preestablished amount (4) An operating lease constitutes a cancelable contractual commitment on the part of the firm leasing the asset (the lessee) to make a series of payments to the firm which actually owns the asset (the lessor) for use of the asset 70 24-4 Prior to January, 1977, most financial leases were not included in the balance sheets of lessee firms They were instead reported in the footnotes to the balance sheet in accordance with APB Opinions and 31 In November, 1976, the accounting profession reversed its long standing position with Statement of Financial Account Standards No 13 entitled "Accounting for Leases." Specifically, Statement 13 requires that any lease which meets one or more of the following criteria be included in the body of the balance sheet of the lessee: (1) The lease transfers ownership of the property to the lessee by the end of the lease term (2) The lease contains a bargain repurchase option (3) The lease term is equal to 75 percent or more of the estimated economic life of the leased property (4) The present value of the minimum lease payments equals or exceeds 90 percent of the excess of the fair value of the property over any related investment tax credit retained by the lessor 24-5 The potential benefits from lease financing include: (1) Flexibility and convenience First, it is argued that leasing provides the firm with flexibility because it allows for piece-meal financing of relatively small asset acquisitions Second, leasing may allow a division or subsidiary manager to acquire equipment without the approval of the corporate capital budgeting committee Third, some lease payment schedules may be structured to coincide with the revenues generated by the asset, or they may be timed to match seasonal fluctuations in a given industry Arguments for the greater convenience of leasing may take many forms It is sometimes stated that leasing simplifies bookkeeping for tax purposes because it eliminates the need to prepare time-consuming depreciation tables and subsidiary fixed asset schedules It is also pointed out that the fixed payment nature of lease rentals allows more accurate forecasting of cash needs Finally, it is frequently noted that leasing allows the firm to avoid the "problems" and "headaches" associated with ownership (2) Lack of restrictions Lease contracts generally not contain protectivecovenant restrictions Furthermore, it is sometimes possible to exclude lease payments from the firm's debt commitments in calculating financial ratios under existing covenants (3) Avoiding the risk of obsolescence This argument states that a lease is advantageous because it allows the firm to avoid the risk that the equipment will become obsolete In actuality, the risk of obsolescence is passed on to the lessee in any financial lease, except in cases of operating cancelable operating leases, in which it is sometimes possible to avoid the risk of obsolescence 71 (4) Conservation of working capital The argument for conservation is that a lease does not require an immediate outflow of cash to cover the full purchase price of the asset and, therefore, the funds are retained in the business (5) 100 percent financing Another alleged benefit of leasing is embodied in the argument that a lease provides the firm with 100 percent financing It is pointed out that the borrow-and-buy alternative generally involves a down payment, whereas leasing does not (6) Tax savings It is also argued that leasing offers an economic advantage in that the tax shield generated by the lease payments usually exceeds the tax shield from depreciation that would be available if the asset were purchased (7) Ease of obtaining credit This alleged advantage of leasing concerns assertion that firms with poor credit ratings are able to obtain assets through leases when they are unable to finance the acquisitions with debt capital SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 24-1A Interest Rate Face Amount Year 10.0% $325,000.00 Payment Interest Principal 50,000.00 50,000.00 50,000.00 50,000.00 268,160.75 32,500.00 30,750.00 28,825.00 26,707.50 24,378.25 17,500.00 19,250.00 21,175.00 23,292.50 243,782.50 Balance 325,000.00 307,500.00 288,250.00 267,075.00 243,782.50 Thus, the fifth year balloon payment will equal the principal remaining at the end of that year of $243,782.50 plus interest for the year of $24,378.25 for a total of $268,160.75 24-2A Interest Rate Equipment Price Number of Payments Rental Payment 12.0% 100,000.00 10 15,802.16 Present Value of the Rental Payments $100,000.00 72 24-3A $100,000 = Payment Payment =  t t 1 (1.18) $100,000 = $31,979.53 3.127 24-4A Year Payment $31,979.53 31,979.53 31,979.53 31,979.53 31,979.53 Interest $18,000.00 15,483.68 12,514.43 9,010.71 4,876.33 Principal $13,979.53 16,495.85 19,465.10 22,968.82 27,103.20 Remaining Balance $86,020.47 69,524.62 50,059.52 27,090.70 (12.50) Rounding errors produced a $12.50 difference in the remaining balance and principal portion of the fifth year payment 24-5A (a) $200,000 = $59,663  t t 1 (1  r) where r = the effective annual rate on the computer sales firm loan  t t 1 (1  r) = $200,000 59,663 = 3.352 Looking in the annuity present value table we find that an r of 15% for a five year loan is 3.352 Thus, the effective rate on the loan is 15% (b ) (c) $250,000 = Payment Payment = $250,000 = $385,080 (1  r) Thus, r (d) 24-6A $250,000 3.274 = $250,000 $385,080 = 9%  t t 1 (1.16) = $76,359.19 (1  r)5 = 6492 The effective rate of interest is lowest on the insurance company loan In addition, the insurance company loan does not require an interim principal or interest payment during the five-year period Bank Loan Alternative: Cost = 14% 73 Manufacturer Financing Alternative: The cost of this alternative is not immediately apparent and must be calculated We know that the following relationship holds for any equal payment installment loan: n Loan Amount = Payment  t t 1 (1  k) where n is the term of the loan and k is the rate of interest charged on the remaining loan balance Using this relationship we can define $400,000 Therefore, = $140,106  t t 1 (1  k)  t t 1 (1  k) $400,000 $140,106 = = 2.855 We now know the present value of an annuity factor that corresponds to a four-year period and the rate of interest on the loan (k) Looking up this factor in the annuity present value table, we find that k = 15 percent Therefore, the bank loan alternative is preferred 24-7A.(a) Evaluating the purchase alternative: IO = $20,000 Annual net cash flows: Annual cash savings Less: depreciation Net revenues before taxes Less: taxes (50%) Book profits $6,000 (4,000) Cash flows $6,000 2,000 (1,000) 6,000 (1,000) Plus: salvage value $5,000 4,000 Annual after-tax cash flow (4) $9,000 NPV = $5,000  t + t 1 (1.12) $4,000 (1.12) - $20,000 = $5,000 (3.037 )+ $4,000 (0.636) - $20,000 = $15,185 + $2,544 - $20,000 = $17,729 - $20,000 = $-2,271 Thus, the asset should not be purchased (b) Evaluating the lease alternative: Calculating principal and interest on a loan of $20,000 at 10% 74 Annual payment = $20,000 / Year  t = t 1 (1.10) $6,309.15 Payment Interest Principal $6,309.15 6,309.15 6,309.15 6,309.15 $2,000.00 1,569.09 1,095.08 573.67 $4,309.15 4,740.06 5,214.07 5,735.48 Remaining Balance $20,000.00 15,690.85 10,950.79 5,736.72 1.24 Rounding errors produced a $1.24 difference in the remaining balance and principal portion of the fourth year payment (1) Year Solving for  t 1 Ot(1-T) - R(1-T) $500 500 500 500 $3,000 3,000 3,000 3,000 O t (1  T)  R t (1  T)  I t T  D t T (Term one) (1  rb ) t - It T $1,000 785 548 287 Vn (1  k s ) n (2) Solving for - (3) Adding IO (4) Net advantage of leasing - DtT $2,000 2,000 2,000 2,000 Discount = SUM Factor 5% -$5,500 0.952 - 5,285 0.907 - 5,048 0.864 - 4,787 0.823 Present Value -$ 5,236 - 4,794 - 4,361 - 3,940 (Term one) = -$18,331 (Term two) = -2,544 20,000 ($875) Since the asset's NAL is negative, the asset should not be leased 75 24-8A.