This Document Contains Chapters 17 to 18 Brealey 5CE Solutions to Chapter 17 1. a. i, iii b. iv, ix c. ii, v d. vii e. i f. viii g. vii 2. a. Rational reason for an operating lease but not for a financial lease. b. Rational reason for an operating lease but not for a financial lease. c. Not a rational reason. This can be accomplished through borrowing too. d. Rational reason. A major reason for leasing. e. Not a rational reason. Financial analysts can see through the accounting effects of leasing. f. Rational reason, especially for small companies. g. Not a rational reason. If there is a valid reason for capital expenditure controls, they should apply to leasing too. 3. a. False. Operating leases are costly because of the lessee’s option to cancel the lease. Don’t buy an option if you don’t need it. b. False. Lease obligations are disclosed in footnotes or capitalized. Lease financing not hidden. 4. a. True, typically leases are set up with the first payment due immediately. b. True. The accounting rules (GAAP) specify the conditions under which a financial lease must be capitalized on the balance sheet. However, it is 17-1 This Document Contains Chapters 17 to 18 possible to set up the financial lease so that it does not meet these conditions. The financial lease can be treated as off-balance sheet financing, just as operating leases are treated. c. True. The riskiness of the lease is similar to the riskiness of the firm’s secured borrowing. Thus it makes sense to discount the lease cash flows at the firm’s cost of a bank loan. d. False. The equivalent loan’s principal repayment plus after-tax interest payments (otherwise known as after-tax debt service) exactly match the after-tax cash flows of the lease. The equivalent loan’s principal, the amount borrowed through the equivalent loan, may not equal to the initial cash inflow of the lease. We look at the equivalent loan amount to see whether it is greater or smaller than the initial lease cash inflow. e. True. Borrow through the lease if it offers more financing than an equivalent loan. f. True. By leasing the capital cost allowance of the lease is used by the lessor, who has taxable income to shelter, and not by the lessee, who has no taxable income. g. True. As interest rates increase, the advantage of transferring the capital cost allowance to a higher-taxed lessor increases. From the lessee’s perspective, the cost of foregoing the CCA decreases, making the lease more attractive. 5. a. The value of the equivalent loan is the present value of the after-tax lease cash outflows, discounted at the after-tax cost of borrowing, (1 - .3) × .10 = .07, 7%: Equivalent loan = 26,800 1.07 + 22,200 1.072 + 17,600 1.073 = $58,803.91 b. Value of the lease = NPV of lease = Initial lease cash inflow – equivalent loan = 62,000 – 58,803.91 = $3,196.09. The lease will add positively to the value of the purchase. c. NPV of buying machine and entering the lease = -5,000 + 3,196.09 = -$1,803.91 It should not invest. The lease’s positive value does not the offset the machine’s negative NPV. The company would be happy to sign the same lease on a more attractive asset. 17-2 6. “100 percent financing” is not a unique advantage to the lessee because precisely the same cash flows can be arranged through borrowing (as an alternate source of financing for the acquisition of an asset.) 7. a. We assume that had the forklift been purchased, rather than leased, the purchase would occur at the end of Year 0, allowing the company to take a CCA deduction in Year 0. At the end of Year 5, the forklift would have been scrapped and worth nothing. A terminal loss equal to the undepreciated capital cost of $20,764 would be taken, resulting a tax savings of .35×$20,764, or $7,267. Lease cash flows: End of Year 0 1 2 3 4 5 Saved cost 75,000 CCA tax shield -3,281 -5,742 -4,307 -3,230 -2,422 -7,267 Lease payment -15,000 -15,000 -15,000 -15,000 -15,000 0 Lease tax shield 5,250 5,250 5,250 5,250 5,250 0 Lease cash flows 61,969 -15,492 -14,057 -12,980 -12,172 -7,267 Details of CCA Tax Shield 0 1 2 3 4 5 UCC 75,000 65,625 49,219 36,914 27,686 20,764 CCA 9,375 16,406 12,305 9,229 6,921 CCA tax shield 3,281 5,742 4,307 3,230 2,422 7,267 Equivalent loan = 15,492 1.0585 + 14,057 1.05852 + 12,980 1.05853 + 12,172 1.05854 + 7,267 1.05855 = $53,292 NPV of leasing rather than borrowing = 61,969 – 53,292 = $8,677 Under these conditions, ABC should lease rather than borrow. c. The salvage value is of higher risk than the lease. It is reasonable to assume it is as risky as the project. We assume that the forklift will be sold at the end of the 5th year. The present value of the salvage value is: PV(Salvage) = 10,000 1.125 = $5,674 b. After-tax interest rate = (1 - .35) × .09 = .0585 17-3 By leasing, the company foregoes the salvage value of $5,674. However, with the salvage value, the CCA must be recalculated. In Year 5, $10,000 is subtracted from the asset pool, leaving undepreciated capital cost of $20,764 - $10,000 = $10,764. Thus the terminal loss is smaller by the amount of the salvage value and the allowable tax savings is .35 × $10,764 = $3,767.4. The change in the tax savings due to the reduced terminal loss is $3,767.4 - $7,267= -$3,499.6 = - $3,500 What discount rate should be used to find the present value of the reduction in tax savings? If the salvage value is uncertain, so too must be the tax consequences. We choose to discount the change in tax savings at 12%. PV(Change in tax savings from reduced terminal loss) = -3,500 1.125 = - $1,986 New NPV of leasing rather than borrowing = $8,677 - $5,674 - $1,986 = $1,017 It still makes sense to lease the forklift. 8. a. After-tax cost of debt = .08 × (1 - .3) = .056 = 5.6% D/E = .5 To convert to D/V think of D/E as .5/1 Then V = D + E = .5 + 1 = 1.5 Thus: D/V = .5/1.5 = 1/3 and E/V = 2/3 WACC = 1/3 × .08 × (1 - .3) + 2/3 × .12 = 0.0987 = 9.87% Assuming that the riskiness of the investment in the new colour printer is the same as Printing World's overall risk, we can discount the cash flows from the investment at Printing World's WACC. Thus, the NPV of the investment is the sum of the present value of all of the project's cash flows, assuming it is financed using the firm's current mix of financing: NPV of purchasing the press = - initial cost + PV(After-tax incremental operating cash flows) + PV(CCA tax savings) Timing of the Purchase and Sale of the Press In this problem, we assume that the press is purchased at the end of Year 0 and the tax savings from the first CCA deduction occurs at Year 0. We also assume that press is sold on the last day of Year 4. Thus terminal loss of $145,774 occurs in Year 4, creating a tax shield of .3 × $145,774, or 17-4 $43,732. Year 0 Year 1 Year 2 Year 3 Year 4 UCC 500,000 425,000 297,500 208,250 145,775 CCA 75,000 127,500 89,250 62,475 0 CCA tax shield 22,500 38,250 26,775 18,743 43,732 PV(CCA tax savings) = 22,500 + 38,250 1.0987 + 26,775 1.09872 + 18,743 1.09873 + 43,732 1.09874 == $123,638 NPV of purchasing the press = - initial cost + PV(After-tax incremental operating cash flows) + PV(CCA tax savings) = -500,000 + (1 - .3) × 215,000 annuity factor(9.87%, 4) + 123638 = -500,000 + 478,410 + 123638= $102,048 With a positive NPV, Printing World should buy the printing press. Note: Discounting the CCA tax savings at WACC is consistent with the assumptions made in Chapter 9. However, it is inconsistent with the use of the after-tax cost of debt to discount the lease cash flows. Why should the same cash flows be discounted at different rates? What is the technically correct discount rate? It depends on the assumed riskiness of the CCA tax savings. If the company is confident that it will have sufficient taxable income to take advantage of the CCA, then the appropriate discount rate for the CCA tax savings is after-tax cost of debt, rather than WACC. This would be consistent with the discount rate used to evaluate the lease cash flows. The present value of the CCA tax shield, discounted at the after-tax cost of debt, is: PV(CCA tax savings) = 22,500 + 38,250 1.056 + 26,775 1.0562 + 18,743 1.0563 + 43,732 1.0564 = $133,816 This makes the new printing press an even more attractive investment. However, the common business practice is to discount the project's cash flows at the appropriate project cost of capital (WACC) and the evaluate the lease cash flows at the after-tax cost of debt. Thus the inconsistency in the discount rates is ignored. 17-5 . b. Cash flows from leasing rather than borrowing to purchase the press: Year 0 Year 1 Year 2 Year 3 Year 4 Saved cost of press 500,000 Lost CCA tax shield -22,500 -38,250 -26,775 -18,743 -43,732 Lease payment -112,000 -112,000 -112,000 -112,000 0 Lease payment tax shield 33,600 33,600 33,600 33,600 0 Cash flow of lease 399,100 -116,650 -105,175 -97,143 -43,732 NPV of leasing rather than borrowing = 399,100 - 116,650 1.056 - 105,175 1.0562 - 97,143 1.0563 - 43,732 1.0564 = $399,100 - $322,441 = $76,659 Yes, Printing World should accept the offer to lease. Despite having to give up the CCA tax savings, the present value of the incremental lease cash flows is positive. Shareholders of Printing World are better off if the company leases rather than borrows to purchase the press. The total NPV from acquiring the press and leasing it is: = NPV of purchasing the press + NPV of leasing rather than borrowing = $102,048+ $76,659= $178,707 . 9. a. No cost of equity is provided. Use the after-tax cost of debt as the discount rate. Assume that the riskiness of the lease cash flows is equivalent to the riskiness of the firm’s debt. The same will be assumed about the riskiness of the salvage value (since no cost of equity is provided). After-tax cost of debt = (1-tax rate) rd = (1-.3)×.07 = .049 Using the formula approach, equation 17.1: NPV of leasing = Saved cost of buying equipment – PV(after-tax lease payments) – PV(CCA tax shield from equipment) – PV(salvage value) Saved cost of buying equipment = $900,000 Annual after-tax lease payments = (1-tax rate) × annual lease payment = (1-.3) × $155,000 = $108,500 The 6 after-tax lease payments are 6 year annuity due: PV(after-tax lease payments) = $108,500 PVAD(4.9%,6) = $579,449.59 Assume that the equipment would have been sold just after the end of the 6th year of use, making the present value of lost salvage value: PV(salvage value) = $150,000/(1.049)6 = $112,574.06 17-6 PV(CCA tax savings), using Equation 9.7, Chapter 9, page 256: = (1 .5 ) 1 (1 ) (1 ) c c t CdT r SdT r d r r d r + − + + + + 6 900,000(.25)(.3) (1 .5(.049) 150,000(.25)(.3) 1 .049 .25 (1 .049) .049 .25 (1 .049) + = − + + + + = 220,479.93 – 28237.64 = 192,242.29 NPV of leasing rather than buying = $900,000 - $579,449.59 - $192,242.29 - $112,574.06 = $15,734.06 The NPV of leasing rather than buying is positive. Therefore, BigCo should lease rather than buy the equipment. b. To solve for the maximum lease payment, rearranging the NPV formula: PV(after-tax lease payments) = Saved cost of buying equipment –PV(CCA tax shield from equipment) – PV(salvage value) - NPV of leasing rather than buying Set the NPV of leasing to zero and substitute the values for the present value of the CCA tax shield and the present value of the salvage value: PV(after-tax lease payments) =$900,000 - $192,242.29 - $112,574.06 – 0 = $595,183.65 PV(after-tax lease payments) = annual after-tax lease payment × PVAD(4.9%,6) = $595,183.65 Using a calculator to solve for the payment (make sure to remember that this is an annuity due. Set up the calculator to solve with the payment at the beginning of the period): n = 6, i = 4.9, FV = 0, PV = -595,183.65 and compute PMT = 116,866.84 This is after-tax, making the actual lease payment = after-tax lease payment/(1-tax rate) = $116,886.84/(1-.3) = $166,981.2 The maximum annual lease payment is $159,181.32 10. Lease Cash Flows 0 1 2 3 4 5 6 Saved cost of a new equipment 900,000 Lost salvage value -150,000 Lost CCA tax shield (see below) 33,750 59,063 44,297 33,223 24,917 27,938 Lease payment 155,000 155,000 155,000 155,000 155,000 155,000 Lease payment tax shield 46,500 46,500 46,500 46,500 46,500 46,500 Cash flow of lease 791,500 -142,250 -167,563 -152,797 -141,723 -133,417 -177,938 17-7 PV(Cash flow of lease) 791,500 -135,605 -152,274 -132,370 -117,041 -105,035 -133,541 NPV lease 15,734 The NPV of the lease is $15,734, the same as calculated in Question 9 (a) using a discount rate of 4.9 percent representing the after-tax cost of debt. Calculating the CCA Tax Shield For years 1 to 6, the CCA tax shield is easily calculated using the CCA tax shield formula: undepreciated capital cost (UCC) times the CCA rate (d) times the tax rate (Tc). 0 1 2 3 4 5 6 UCC 900,000 787,500 590,625 442,969 332,227 249,170 CCA 112,500 196,875 147,656 110,742 83,057 62,292 CCA tax shield 33,750 59,063 44,297 33,223 24,917 18,688 The equipment is sold for $150,000 right after the end of Year 6. The UCC at the start of Year 7 is UCC6 – CCA6 = 249,170 – 62,292 = $186,878. The equipment is sold for less than this remaining UCC. Thus for years 7 and on, BigCo can continue to take CCA on the remaining value of the equipment in the asset pool, even though the equipment was sold. Calculate the remaining undepreciated capital cost after selling the equipment: Subtract the salvage value from the UCC at the start of Year 7: UCC7 = 186,878 - 150,000 = $36,878 Then use the CCA tax shield formula to determine the remaining CCA tax shield after the equipment is sold. PV(CCA tax shield from Year 7 on, as of the end of Year 6) = UCC7dTc r + d 36,878(.25)(.3) = .049 + .25 = 9,250 To get the entry for the CCA tax shield shown in the lease cash flows table above, add present value of CCA tax shield for Year 7 and beyond (as of the end of Year 6) to the CCA tax shield for Year 6 = 18,688 + 9,250 = 27,938 11. The leasing of trucks, airplanes, or computers is big business because each such asset requires a significant outlay of cash and each asset is used by many companies that are marginally profitable. Also, in each case standardization of the asset leased leads naturally to standardization of the contracts; this, in turn, provides low administrative and transactions costs. 12. Yes, but because operating leases are generally much shorter than financial leases, the value of this advantage is not nearly as great for operating leases. 17-8 13. a. With a 20% tax rate, the tax savings from the lease payment reduces from .35 × 18,500, or $6,475, to .20 × 18,500, or $3,700. However, the CCA tax savings are worth less now and reducing the lost CCA tax shield. Finally, the lower tax rate increases the after-tax cost of debt to (1 - .2) × .10, or 8%. The lease cash flows are summarized below: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Saved cost of backhoe 100,000 Lost CCA tax shield -3,000 -5,100 -3,570 -2,499 -1,749 -1,225 -857 -2,000 Lease payment -18,500 -18,500 -18,500 -18,500 -18,500 -18,500 -18,500 Lease payment tax shield 3,700 3,700 3,700 3,700 3,700 3,700 3,700 Cash flow of lease 82,200 -19,900 -18,370 -17,299 -16,549 -16,025 -15,657 -2,000 Tax Shield Calculation UCC 100,000 85,000 59,500 41,650 29,155 20,409 14,286 10,000 CCA (CCA rate = 30%) 15,000 25,500 17,850 12,495 8,747 6,123 4,286 CCA tax shield 3,000 5,100 3,570 2,499 1,749 1,225 857 2,000 NPV of leasing rather than borrowing = 82,200 - 19,900 1.08 - 18,370 1.082 - 17,299 1.083 - 16,549 1.084 - 16,025 1.085 - 15,657 1.086 - 2,000 1.087 = $188 The lower tax rate increases the lease NPV from -$221 to +$188. Why? Leasing means giving up the tax saving from owning. If the tax rate of the lessee goes down, it makes leasing more valuable, relative to buying, because the lost tax savings are smaller. b. Using the formula approach: Saved cost of buying equipment = $100,000 Annual after-tax lease payments = (1-tax rate) × annual lease payment = (1-.35) × $18,500 = $12,025 The 7 after-tax lease payments are 7 year annuity due: PV(after-tax lease payments) = $12,025 × PVAD(6.5%,7) = $70,238.19 The CCA rate, d, is 30%. When the equipment is scrapped for zero dollars, the asset pool is closed and the firm gets to take a terminal loss equal to the balance in the asset pool after the end of Year 6 (which is also the beginning of Year 7). To work out the balance in the asset pool after depreciating the equipment for 6 years you can resort to using a table: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Tax Shield Calculation 17-9 UCC 100,000 85,000 59,500 41,650 29,155 20,409 14,286 CCA 15,000 25,500 17,850 12,495 8,747 6,123 CCA tax shield 5,250 8,925 6,248 4,373 3,061 2,143 The above table shows that the balance in the asset pool after the end of Year 6 is $14,286. This number could also be calculated by using this formula for calculating the UCC balance at the end of 6 years: UCC6 = (1-.5×d)(1-d)5×C = (1-.5×.3)(1-.3)5(100,000) = 14,285.95 (which rounds to $14,286) To allow for the terminal loss taken in Year 7, which equals the remaining balance in the asset pool times the tax rate, and also the fact the asset pool is closed (giving up the future CCA on the remaining UCC) Equation 9.7, Chapter 9, page 256 is modified to be: = (1 .5 ) 6 1 6 6 1 7 (1 ) (1 ) (1 ) c c c CdT r UCC dT UCC T r d r r d r r + − + + + + + + 6 7 100,000(.3)(.35) (1 .5(.065) 14,286(.3)(.35) 1 14,286(.35) 1 .065 .3 (1 .065) .065 .3 (1 .065) (1 .065) + = − + + + + + + = $27,889.25 - $2,816.5 + $3,217.6 = $28,290.35 NPV of leasing rather than buying = $100,000 - $70,238.19 -$28, 290.35= $1,471.46 which can be rounded to $1,471 Using the table approach: Moving the first CCA payment to the end of the first year: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Saved cost of backhoe 100,000 Lost CCA tax shield -5,250 -8,925 -6,248 -4,373 -3,061 -2,143 -5,000 Lease payment -18,500 -18,500 -18,500 -18,500 -18,500 -18,500 -18,500 Lease payment tax shield 6,475 6,475 6,475 6,475 6,475 6,475 6,475 Cash flow of lease 87,975 -17,275 -20,950 -18,273 -16,398 -15,086 -14,168 -5,000 Tax Shield Calculation UCC 100,000 85,000 59,500 41,650 29,155 20,409 14,286 CCA 15,000 25,500 17,850 12,495 8,747 6,123 CCA tax shield 5,250 8,925 6,248 4,373 3,061 2,143 5,000 NPV of leasing rather than borrowing = 87,975 - 17,275 1.065 - 20,950 1.0652 - 18,273 1.0653 - 16,398 1.0654 - 15,086 1.0655 - 14,168 1.0656 - 5,000 1.0657 17-10 = $1,471 With a different treatment of CCA, the lease NPV increases from -$221 to +$1,471. The difference here is that the CCA tax savings are worth less if they are delayed. Going with the lease means giving up less valuable CCA tax savings. c. Rather than work out all the cash flows, we will just look at the change in the cash flows associated with the treatment of the asset. With many other assets in asset pool and a zero salvage value, the CCA tax savings are calculated as if the company never sold the asset. Instead of a terminal loss, Greenfield needs to figure out the CCA tax savings from the perpetual CCA. The balance in the asset pool at the end of Year 6 is $10,000. The CCA tax savings from depreciating this forever is: PV(Tax savings from not closing the asset pool after the end of Year 6) = C d Tc r + d = .065 + .3 10,000×.3×.35 = $2,877 Previously, Greenfield had been expecting a terminal loss of $10,000 and its tax savings on terminal loss: .35× $10,000 = $3,500. Notice this terminal loss is at the end of Year 7. The present value at the end of Year 6 is $3,500/(1.065) = $3,286. To figure out the new lease NPV, remove the tax effects of the terminal loss and replace it with the tax effects of not closing the pool. The incremental cash flows at the end of Year 6 from having other assets in the pool = - $2,877 + $3,286 = +$409. The present value today is $409/(1.065)6 = $280 NPV of leasing = - $221 + $280 = $59. (slightly different than $60 reported in the book due to rounding). Note: Look back to Chapter 9 for the present value of a perpetual tax shield: PV(Tax savings in perpetuity) = C d Tc r + d × 1 + .5 × r 1 + r We dropped the second term because there is no need to adjust for the half- year rule. No asset is purchased in Year 7. 14. a. This question can be solved by trial and error, especially if you use a spreadsheet. However, it can also be solved analytically. The minimum payment is lease payment that gives a zero NPV to the lessor: 17-11 NPV = 0 = -100,000 + PV(CCA tax savings) + PV(After-tax lease payments) PV(CCA tax savings) (from Table 17.1) = 5,250 + 8,925 1.065 + 6,248 1.0652 + 4,373 1.0653 + 3,061 1.0654 + 2,143 1.0655 + 1,500 1.0656 + 3,500 1.0657 = 29,983 PV(After-tax lease payments) = 100,000 – 29,983 = 70,017 The lease payments are an annuity with payments at the beginning of each period: 70,017 = after-tax lease payment × annuity due factor(6.5%,7 years) Using the annuity due formula or setting the calculator for payments at the beginning of the period [PV = (-)70,017, n = 7, i = 6.5%, FV = 0, solve for PMT]. The minimum after-tax lease payment is $11,987. The before-tax payment is therefore $11,987/(1-.35) = $18,442. b. To solve for the maximum payment Greenfield could pay, find the lease payment that makes the NPV of leasing equal to zero. Remember, Greenfield is assumed to pay no tax and does not have the tax savings from CCA. NPV = 0 = +100,000 - PV(lease payments) The lease payments are an annuity with payments at the beginning of each period: 100,000= lease payment × annuity due factor(10%,7 years) Using the annuity due formula or setting the calculator for payments at the beginning of the period [PV = (-)100,000, n = 7, i = 10%, FV = 0, solve for PMT]. The maximum lease payment is $18,673. 15. a. From question 14, we know that the minimum lease payment acceptable to the lessor is: NPV = 0 = -100,000 + PV(CCA tax savings) + PV(After-tax lease payments) Discount rate = (1-.5)×.10 = .05 = 5% CCA Tax Savings with a 50% tax rate: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 UCC 100,000 85,000 59,500 41,650 29,155 20,409 14,286 10,000 CCA (CCA rate = 30%) 15,000 25,500 17,850 12,495 8,747 6,123 4,286 17-12 CCA tax shield 7,500 12,750 8,925 6,248 4,373 3,061 2,143 5,000 PV(CCA tax savings) = $44,284 PV(After-tax lease payments) = 100,000 – 44,284 = $55,716 The lease payments are an annuity with payments at the beginning of each period: 55,716 = after-tax lease payment × annuity due factor(5%,7 years) Using the annuity due formula or setting the calculator for payments at the beginning of the period [PV = (-)55,716, n = 7, i = 5%, FV = 0, solve for PMT]. The minimum after-tax lease payment is $9,170. The before-tax payment is therefore $9,170/(1-.5) = $18,341. Greenfield’s NPV of leasing = +100,000 – 18,341×annuity due factor(10%,7) = 100,000 – 98,221 = $1,779. The total gain in NPV from the leasing arrangement = Lessor's NPV + Greenfield's NPV = 0 + $1,779 = $1,779. By comparison, with the original tax rate for the lessor of 35%, the total gain in NPV was $928 + $221, or $1,149. We have shown that the higher the tax rate of the lessor, relative to the lessee, the greater the benefit from leasing. b. With a CCA rate of 35%, tax rate of 35%, and cost of debt of 10%, the CCA tax savings will be: UCC 100,000 82,500 53,625 34,856 22,657 14,727 9,572 6,222 CCA (CCA rate = 35%) 17,500 28,875 18,769 12,200 7,930 5,154 3,350 CCA tax shield 6,125 10,106 6,569 4,270 2,775 1,804 1,173 2,178 PV(CCA tax savings) = $30,620 PV(After-tax lease payments) = 100,000 – 30,620 = $69,380 The lease payments are an annuity with payments at the beginning of each period: 69,380 = after-tax lease payment × annuity due factor(6.5%,7 years) Using the annuity due formula or setting the calculator for payments at the beginning of the period [PV = (-)69,380, n = 7, i = 6.5%, FV = 0, solve for PMT]. The minimum after-tax lease payment is $11,878. The before-tax payment is therefore $11,878/(1-.35) = $18,274. Greenfield’s NPV of leasing = +100,000 – 18,274×annuity due factor(10%,7) 17-13 = 100,000 –97,862 = $2,138. The total gain in NPV from the leasing arrangement = Lessor's NPV + Greenfield's NPV = 0 + $2,138= $2,138. By comparison, with the original CCA rate of 30%, the total gain in NPV was $928 + $221, or $1,149. We have shown that the higher the CCA rate, the greater the benefit from leasing. c. Continue to assume that the lessor will depreciate the asset for 7 years. The present value of the CCA tax shield, from question 12(a) is 29,983. PV(After-tax lease payments) = 100,000 – 29,983 = 70,017 The lease payments are an annuity with payments at the beginning of each period for only 4 years: 70,017 = after-tax lease payment × annuity due factor(6.5%,4 years) Using the annuity due formula or setting the calculator for payments at the beginning of the period [PV = (-)70,017, n = 4, i = 6.5%, FV = 0, solve for PMT]. The minimum after-tax lease payment is $19,191. The before-tax payment is therefore $19,191/(1-.35) = $29,525. Greenfield’s NPV of leasing = +100,000 – 29,525×annuity due factor(10%,4) = 100,000 – 102,949 = -$2,949. The total gain in NPV from the leasing arrangement = Lessor's NPV + Greenfield's NPV = 0 -$2,949= -$2,949. By comparison, with the original 7 year lease contract, the total gain in NPV was $928 + $221, or $1,149. We have shown that the shorter the lease, the lower is the benefit from leasing. d. With a 20% interest rate before tax, or (1-.35) × 20% = 13% after-tax, the present value of the CCA tax savings becomes: PV(CCA tax savings) (from Table 17.1) = 5,250 + 8,925 1.13 + 6,248 1.132 + 4,373 1.133 + 3,061 1.134 + 2,143 1.135 + 1,500 1.136 + 3,500 1.137 = $26,321 PV(After-tax lease payments) = 100,000 – 26,321 = $73,679 17-14 The lease payments are an annuity with payments at the beginning of each period: 73,679 = after-tax lease payment × annuity due factor(13%,7 years) Using the annuity due formula or setting the calculator for payments at the beginning of the period [PV = (-)73,679, n = 7, i = 13%, FV = 0, solve for PMT]. The minimum after-tax lease payment is $14,743. The before-tax payment is therefore $14,743/(1-.35) = $22,682 Greenfield’s NPV of leasing = +100,000 – 22,682×annuity due factor(20%,7) = 100,000 – $81,759 = $18,241 The total gain in NPV from the leasing arrangement = Lessor's NPV + Greenfield's NPV = 0 + $18,241 = $18,241 By comparison, with the original interest rate 20%, the total gain in NPV was $928 + $221, or $1,149. We have shown that the higher the interest rate, the greater is the benefit from leasing. 16. Start with the minimum payment the lessor would be happy with: NPV = 0 = -100,000 + PV(CCA tax savings) + PV(After-tax lease payments) With a zero interest rate, the present value of the CCA tax savings is simply their sum: PV(CCA tax savings) (from Table 17.1) = 5,250 + 8,925 1.0 + 6,248 1.02 + 4,373 1.03 + 3,061 1.04 + 2,143 1.05 + 1,500 1.06 + 3,500 1.07 = 35,000 PV(After-tax lease payments) = 100,000 – 35,000 = 65,000 With a zero interest, the before-tax annual lease payment is $65,000/7 = $9,286. The minimum after-tax lease payment is $9,286/(1 - .35) = $14,286. With a zero interest rate, the present value of the lease payments is simply 7 × $14,286 = $100,002. Greenfield’s NPV of leasing = +100,000 – $100,002 = -$2. 17-15 Even with the minimum possible lease payment, Greenfield’s NPV is negative. With more decimal places, it would exactly equal 0. There is no advantage to leasing if the interest rate is zero. 17. a. Nodhead College NPV of leasing = +250,000 - 55,000 × annuity due factor(8%,6) = 250,000 – 274,599 = -$24,599 b. Discount rate = (1 - .35) × .08 = .052 Tax saving from CCA Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 UCC 250,000 212,500 148,750 104,125 72,888 51,021 35,715 CCA (CCA rate = 30%) 37,500 63,750 44,625 31,238 21,866 15,306 CCA tax shield 13,125 22,313 15,619 10,933 7,653 5,357 12,500 PV(CCA tax savings) = $77,466 Compulease NPV of leasing = -250,000 + (1 - .35) × 55,000 × annuity due factor((1-.35)× 8%,6) + 77,466 = -250,000 + 189,677 + 77,466 = $17,143 c. Overall gain from lease = sum of the NPV of the lessor and lessee = 17,143 – 24,599 = -$7,456 18. NOTE: Students should be looking for the minimum lease payment acceptable to the lessor. The lessor likely has no upper bound on the maximum acceptable lease payment!!! The after-tax cost of debt = (1-.35) × .1 = .065 Look back to Chapter 9 for the present value of a perpetual tax shield: PV(Tax savings in perpetuity) = C d Tc r + d × 1 + .5 × r 1 + r PV(CCA tax savings to perpetuity) = 100,000×.3×.35 .065 + .3 × 1 + .5 × .065 1 + .065 = $27,889 The lessor’s minimum NPV of leasing 0 = - 100,000 + PV(after-tax lease payments) + 27,889 PV(After-tax lease payments) = 100,000 – 27,889 = $72,111 17-16 The lease payments are an annuity with payments at the beginning of each period: 72,111 = after-tax lease payment × annuity due factor(6.5%,8 years) Using the annuity due formula or setting the calculator for payments at the beginning of the period [PV = (-)72,111, n = 8, i = 6.5%, FV = 0, solve for PMT]. The minimum after-tax lease payment is $11,120. The before-tax payment is therefore $11,120/(1-.35) = $17,108. The minimum payment the lessor will accept is $17,108. 19. The IRR of the lease is the discount rate, r, that makes the present value of the lease payments equal to zero: 2 3 62,000 26,800 22, 220 17,600 0 − 1+ r − (1+ r) − (1+ r) = To solve for r, use trial and error, a calculator or spreadsheet. Using Excel function IRR gives the discount rate of 3.9459%. The problems with using IRR with leasing are the same problems that are discussed in Chapter 8. However, four of these problems are particularly bothersome here: a. Multiple roots rarely occur in capital budgeting since the expected cash flows usually only change signs once. With leasing, this is often not the case. A lessee will have an immediate cash inflow, a series of outflows for a number of years, and then an inflow during the last year. With two changes of sign, there may be, and in practice frequently are, two solutions for the IRR. b. Another problem is that risk is not constant. For the lessee, the lease payments are fairly riskless and the interest rate should reflect this. The salvage value for the asset, however, is probably much riskier. Thus, you need two discount rates. IRR only gives one rate, and thus, each cash flow is not implicitly discounted to reflect its risk. c. If the companies do not pay tax or pay at a constant rate, then IRR should be calculated from the lease cash flows and compared to the after-tax rate of interest. However, if the company is in a temporary non-taxpaying position, its cost of capital changes over time, and there is no simple standard of comparison. d. The IRR method cannot be used to choose between alternative lease bids with different lives or payment patterns. 17-17 20. a. Proponents of this view note that a firm paying no taxes already has an advantage over tax-paying companies in the development of new projects, even without leasing. In addition, leasing for a company in this position allows for a shifting of tax shields from lessee to lessor. The government loses and the lessee and/or lessor gains. Many people feel that the combination of these two advantages is more than is necessary to encourage non-taxpaying companies to invest. b. The argument for this view is as follows: If the government feels more investment is needed, then allowing non-tax-paying companies to take advantage of depreciation tax shields, through leasing, should help. Why make investment incentives like accelerated depreciation credit available only to currently profitable companies? If such companies end up with too much of a tax break, then the solution should be to restrict the tax loss carryforward rather than change the tax rules on leasing. 21. This exercise will help students realize the great number of leased assets. The price data is not readily available any more. 22. We will ignore the revenues generated by operating the bush plane. We assume that these revenues are the same, regardless of whether Magna owns or leases the plane. We are seeking least costly way to acquire the use of the plane during the contract period. Notice that the lease is a net lease. Magna must cover the operating costs of the plane. Assume that the operating costs are identical whether Magna buys or leases the plane and therefore can be ignored. After-tax cost of borrowing = (1-.35) × .09 = .0585 = 5.85% WACC = .14 = 14% Plane will be sold after 5 years for $300,000, and for $400,000 if it is sold after 1 year. To find the CCA tax savings, we use equation from Chapter 9. Alternatively, the tax savings can be calculated directly with a table. We assume that the riskiness of the tax savings is similar to the firm’s cost of borrowing. (Another approach would be to assume that the riskiness of the salvage value is higher and therefore the tax savings implications will also be discounted at a higher rate, say at WACC). (A third approach is to discount all of the CCA tax savings at WACC – but then you must also discount them at that same rate when figuring out the value of the incremental cash flows of leasing rather than borrowing. Be consistent in your assumptions.) 17-18 PV(CCA tax savings) = C d Tc r + d × 1 + .5 × r 1 + r - S d Tc r + d × 1 (1 + r)5 PV(CCA Tax Savings, if keep plane for 5 years) = 500,000 ×.25×.35 .0585+.25 × 1 + .5 × .0585 1 + .0585 - .0585+.25 300,000×.25×.35 ×(1 + 1 .0585)5 =73,861 PV(CCA Tax Savings, if keep plane for 1 year) = 500,000 ×.25×.35 .0585+.25 × 1 + .5 × .0585 1 + .0585 - .0585+.25 400,000×.25×.35 ×(1 + 1 .0585)1 = 30,714 Cost of Buying the Plane 1. Contract is renewed after 1 year Cost = -500,000 + 1 1.145 × 300,000 + 73,681 = -270,508 2. Contract is not renewed after 1 year Cost = -500,000 + 1 1.14 × 400,000 + 17,807 = -131,316 Expected cost of buying the plane = .8 × (-270,508) + .2(-131,316) = -$242,670 Cost of Leasing the Plane 1.Contract is renewed after 1 year Cost = (1-.35)×(-75,000)×annuity due factor(.0585,5) = -$218,256 2. Contract is not renewed after 1 year Assume that Magna can lease the plane for the same amount that it would have paid. Therefore, the cost is only the lease payments in the first year. Cost = (1-.35)×(-75,000) = -$48,750 Expected cost of leasing the plane = .8 × (-218,256) + .2 × (-48,750) = -$184,355 Without considering transactions costs, it is cheaper to lease the plane than to buy it. If Magna has trouble re-leasing the plane, the advantage to leasing declines. For example, if Magna had trouble subleasing the plane and ended up having to make 17-19 a second lease payment (PV = 48,750/(1.0585) = $46,056, the expected cost of leasing would increase .2 × 46,056 = $9,211. If it never re-leases the plane, the cost if the contract is not renewed is the full cost of the lease: $218,256. However, this is still lower than the expected cost of owning. It makes financial sense to lease, rather than buy the plane to manage the contract. 23. The discount rate for Years 1 and 2 is 10% and is 6.5% for the other years. 0 1 2 3 4 5 6 7 Saved cost of a backhoe 100,000 Lost CCA tax shield 0 0 0 -4,373 -3,061 -2,143 -1,500 -3,500 Lease payment -18,500 -18,500 -18,500 -18,500 -18,500 -18,500 -18,500 Lease payment tax shield 0 0 0 6,475 6,475 6,475 6,475 Cash flow of lease 81,500 -18,500 -18,500 -16,398 -15,086 -14,168 -13,525 -3,500 NPV = 81,500 - 18,500 1.1 - 18,500 1.12 - 1 1.12 ×( 16,389 1.065 + 15,086 1.0652 + 14,168 1.0653 + 13,525 1.0654 + 3,500 1.0655 ) = 5,189 We’ve made a strong assumption that the CCA deductions vanish in Years 1 to 3. However, the company can accumulate the CCA deductions and use them in later years. The CCA rate gives the maximum CCA deduction but a firm is not obligated to use it. Having higher tax savings forgone in Years 3 on would diminish the advantage of leasing. 24. Internet Expected outcome: Wal-Mart owns more of its real estate than does Abercrombie & Fitch. Abercrombie & Fitch stores are more commonly found in big shopping malls where retail space is leased. Wal-Mart’s long-term debt ratio excluding value of leases was about 32% at the end of fiscal 2009, and 36% at the end of fiscal 2008. Abercrombie & Fitch, however, had only 5.7% long-term debt ratio for 2009 and 7.8% for 2008. Students should find that the operating leases of Abercrombie & Fitch are substantially bigger fraction of revenues than are Wal- Mart's. 25. Internet: Leasing terms Expected Results: Terms related to terminating (or not terminating) a lease: HELL-OR-HIGH-WATER CLAUSE A clause in a lease that reiterates the unconditional obligation of the lessee to pay rent for the entire term of the lease, regardless of any event affecting the equipment or any change in the circumstances of the lessee. 17-20 NON - CANCELABLE LEASE Any lease which cannot be cancelled during its term. In order to terminate the lease the Lessee will be expected to pay the remaining rentals due to the end of the term. Most leasing Cos will discount this amount to at least in part reflect a pre-payment. The discount rate is always lower than the effective rate (i.e. less than a full rebate of “unearned interest”). Terms related to asset disposition at the end of the lease: BARGAIN PURCHASE OPTION A lease provision allowing the lessee, at its option, to purchase the equipment for a price predetermined at lease inception, that is substantially lower than the expected fair market value at the date the option can be exercised. i.e. $1.00! CLOSED END LEASE wherein the lessee is not expected or required to exercise an option to purchase the leased equipment. Most commonly seen in automobile leases from dealers and manufacturers. At the end of the lease the vehicle may be returned subject to mileage and condition of vehicle restrictions (which if not met can exact penalties). FAIR MARKET PURCHASE OPTION An option to purchase leased property at the end of the lease term at its then fair market value. The lessor does not have the ability to retain title to the equipment if the lessee chooses to exercise the purchase option. HIRE PURCHASE Term originating in the UK for a lease with a nominal purchase option at the end OPEN-END LEASE A lease in which the lessee guarantees that the lessor will realize a minimum value from the sale of the asset at the end of the lease. The term is restricted to car leasing PURCHASE OPTION A provision by which a lessee has the right to purchase the equipment (usually at the end of or close to the end of the lease). The purchase option may be stated at a specified amount or at fair market value. PUT OPTION The requirement to purchase equipment at a particular time and at a predetermined price. In a lease transaction, this is a lessor’s right to force the lessee (or some third party) to purchase the equipment at the end of the lease term. STRETCH LEASE A lease with an option to purchase prior to the end of the term where the option is roughly equal to the value of the remaining rentals. Very common structure. Said to comply with IT233 26. Internet: Reasons for leasing 17-21 Expected Results: An astute student will realize that some of these arguments are really the same reason we said were valid reasons to lease: lessors have expertise in the resale of used equipment, have a tax reason to want the CCA on the equipment and able to offer flexibility in structuring financing that might be more difficult to get from the bank. The reason that it is the use, not the ownership, of the asset that generates income relates to the value of the asset once the company no longer wants the use of the asset and is a valid reason to enter into an operating lease. Recall, we distinguished between operating leases (those where the asset is needed only for a short part of the asset’s life) versus financial leases (where the asset is essentially worn out by the end of the lease). Clearly, leasing when you only want to have use of the asset for a short period of its life can make sense – the convenience of not having to deal with the resale of the asset. By owning the asset, you take on the risk of selling the asset when you no longer want it – if some other company is better at dealing with used assets (because of standardization leading to lower costs), it may make sense to enter into an operating lease. The argument about use versus ownership is much less applicable to financial leases – the equipment is worn out by the end of the lease anyway, leasing is essentially the same as owning. However, the notion the leasing “conserves working capital” is just another way to say that leasing is 100% financing – a bogus reason to lease (To their credit, Canada Capital Leasing even acknowledges that borrowing also conserves cash). Some of the arguments relate the making the financial statements look better than they would otherwise – reduced taxes for accounting purposes (see “Deferring Taxes”, and being able to use off-balance sheet accounting for the lease (see “Operating Leases”). We know that neither of these reasons increases the actual cash flow of the company (taxes are the same, regardless of how the lease is reported in the financial statements). Finally, they argue that by leasing you might be able to fool the bank into thinking you have less “debt” – that’s implied in the “keeps bank operating line unencumbered). Of course, it makes sense to borrow from banks that can’t understand finance. But don’t count on finding many such banks!!! 27. Internet: Using Lease or Buy Calculator Tips: Tell your students to not be frustrated by this exercise!!! It is a great example of how important assumptions are. It took us several hours to figure out the assumptions imbedded in the calculations. You decide how much to give away to your students. General assumptions The interest rate is assumed to be compounded monthly EXCEPT when discounting annualized amounts. When discounting annualized amounts, the 17-22 interest rate is taken as an annual rate. For example, you enter 12% as the interest rate. This will be interpreted as 12%/12 = 1% per month for determining the loan payments and the annual cost of the lease (find the present value of 12 monthly lease payments). However, when the present value of any annual payment is determined, it is assumed that the discount rate is 12%, compounded annually. This is NOT equivalent to 12%, compounded monthly. We think that the better annual discount rate to use is the annual equivalent to 12%, compounded monthly: (1.01)12 – 1 = 12.683%. Lease assumptions: - payments made in advance Buy/Borrow assumptions: - loan payments are made at the end of each month. Expected results: The most obvious way to figure out the monthly lease payments that makes someone indifferent between leasing and buying is to let the calculator give you the present value of the cash flows associated with buying. Plug into the right side of calculator (Cost of Buying) the following: tax rate = 40 loan term = 3 annual interest rate = 10 cost = 100000 salvage = 0 CCA rate = 30 (look up the CCA rate for a Class 38 asset) It will give the total cost of the loan as $65,822.41. Next, solve for the lease payment that has the same present value as the cost of the loan. Remember payments are made in advance and will be the after-tax lease payment. Discount at the after-tax cost of borrowing, (1-.4)×10%/12 = 6%/12 = .5% per month: 65,822.41 = After-tax PMT × annuity due factor (.5%, 36 months) After-tax PMT = 1,992.5 Before-tax PMT = After-tax PMT/(1-.4) = 1992.5/.6 = $3320.83 Plug that number back into the calculator as the monthly lease payment. IT DOESN’T work!!! It says the lease is costs $100.52 more than the loan! Why doesn’t the answer say the difference is zero??? Because of the imbedded assumption about discounting annual amounts at a different rate than monthly amounts. In order to get the lease payment that makes you indifferent between leasing and buying, given the assumptions imbedded in the calculator, do the following: 17-23 What after-tax annualized lease amount, paid in advance for 3 years, has a cost equivalent to the buy/borrow option: 65,822.41 = after-tax annualized lease amount × annuity due factor (6%, 3 years) After-tax annualized lease amount = 23,230.95 Before-tax annualized lease amount = 23,230.95/.6 = 38,718.25 Now find a monthly lease payment such that in a year, its present value is 38,718.25: 38,718.25 = monthly lease payment × annuity due factor( .5%, 12 months) Monthly lease payment = 3,315.76 Plug that lease amount into the calculator. The cost of the lease is 65,822.30 and the cost of the buy/borrow is 65,822.41, a difference of only $0.11. Close enough. Some Other Points. 1. What should be the total cost of buy/borrowing? Total cost of buy/borrowing = cost of equipment + amount advanced through the loan – PV(principal and interest paid on the loan) – PV(tax savings from CCA from buying the equipment) The sum of second and third terms in the total cost should be zero. You borrow $100,000 at 10% and repay principal and interest with a present value of $100,000. Otherwise, you have not borrowed at 10%. The total cost is then the cost of the equipment less the tax savings generated. Unfortunately, the Lease or Buy Calculator does NOT give this result. Again, the reason is the unfortunate decision to discount annual payments at an interest rate NOT equal to the annual equivalent of the monthly interest rate used. 2. If you want to figure out how they calculated the loan payments, here’s what to do: Monthly loan payment: 100,000 = PMT × regular annuity factor (10%/12, 36) = 3,226.72 Annualized loan payment = 3,226.72 × regular annuity factor ((1-.4)×10%/12, 12) = 37,491.05 (this is essentially equal to the loan repayment amount reported in the Buy table of the calculator) How much of the first year’s payments are interest, how much are principal repayment? Figure out the interest on each month’s outstanding balance and discount it back to the start of the year (use the after-tax cost of debt as the discount rate). This is the tedious part of the calculation. A spreadsheet really speeds up the