This page is designed to help you master the core concepts of lease financing. The problems below cover a variety of scenarios, from evaluating lease agreements to comparing the costs of leasing and buying. Use the interactive sections to test your knowledge before viewing the solutions.
Problem Statement: The Tata Company is deciding whether to lease or purchase a new truck. The cost of the truck is Tk. 40,000, and it will be depreciated by the straight-line method over 4 years to a salvage value of Tk. 10,000. The company can borrow at an annual interest rate of 10% to purchase the truck. The company can also lease the truck for 4 years with lease payments of Tk. 10,000 per year, payable at the beginning of each year. The corporate tax rate is 40%. The truck has a useful life of 4 years. The company is in the business of transporting goods and the truck is used for the business. The maintenance cost of the truck is Tk. 1,000 per year, and this will be paid by the company in both cases (lease or purchase).
i. Calculate Tata's PV cost of leasing.
ii. Calculate Tata's PV cost of owning and make a decision.
Solution:
We compare the PV cost of leasing to the PV cost of owning. The discount rate is the after-tax cost of debt: $10\% \times (1 - 0.40) = 6\%$.
i. