Question

World of Leasing Limited (WLL) is trying to determine the lease payment it should quote for the construction trucks it is considering purchasing for leasing. Assume that each truck costs $200,000, has a 5 year useful life and a CCA rate of 50%. Before tax operating cost of the truck is $50,000 per year paid by the owner (lessor) of the asset. The corporate tax rate is 40%, before tax cost of debt is 8%, and risk free rate is 4%. Cost of capital is 10%. CCA tax shield will be claimed at the end of the year and the lease payment and operating costs will be at the beginning of the year.

a. Determine the annual lease payment if the resale value of the truck is $60,000 after 5 years. Assume asset pool is open.

b. Determine the annual lease payment if the resale value of the truck is $60,000 after 5 years. Assume asset pool is closed.

c. Continuing with b) above, suppose OnlyLease Inc. (OLI) has a corporate tax rate of 0%, cost of debt is 8%, and cost of capital is 12%. What is the maximum lease payment OLI would be willing to make?

d. Within what range of values WLL and OLI can make a deal?

Answer 1

Solution to part a:

After tax interest rate = i = 8% (1 – 0.40) = 4.8%

PV of CCATS = (CdT_c / i + d) (1 + 0.5i / 1 + i) – (SdT_c / i + d) (1 / (1 + i)^t)

= ($200,000 * 0.50 * 0.40 / 0.04 + 0.50) (1.02 / 1.04) – ($60,000 * 0.50 * 0.40 / 0.04 + 0.50)

(1 / (1.04)⁵)

= $72,650 - $18,265 = $54,385

PV of resale value = $60,000 / (1.10)⁵ = $37,255

PV of after tax operating costs = $50,000 * (1 – 0.40) * [1 – (1 / 1.048⁵) / 0.048] * (1.048) = $136,875

Amount to be recovered from the lease payments = $200,000 - $54,385 - $37,255 + $136,875

= $245,235

After tax lease payment = $245,235 / [1 – (1 / 1.048⁵) / 0.048] * (1.048) = $53,750 per year

Before tax lease payment = $53,750 / (1 – 0.40) = $89,584 per year.

Solution to part b:

Year	UCCbeg	CCA	CCATS
1	$200,000	$50,000	$20,000
2	$150,000	$75,000	$30,000
3	$75,000	$37,500	$15,000
4	$37,500	$18,750	$7,500
5	$18,750	$9,375	$3,750

UCC at the end of 5 years = $9,375

After tax salvage value at the end of 5 years = $60,000 - ($60,000 - $9,375) * 0.40 = $39,750

PV of after tax salvage value = $39,750 / (1.10)⁵ = $24,682

PV of CCATS = ($20,000 / 1.04) + ($30,000 / 1.04²) + ($15,000 / 1.04³) + ($7,500 / 1.04⁴) +

($3,750 / 1.04⁵)

        = $19,231 + $27,737 + $13,335 + $6,411 + $3,082

        = $69,796

Amount to be recovered from lease payments = $200,00 - $24,682 - $69,796 + $136,875

= $242,397

After tax lease payment = $242,397 / [1 – (1 / 1.048⁵) / 0.048] * (1.048) = $53,128

Before tax lease payment = $53,128 / (1 – 0.40) = $88,547 per year

Solution to part c:

After tax interest rate = i = 8%

PV of resale value = $60,000 / (1.12)⁵ = $34,046

PV of operating costs = $50,000 / [1 – (1 / 1.08⁵) / 0.08] * (1.08) = $215,606

PV of lease payments = $200,000 - $34,046 + $215,6060 = $381,560

L = $381,560 / [1 – (1 / 1.08⁵) / 0.08] * (1.08) = $88,485 per year

Solution to part d:

Deal cannot be made.