calculations, shown below: Principal and interest payment each month 17-24 Amount borrowed 100000 Monthly payment $3,226.719 Before-tax interest rate 0.00833333 After-tax interest rate 0.00666667 Month: 1 2 3 4 5 6 Outstanding loan 100000.0 97606.6 95193.3 92759.8 90306.1 87832.0 Interest on loan =outstanding loan × .10/12 833.3 813.4 793.3 773.0 752.6 731.9 Principal repayment 2393.4 2413.3 2433.4 2453.7 2474.2 2494.8 Month: 7 8 9 10 11 12 Outstanding loan 85337.2 82821.6 80285.1 77727.4 75148.4 72547.9 Interest on loan 711.1 690.2 669.0 647.7 626.2 604.6 Principal repayment 2515.6 2536.5 2557.7 2579.0 2600.5 2622.2 The present value of the 12 monthly interest payments for the first year of the loan, discounted at .5% is 8386.2 Repeat the process for the second and third years of the loan. 17-25 Solution to Minicase for Chapter 17 Rachel Gold has analyzed the possible lease-financing of a new dredger. The output from her spreadsheet is below. First she calculated the NPV of the proposed investment. This confirmed her suspicion that the acquisition of the dredger using ordinary financing was not attractive. The NPV was - $1,335,000. Could either of the lease proposals generate positive NPVs more than offsetting this negative amount? Not at the lease rates offered: As the spreadsheet shows, the NPV of the Mt. Zircon and First Cookham offers were +$19,500 and +$53,810, respectively. Neither was enough to offset the -$1,335,000 NPV of acquiring the dredger with normal financing. Rachel then calculated NPVs from the lessors’ points of view. Was there any room to negotiate better lease rates? Mt. Zircon’s NPV was about $122,500 with the present lease payment. Rachel tried other lease rates, and discovered that Mt. Zircon could break even with a payment of about $533,500 per year. This would generate an NPV for Halverton of about +$531,740. However, this was still less than the negative NPV of acquiring the dredger with ordinary financing. First Cookham’s NPV was about -$211,820, under her assumptions about the use of the dredger after Year 7. There seemed little chance of a better offer from them. On the basis of her analysis, Rachel decided to recommend that the entire dredger project be abandoned. It was not worth investing any money. There was still the chance that Halverton’s top management would insist on acquiring the new dredger. Which one to recommend? The NPV of the First Cookham’s lease was higher than Mt. Zircon’s. But it had a crucial difference: it expired after 7 years and the project was planned to run 9 years. Halverton would still need a dredger for 2 more years after the First Cookham’s lease ran out. Was it sensible to simply compare the lease NPVs when they covered different amounts of time? If she could assume that Halverton would purchase the dredger for a nominal amount, say $1, from First Cookham at the end of their lease, then the lease NPV of $53,810 made sense. She doubted that First Cookham would agree to that. If Halverton had to arrange another lease for the last 2 years, the NPV could go negative. For example, leasing at $100,000 a year for the last 2 years made the total 9-year NPV equal -$22,640. Rachel decided that if Halverton went with the shorter First Cookham lease, they would have to negotiate a plan for the last two years. When she knew what Halverton’s costs would be for the last two years, then she could pick the best lease financing. Rachel was not fooled by Mt. Zircon’s claims that their lease “would preserve Halverton’s capital for other uses” and would “allow a very attractive return on equity.” She realized that signing a financial lease creates a debt-equivalent liability that should be compared to borrowing through normal channels. Note also that Rachel concentrated on the leases’ NPVs, not on their percentage IRRs. 17-26 Project Cash Flows for Halverton of Acquiring Dredger Note: all cash flows in $000s Year 0 1 2 3 4 5 6 7 8 9 Equipment cost -3,500 Operating cash flow 470 470 470 470 470 470 470 470 470 Total -,3500 470 470 470 470 470 470 470 470 470 NPV of buy dredger = -3,500 + 470 × annuity factor(16%,9 years) = -$1,335,000 Mount Zircon Lease: Halverton’s NPV of Leasing Year 0 1 2 3 4 5 6 7 8 9 Saved cost of dredger 3,500 Lease payment -550 -550 -550 -550 -550 -550 -550 -550 -550 -550 Cash flow of lease 2,950 -550 -550 -550 -550 -550 -550 -550 -550 -550 Halverton’s cost of borrowing = 12% (not in a tax-paying situation) Halverton’s NPV of Leasing rather than borrowing to acquire dredger = 2,950 – 550 × annuity factor(12%,9) = 19.5, or $19,500 NPV of acquiring the dredger with a lease = -1,335,000 + 19,500 = -$1,315,500 Mount Zircon Lease: Mount Zircon’s NPV of Leasing Assume that Mt. Zircon will close the asset pool after the end of the 9th year, taking a terminal loss on the balance left in the pool in the 10th year. The salvage value is assumed to be zero after 9 full years of operation. Lease Cash Flows 0 1 2 3 4 5 6 7 8 9 10 Cost of dredger -3,500 CCA tax shield 184 312 219 153 107 75 53 37 26 18 42 Lease payment 550 550 550 550 550 550 550 550 550 550 Lease payment tax -193 -193 -193 -193 -193 -193 -193 -193 -193 -193 Cash flow of lease -2,959 670 576 511 465 433 410 394 383 376 42 17-27 Mount Zircon’s NPV of leasing = PV(cash flow of lease) = $122,460 First Cookham Lease: Halverton’s NPV of Leasing Lease Cash Flows 0 1 2 3 4 5 6 7 Saved cost of dredger 3,500 Lease payment -619.4 -619.4 -619.4 -619.4 -619.4 -619.4 -619.4 -619.4 Cash flow of lease 2,880.6 -619.4 -619.4 -619.4 -619.4 -619.4 -619.4 -619.4 Halverton’s NPV of Leasing rather than borrowing to acquire dredger = 2,880.6 – 619.4 × annuity factor(12%,7) = 53.81 or $53,810 NPV of acquiring the dredger with a lease = -1,335,000 + 53,810 = -$1,281,190 First Cookham Lease: First Cookham’s NPV of Leasing Rachel decided to assume that First Cookham would expect that the dredger to be in operation for 9 years, even though First Cookham offered only a 7 year lease. Thus, the tax savings from the CCA would be same as for Mt. Zircon. She then wondered what use the dredger would be put to during those last two years. For now, she decided to assume the dredger would sit idle. Lease Cash Flows 0 1 2 3 4 5 6 7 8 9 10 Cost of dredger -3,500 CCA tax shield 184 312 219 153 107 75 53 37 26 18 42 Lease payment 619 619 619 619 619 619 619 0 0 0 0 Lease payment tax -217 -217 -217 -217 -217 -217 -217 0 0 0 0 Cash flow of lease -2,914 715 621 556 510 478 455 37 26 18 42 First Cookham’s NPV of leasing = PV(cash flow of lease) = -$211,820 17-28 Brealey 5CE Solutions for Chapter 18 1. a. May 7: Declaration date June 6: Last with-dividend date June 7: Ex-dividend date June 11: Record date July 2: Payment date b. The stock price will fall on the ex-dividend date, June 7. The price falls on this day because, as the stock goes ex-dividend, the shareholders are no longer entitled to that dividend. c. The annual dividend is $.075 × 4 = $.30. The dividend yield is $.30/$27 = .011 = 1.1% d. The payout ratio is $.30/$1.90 = .158 = 15.8% e. A 10 percent stock dividend is equivalent to a 1.10 for 1 stock split. Shares outstanding increase by 10%, while the firm’s assets are unchanged. The stock dividend therefore will reduce the stock price to $27/1.10 = $24.55. 2. a. True. b. True. c. True. The effective rate can be lower than the stated rate because the realization of gains can be deferred, which reduces the present value of the tax obligation. d. True. Canadian corporations are not taxed on dividends received from other Canadian corporations. 3. a. The stock price will fall to $40 × 4/5 = $32. b. The stock price will fall by a factor of 1.25 to $40/1.25 = $32. c. A share repurchase will have no effect on price per share. 18-1 4. Your dividend income will increase from $750 to $1000. If you view the dividend as excessive, you can invest the extra $250 in the firm. Use part of the dividend proceeds to buy 5 shares of stock at $50 per share. When the stock goes ex-dividend, the share price will fall by $1.00 instead of $.75, but you will increase the number of shares you hold, and thereby offset the impact of the higher payout policy. 5. The manager cannot be correct. If all shareholders have the right to buy additional shares at the deep discount, then none of them individually can benefit. As the additional shares are sold at below-market prices, the share price will gradually fall, precisely offsetting the value of the discount. This is analogous to the firm issuing rights to existing shareholders to buy additional shares at a discount. (See Chapter 14.) The value of the right is offset by the fall in the share price. The firm cannot create value by selling discounted shares. One benefit of the program that the manager does not mention is that if the DRIP elicits a significant cash inflow, the firm may not need to issue equity in the future, thereby saving the costs of a future equity issue. 6. The high rate of share repurchase at a time of low dividend payout rates probably was not a coincidence. Instead, it seems likely that firms were using share repurchase as an alternative to increasing dividends. 