(a) The basic analytical relationship needed to solve for installment payments is found below: n Loan Amount  t t 1 (1  k) = Payment Thus, for the first part of this exercise 10 $100,000  t t 1 (1.15) = Payment or 10 Payment = $100,000 ÷ (  t 1 ) (1.15) t 10 We recognize the summation term  t as a present t 1 (1.15) value annuity factor which is found in Appendix E Thus, Payment = $100,000 ÷ 5.019 = $19,924.29 (b) In this problem we must recall the procedure for quarterly compounding In general, the payment relationship in (a) becomes mn Loan Amount = Payment  t t 1 (1  k/m) where m is the number of compounding periods in a year (e.g., m = for quarterly compounding) Thus, 20 $100,000 = Payment  t t 1 (1.0375) Since the tables in Appendix E not have fractional rates we must solve for the present value annuity interest factor algebraically Payment = $100,000 ÷ 13.8962 = $7,196.21 76 (c) This problem requires that we first solve for the annual installment payments for each of the next five years based upon a 30-year installment period, i.e., 30 Payment = Loan amount ÷  t 1 (1  15) t or Payment = $100,000 ÷ 6.566 = $15,229.97 Next, we have to calculate the outstanding or remaining balance of the loan at the end of the fifth year where five annual installments of $15,229.97 have been made To this, we must go through the calculations outlined in Table 24-1 Remaining Year Loan Payment Interest Principal Balance $100,000.00 $15,229.97 $15,000.00 $ 229.97 99,770.03 15,229.97 14,965.50 264.47 99,505.56 15,229.97 14,925.83 304.14 99,201.42 15,229.97 14,880.21 349.76 98,851.66 113,679.41 14,827.75 98,851.66 Thus, the fifth year balloon payment will equal the principal remaining at the end of that year of $98,851.66 plus interest for the year of $14,827.75 for a total of $113,679.41 This type of loan agreement is frequently used by homeowners who give buyers a second loan on a home purchase The loan will usually be amortized or have installment payments calculated over a 30-year period but require full repayment in a 5- or 10-year period 77 SOLUTION TO INTEGRATIVE PROBLEM (a) Initial outlay (IO) = $60,000 Computing annual net cash flows Book profits $27,000 (12,500) Annual cash savings Less: depreciation Net revenues before taxes Less: taxes (50%) Cash flows $27,000 14,500 (7,250) 27,000 (7,250) Annual after-tax cash flows (1-3) Plus: salvage value $19,750 10,000 Annual after-tax cash flow (4) $29,750 Years 1-3 Year Calculating NPV (P): NPV(P) = $19,750  t t 1 (1.12) + $10,000 - $60,000 = $19,750(3.037) + $10,000(0.636) - $60,000 = $59,980.75 + $6,360 - $60,000 = $6,340.75 Thus, the computer should be acquired via normal purchase financing, as it has a positive NPV(P) of $6,340.75 (b) Calculating principal and interest components of a loan equal to the full $60,000 purchase price of the asset: Loan payment = $60,000 ÷ Year  t = t 1 (1.08) $18,115.94 Payment Principal Interest $18,115.94 18,115.94 18,115.94 18,115.94 $13,315.94 14,381.22 15,531.71 16,774.25 $4,800.00 3,734.72 2,584.23 1,341.69 Remaining Balance $60,000.00 46,684.06 32,302.84 16,771.13 (3.12) Rounding errors produced a $3.12 difference in the remaining balance and principal portion of the fourth year payment 78 (1) Year After-tax operating expenses paid by lessor Ot(1-T) After-tax rental expenses - 1,000 1,000 1,000 1,000  t 1 Solving for Rt(1-T) O t (1  T)  R t (1  T)  I t T  D t T (1  rb ) t Tax Shelter on loan (interest lost by leasing) - $9,000 9,000 9,000 9,000 It T (Term one) Depreciation Tax Shelter - $2,400 1,868 1,292 671 TDt Total SUM = $6,250 6,250 6,250 6,250 Discount Factor 4% x -$16,650 -16,118 - 15,542 - 14,921 (Term one) 591 (c) Vn Solving for: - (3) Adding: IO: (4) Net Advantage of Leasing (NAL) (1  k s ) n = - 10,000 (2) (1.12) = (Term two) (Term three) DF 0.962 0.925 0.889 0.855 = Present Value = PV -$16,017 - 14,909 - 13,817 - 12,757 - $57,500 = - 6,360 = 60,000 $ (3,860) The NAL is negative, indicating that lease financing is not preferred to normal purchase financing That is, the net present value of the asset, if leased, is equal to NPV(P) + NAL or $6,340 - $3,860 = $2,480 The asset should not be leased Solutions to Problem Set B 24-1B Interest Rate Face Amount Year Payment 12.0% $300,000.00 Interest 60,000.00 60,000.00 60,000.00 60,000.00 207,531.67 Principal 36,000.00 33,120.00 