7. First, this statement violates the notion of efficient markets. One cannot identify “the bottom of the market” until after the fact. In addition, if the firm pays a cash dividend, and I do not use my proceeds to purchase shares in the firm, then I have in effect reduced my investment in the firm: the value of my shares falls. This is no different from the situation I would face if I had sold enough shares to raise the same amount of cash. 8. a. P = $1,000,000/20,000 = $50 b. The price tomorrow will be $1 per share lower, or $49. 9. a. After the repurchase, the market value of equity falls to $980,000, and the number of shares outstanding falls by $20,000/$50 = 400 shares to 19,600 shares. Price per share is $980,000/19,600 = $50, unchanged. An investor who starts with 100 shares and sells two shares to the company ends up with $4,900 in stock and $100 in cash, for a total of $5,000. 18-2 b. If the firm pays a dividend, the investor would have 100 shares worth $49 each and $100 cash, for a total of $5,000. This is identical to the investor’s position after the stock repurchase. 10. A 2 percent stock dividend will have no cash implications. The total market value of equity will remain $1,000,000, and shares outstanding will increase to 20,000 × 1.02 = 20,400. Price per share will fall to $1,000,000/20,400 = $49.02. The investor will end up with 102 shares worth 102 × $49.02 = $5,000. The value of the position is the same as under the cash dividend or repurchase, but the allocation between shares and cash differs. 11. Compare a $10 dividend to a share repurchase. After the first $10 cash dividend is paid (at the end of the year), the shareholders can look forward to a perpetuity of further $10 dividends. The share price in one year (just after the firm goes ex- dividend) will be $100, and the investors will have just received a $10 cash dividend. If instead the firm does a share repurchase in year 1 (just before the stock would have gone ex-dividend), the share price would be $110 (representing the value of a perpetuity due, with the first payment coming immediately). For $10 million, it could repurchase 90,909 shares. After the repurchase, the total value of outstanding shares will be $100 million, exactly the same as if the firm had paid out the $10 million in a cash dividend. With only 909,091 shares now outstanding, each share will sell for: $100 million/909,091 shares = $110. Thus, instead of getting a $10 dividend, shareholders see the value of each share increase by $10. In the absence of taxes, they are indifferent between the two outcomes. 12. a. The after-tax value of the dividend to shareholders equals $2 × (1 – .28) = $1.44. This is the amount by which the stock price ought to fall when the stock goes ex- dividend. The only difference in the share price before and after the ex-dividend moment is the claim to the (after-tax) dividend. b. Nothing special should happen when the cheques are sent out. The claim to the dividend is determined by who owns the shares at the ex-dividend moment. By the time of the payment date, stock prices already reflect any impact of the dividend. 13. a. 1000 × 1.25 = 1250 shares Price per share will fall to $50/1.25 = $40. Value of equity initially is 1000 × $50 = $50,000. 18-3 It remains at 1250 × $40 = $50,000. b. A 5 for 4 split will have precisely the same effect on price per share, shares held, and the value of your equity position as the stock dividend. In both cases, the number of shares held increases by 25%. 14. a. After the dividend is paid, total market value of the firm will be $90,000, representing $45 per share. In addition, the investor will receive $5 per share. So the value of the share today is $50. b. Dividend Income = $5.00 Grossed Up Dividend = 1.25 x $5.00 = $6.25 Gross Federal Tax = 0.26 x $6.25 = $1.625 Less: Federal Dividend Tax Credit = 0.1333 x $6.25 = $0.833 Net Federal Dividend Tax = $0.792 Gross Provincial Tax = 0.1339 x $6.25 = $0.837 Less: Provincial Dividend Tax Credit = 0.051 x $6.25 = $0.319 Net Provincial Dividend Tax = $0.518 Net Tax on Dividend Income = $1.31 After-Tax Dividend Income = $3.69 Dividend Tax Rate = $5.00 100 26.2% $1.31 × = c. If the dividend is taxed at 26.2 percent, then the investor will receive an after- tax cash flow of $5 (1 – 0.262) = $3.69, so the price today will be only $45 + $3.69 = $48.69. This is less than the price in “a” by the amount of taxes investors pay on the dividend. 15. a. The repurchase will have no tax implications. Because the repurchase does not create a tax obligation for the shareholders, the value of the firm today is the value of the firm’s assets, $100,000, divided by 2000 shares, or $50 per share. The firm will repurchase 200 shares for $10,000. After the repurchase, the stock will sell at a price of $90,000/1800 = $50 per share, the same as before the repurchase. b. An investor who owns 200 shares and sells 20 shares to the firm will receive 20 × $50 = $1000 in cash and be left with 180 shares worth $9000, for a total value of $10,000. In the absence of taxes, this is precisely the cash and share value that would result if the firm paid a $5 per share cash dividend. If the 18-4 firm had paid the dividend, the investor would have received a cash payment of 200 × $5 = $1000, and each of the 200 shares would be worth $45, as we found in Problem 14.a. c. We compute the value of the shares once the firm announces its intention to pursue a stock repurchase or pay a dividend, and investors can calculate the after-tax value of the shares. If the firm pursues a share repurchase, today’s share price is $50, and the value of the firm is $50 × 2000 = $100,000. If instead the firm pays a dividend, the with-dividend stock price is $48.692 (see Problem 14.c) so the value of the firm is only $97,384. This is $2616 less than the value that would result if the firm pursued a share repurchase. The $2616 difference represents the taxes that will be paid on the $10,000 in dividends ($5 per share × 2000 shares). 16. a. Price = PV(after-tax dividend plus final share price) = $2(1 − .28) + $20 1.10 = $19.49 b. Before tax return = Dividend + Capital gain Price = $19.49 $2 + ($20 − $19.49) = .129 = 12.9% c. Price = PV(after-tax dividend plus final share price) = $3(1 −1.10 .28) + $20 = $20.15 d. Before-tax return = Dividend + Capital gain Price = $3 + ($20 − $20.15) $20.15 = .141 = 14.1% The before-tax return is higher because the higher dividend creates a greater tax burden. The before-tax return must rise to provide the same after-tax return of 10%. 17. a. You could find relevant information by using Yahoo or Google. For instance, a search on Google in September 2011 lead to information on Leon’s Furniture Limited, a furniture retailer, which recently announced the company's intention to repurchase up to 3,489,818 common shares, representing 4.99% of the outstanding shares as at August 28, 2011. The primary reason for the share repurchase, given by the company, is to enhance liquidity for shareholders while providing the company with the opportunity to buy back its shares when it appears attractive to do so. Reasons for share repurchases tend to differ across companies. 18-5 b. As of September 2011, some representative well known companies which offer Dividend Reinvestment Plans (DRPs) include: BCE Inc., CAE Industries, Magna, and Canadian Tire. Those that offer Share Purchase Plans (SPPs) include: Enbridge, Suncor, and TransAlta. Some advantages of DRPs and SPPs include: • Savings to investors on brokerage commissions. • Some investors may have an option to purchase additional shares. • Shares bought through these plans are often at a discount. • These plans enable investors to accumulate their holdings in the particular stocks carrying such plans. Disadvantages of DRPs and SPPs may include the following: • dividends reinvested through such plans may typically represent taxable income. • These plans enable purchases at specific intervals (for instance, monthly or quarterly) and may not be suitable to those investors who need the flexibility to be able to be able to buy or sell stocks quickly. • These plans are typically useful as long-term investment vehicles. c. As of September 2011, there is only one company listed, which is Leader Capital Markets Ltd.: Declaration date (September 1, 2011) - date on which, the dividend payment is announced. Ex dividend date (September 11) – cut off date set by the stock exchange, usually two business days prior to the record date. Record Date (September 8) – date on which, the firm announce that it will send a dividend cheque to all shareholders recorded on its book Payable Date (September 22) – date on which, the dividend cheques are mailed to investors. 18. a. A pension fund would not care about the dividend payout policy and therefore would be indifferent between Hi and Lo. Because the pension fund pays no taxes, it will focus only on the total pretax rate of return. b. With the dividend tax credit, an individual’s preference would depend on her or his tax bracket. A low-taxed individual will, likely, have a lower tax rate on dividend income than on capital gains income. This individual will, therefore, prefer a high dividend payout and opt for the Hi shares. On the other hand, an individual in a high-tax bracket should have a preference for a low dividend payout policy and therefore prefer the Lo shares. For this individual, the stated 18-6 tax rate on capital gains is lower than the rate on dividend income. Moreover, the ability to defer recognition of capital gains confers a further advantage to a low payout policy. c. A corporation prefers a high payout ratio and therefore prefers the Hi shares. The exclusion of dividend income from taxable income makes dividends more valuable than capital gains on an after-tax basis. 19. The increase in stock prices reflects the positive information contained in the dividend increase. The stock price increase can be interpreted as a reflection of a new assessment of the firm’s prospects, not as a reflection of investors’ preferences for high dividend payout ratios. 20. a. True. b. False. Firms smooth out dividends and do not maintain a strict proportional relationship between current earnings and dividends. They move dividends only part way toward the dividend target when earnings change. c. True. d. False. Firms seem reluctant to reduce dividends and therefore do not increase dividends in response to earnings increases that are not expected to persist, or that are not expected to be representative of long-run earnings prospects. 21. a. High-risk companies tend to have low dividend payout ratios to reduce the risk of dividend cuts in the future. They have low P/E ratios because a high risk premium reduces the present value of an expected stream of earnings or dividends. b. Firms that experience a temporary decline in profits will have high payout ratios because they try to stabilize dividends despite the fact that earnings have fallen. Their P/E ratios will tend to be higher if the earnings decline is expected to be temporary. The stock price will reflect the entire stream of future earnings, not just the temporarily low level of current earnings. c. Companies that expect a decline in profits tend to have low payout ratios since the current dividend paid reflects, in part, the lower expected future profits and will seem high relative to current profits. The P/E ratio also will be low because the price will reflect the anticipation of lower future earnings. d. Growth companies usually have low payout ratios because these firms have ample investment opportunities and can reduce the costs involved in issuing 18-7 new securities by retaining and reinvesting earnings. Their P/E ratio will be high because the stock price reflects the anticipation of future earnings growth. 22. Companies with unpredictable earnings levels are afraid to commit to dividend levels that might be unsustainable if earnings fall in the future. Therefore, they choose lower target payout ratios relative to current earnings. They also respond more cautiously to increases in earnings, waiting to see whether long-run earnings are high enough to justify an increase in the dividend level. 23. Dividend Yield Div. Payout Ratio (%) Retention Rate (%) 2010 2010 2009 2010 2009 Enbridge Inc 3.0 67.5 36.0 32.5 64.0 BCE 5.4 64.3 76.2 35.7 23.8 Royal Bank 4.4 59.4 79.1 40.6 20.9 All three companies are relatively mature companies, and as such have dividend policies which seek to set stable dividend yields and target dividend payout ratios. 24. a. The pension fund pays no taxes. The individual pays 27.92 percent taxes on dividends and 20.08 percent taxes on capital gains. Dividend Tax Rate: = [(1.25 x 0.29) – (1.25 x 0.1333)] + [(1.25 x 0.1116) – (1.25 x 0.045)] = 0.2792 Capital Gains Tax Rate: = 0.5 (0.29) + 0.5 (0.1116) = 0.2008 The corporation pays no tax on dividends and capital gains tax of: 0.5 (0.28) = 0.14 18-8 The after-tax rate of return for each investor equals: Dividend (1 – Dividend Tax) + Capital Gains (1 – Capital Gains Tax) Price We can use this formula to construct the following table of after-tax returns: Stock Investor Pension Fund Corporation Individual A 10% 8.60% 7.992% B 10% 9.30% 7.6% C 10% 10.00% 7.208% b. For such investors, the dividend tax rate is: = [(1.25 x 0.16) – (1.25 x 0.1333)] + [(1.25 x 0.062) – (1.25 x 0.045)] = (0.2 – 0.167) + (0.0775 – 0.05625) = 0.033 + 0.02125 = 0.05425 The capital gains tax rate is: = 0.5 (0.16) + 0.5 (0.062) = 0.08 + 0.031 = 0.111 The after-tax dollar proceeds from the shares equals: = Dividends x (1 – 0.05425) + Capital Gains x (1 – 0.111) If these proceeds are to provide an 8% after-tax return, then: 0.08 x P0 = (Dividend x 0.9458) + (Capital Gains x 0.889) or P0 = (Dividend x 0.9458) + (Capital Gains x 0.889) 0.08 Using this formula for each stock, we find: Stock Price A (0 x 0.9458) + (10 x 0.889) = $111.13 0.08 18-9 B (5 x 0.9458) + (5 x 0.889) = $114.68 0.08 C (10 x 0.9458) + (0 x 0.889) = $118.23 0.08 Notice that a larger proportion of before-tax returns paid in the form of dividends results in a lower stock price. 25. a. If the firm pays a dividend, the stock price will fall to $19 per share. If the firm does a stock repurchase, the market value of equity will fall to $19,000 and the number of shares will fall by $1000/$20 = 50 shares. The stock price will remain at $19,000/950 = $20 per share. b. If the firm pays a dividend, earnings per share will be EPS = $2000/1000 = $2. If the firm does the repurchase, EPS = $2000/950 = $2.105. c. If the dividend is paid, the price-earnings ratio will be $19/$2 = 9.5. If the stock is repurchased, the price-earnings ratio will be $20/$2.105 = 9.5, the same as if the dividend is paid. d. We have just shown that dividends per se do not have an effect on the P/E ratio. The stock sells at the same P/E multiple regardless of whether the firm pays a dividend or repurchases shares. The most likely reason that firms with high dividend payouts have high price- earnings ratios is that both ratios are computed using current earnings rather than trend or long-run earnings. If earnings are temporarily low, the ratio of price to current earnings will be temporarily high. So will the ratio of dividends to current earnings because firms set dividend levels based on long- run earnings prospects. Therefore, we observe a correlation between P/E ratios and payout ratios. Another reason firms with high dividend payout ratios may sell at higher P/E multiples is that these firms tend to be in more mature industries with lower risk. If investors thus demand a lower risk premium, they will value the stock at a higher multiple of current dividends and earnings. 26. a. If the entire return on the shares is in the form of dividends the investor earns 8.5% after-tax each year (10% x (1 – 15%)) regardless of the holding period. b. If all of the pre-tax return of 10% is in the form of capital gains, the annualized after-tax return is dependent on the holding period. 18-10 c. Capital gains may be preferred to dividends even when the tax rates are equal because taxes on gains can be deferred. As shown in the table below, after-tax returns rise with longer holding periods as the gain, and corresponding tax, is deferred. Period Total Return Annualized Return % Annualized After-Tax Return % 1 110.00 10.00% 8.50% 5 161.05 12.21% 10.38% 10 259.37 15.94% 13.55% 20 672.75 28.64% 24.34% Solution to Minicase for Chapter 18 You will find an Excel spreadsheet solution for this minicase at the Connect site. The statement of cash flows indicates that, in spite of substantial capital expenditures in 2005 ($2.063 billion), Penn Schumann’s cash balance increased by $1.510 billion in 2005. This increase in cash led to substantial increases in liquidity ratios and decreases in leverage, as shown in the Excel spreadsheet. Dividend payout fell from 42% of net income in 2004 to 35% in 2005 despite a $328 million increase in dividends. If the entire $1.510 billion increase in cash had been instead paid out as dividends, then liquidity would still have increased and leverage would still have decreased (as shown in the spreadsheet), although the changes would of course have been less substantial. The dividend payout ratio would have increased to over 66%. Ms. Rodriquez is probably correct when she states: “I don’t think we should commit to paying out high dividends, but perhaps we could use some of our cash to repurchase stock.” A payout ratio of 66.5% is likely too high to be maintained in the future, but a share repurchase might send a positive signal to the markets without creating the expectation of continued high dividend payout. Should other opportunities arise in the future (i.e., a drug for treatment of liver diseases or an acquisition in the biotech field), Penn Schumann would have the option to retain a larger portion of income without reducing the payout ratio. In addition, since debt ratios would improve even with a share repurchase (as shown in the spreadsheet), Penn Schumann may also have additional borrowing capacity to finance such ventures. A payout in the form of a share repurchase would also serve to alleviate the impression that “we fritter away cash on easy living.” 18-11 Solution Manual for Fundamentals of Corporate Finance Richard A. Brealey, Stewart C. Myers, Alan J. Marcus, Elizabeth Maynes, Devashis Mitra 9780071320573, 9781259272011
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