29,894.40 26,281.73 22,235.54 24,000.00 26,880.00 30,105.60 33,718.27 185,296.13 Balance 300,000.00 276,000.00 249,120.00 219,014.40 185,296.13 Thus, the fifth year balloon payment will equal the principal remaining at the end of that year of $185,296.13 plus interest for the year of $22,235.54 for a total of $207,531.67 24-2B Interest Rate Equipment Price Number of Payments Rental Payment 15.0% 250,000.00 10 43,315.67 Present Value of the Rental Payments $250,000.00 24-3B $100,000 = PAYMENT  t t 1 (1.16) Payment = $24,761.27 24-4B Year Payment $24,758.60 24,758.60 24,758.60 24,758.60 24,758.60 24,758.60 24,758.60 Interest $16,000.00 14,598.62 12,973.03 11,087.34 8,899.93 6,362.55 3,419.18 Principal $8,758.60 10,159.98 11,785.57 13,671.26 15,858.67 18,396.05 21,339.42 Remaining Balance $91,241.40 81,081.42 69,295.85 55,624.59 39,765.92 21,369.87 30.45 Rounding errors produced a $30.45 difference in the remaining balance and principal portion of the seventh year payment 80 24-5B (a)  t t 1 (1  r) $250,000 = $69,000 where r = the effective annual rate on the loan  t t 1 (1  r) = $250,000 = 3.623 69,000 Looking in the annuity present value table we find that an r of 12% for a fiveyear loan is 3.605 Thus, the effective rate on the loan is approximately 12% Actually, it is 11.79% (found using the Rate function in a financial spreadsheet) (b ) (c) = Payment Payment = $91,631.03 $300,000 = $425,000 (1  r) Thus, r (d) =  t t 1 (1.16) $300,000 (1  r)5 $300,000 = 7059 $425,000 = 7.21% The effective rate of interest is lowest on the insurance loan 24-6B Bank Loan Alternative: Cost = 14% Manufacturer Financing Alternative: The cost of this alternative is not immediately apparent and must be calculated We know that the following relationship holds for any equal payment installment loan: n Loan Amount = Payment  t t 1 (1  r) where n is the term of the loan and r is the rate of interest charged on the remaining loan balance 81 Using this relationship we can define $500,000 Therefore, = $175,000  t t 1 (1  r) =  t t 1 (1  r) $500,000 $175,000 = 2.857 We now know the present value of an annuity factor that corresponds to a fouryear period and the rate of interest on the loan (r) Looking up this factor in the annuity present value table, we find that r = 15 percent Therefore, bank loan alternative is preferred 24-7B (a) IO = $25,000 Annual net cash flows: Annual cash savings Less: depreciation Book profits $7,000 (5,000) Cash flows $7,000 2,000 (1,000) 7,000 (1,000) Net revenues before taxes Less: taxes (50%) Annual after-tax Cash flows Plus: salvage value $6,000 5,000 Annual after-tax cash flow (4) NPV = $6,000  t t 1 (1.13) $11,000 + $5,000 (1.13) - $25,000 = $6,000 (2.974) + $5,000 (0.613) - $25,000 = -$4,091.00 Thus, the asset should not be purchased 82 Years 1-3 Year (b) Calculating principal and interest on a loan of $25,000 at 10% Year Payment Interest $8,058.16 8,058.16 8,058.16 8,058.16 $2,750.00 2,166.10 1,517.98 798.56 (1) Solving for  t 1 Year 1  t = t 1 (1.11) Annual payment = $25,000/ $8,058.16 Principal $5,308.16 5,892.06 6,540.18 7,259.60 Remaining Balance $25,000.00 19,691.84 13,799.78 7,259.60 0.00 O t (1 - T) - R(1 - T) - I t T - D t T (1  rb )t Ot(1-T) - R(1-T) It T DtT 625.00 3,500 1,375.00 2,500.00 = SUM -6,750.00 PV Factor 9479 PV -6,398.32 625.00 3,500 1,083.05 2,500.00 -6,458.05 8985 -5,802.56 625.00 3,500 758.99 2,500.00 -6,133.99 8516 -5,223.71 625.00 3,500 399.28 2,500.00 -5,774.28 8072 -4,661.00 Term one= (Term two) = -22,085.59 (2) Solving for - -3,065.00 (3) Adding IO 25,000.00 (4) Net advantage of leasing - $ 150.59 Since the asset's NAL is negative, the asset should not be leased 24-8B (a) The basic analytical relationship needed to solve for installment payments is found below: Loan Amount n t 1 (1  k) t = Payment  83 Thus, for the first part of this exercise $125,000 12 t 1 (1.13) t = Payment  or Payment 12 t 1 (1.13) t = $125,000 ÷  12 t 1 (1.13) t We recognize the summation term  as a present value annuity factor which is found in Appendix E Thus, Payment = $125,000 ÷ 5.918 = $21,122.00 (b) In this problem we must recall the procedure for quarterly compounding In general, the payment relationship in (a) becomes mn t 1 (1  k/m) t Loan Amount = Payment  where m is the number of compounding periods in a year (e.g., m = for quarterly compounding) Thus, $125,000 24 t 1 (1.0325) t = Payment  Since the tables in Appendix E not have fractional rates we must solve for the present value annuity interest factor algebraically or using the "payment" function in a financial spreadsheet software package Payment = $7,581.11 84 (c) This problem requires that we first solve for the annual installment payments for each of the next five years based upon a 30-year installment period, i.e., 30 Payment = Loan amount ÷  t 1 (1  13) t or Payment = $125,000 ÷ 7.496 = $16,675.56 Next, we have to calculate the outstanding or remaining balance of the loan at the end of the fifth year where five annual installments of $16,675.56 have been made To this, we must go through the calculations outlined in Table 24-1 Year Loan Payment Interest $16,675.56 16,675.56 16,675.56 16,675.56 138,917.82 $16,250.00 16,194.68 16,132.16 16,061.52 15,981.70 Principal $ 425.56 480.88 543.40 614.04 122,936.12 Remaining Balance $125,000.00 124,574.44 124,093.56 123,550.16 122,936.12 0.00 Note that the fifth year balloon payment will equal the principal remaining at the end of that year of $122,936.12 plus interest for the year of $15,981.70 for a total of $138,917.82 This type of loan agreement is frequently used by homeowners who give buyers a second loan on a home purchase The loan will usually be amortized or have installment payments calculated over a 30-year period but require full repayment in a 5- or 10-year period 85 24-9B (a) Initial outlay (IO) = $65,000 Computing annual net cash flows Book profits $29,000 (14,250) Annual cash savings Less: depreciation Net revenues before taxes Less: taxes (50%) Cash flows $29,000 14,750 (7,375) 29,000 (7,375) Annual after-tax cash flows (1-3) $21,625 Plus: salvage value Years 1-3 8,000 Annual after-tax cash flow (4) $29,625 Year Calculating NPV (P): NPV(P) = $21,625  t 1 (1.14) t + $8,000 (1.14) - $65,000 = $21,625 (2.914) + $8,000 (0.592) - $65,000 = $2,751.25 Thus, the computer should be acquired via normal purchase financing, as it has a positive NPV(P) of $2,745.67 (b) Year Calculating principal and interest components of a loan equal to the full $65,000 purchase price of the asset: Loan payment = $65,000 /  t = $19,624.85 t 1 (1.08) Payment Principal Interest $19,624.85 19,624.85 19,624.85 19,624.85 $14,424.85 15,578.84 16,825.15 18,171.16 $5,200.00 4,046.01 2,799.70 1,453.69 86 Remaining Balance $65,000.00 50,575.15 34,996.31 18,171.16 0.00 (1) Solving for  t 1 Year After-tax operating expenses paid by lessor Ot(1-T) 1,125 1,125 1,125 1,125 After-tax rental expenses - Rt(1-T) $10,000 10,000 10,000 10,000 599 (c) O t (1  T)  R t (1  T)  I t T  D t T (1  rb ) t Tax Shelter on loan (interest lost by leasing) - It T Depreciation Tax Shelter - $2,600.00 2,023.01 1,399.85 726.85 8,000 (2) Solving for - = - (3) Adding: IO: (4) Net Advantage of Leasing (NAL) (1.14) TDt $7,125 7,125 7,125 7,125 = Discount Factor 4% Total = SUM x -$18,600.00 -18,023.01 - 17,399.85 - 16,726.85 DF Present Value = 0.962 0.925 0.889 0.855 (Term one) = -$64,333 (Term two) = - 4,736 (Term three) = 65,000 $ (4,069) The NAL is negative, indicating that lease financing is not preferred to normal purchase financing PV -$17,893 - 16,671 - 15,468 - 14,301 ... 24- 3B $100,000 = PAYMENT  t t 1 (1.16) Payment = $24, 761.27 24- 4B Year Payment $24, 758.60 24, 758.60 24, 758.60 24, 758.60 24, 758.60 24, 758.60 24, 758.60 Interest $16,000.00 14,598.62 12,973.03 11,087.34... of the asset: Loan payment = $65,000 /  t = $19, 624. 85 t 1 (1.08) Payment Principal Interest $19, 624. 85 19, 624. 85 19, 624. 85 19, 624. 85 $14, 424. 85 15,578.84 16,825.15 18,171.16 $5,200.00 4,046.01... when they are unable to finance the acquisitions with debt capital SOLUTIONS TO END-OF -CHAPTER PROBLEMS Solutions to Problem Set A 24- 1A Interest Rate Face Amount Year 10.0% $325,000.00 Payment Interest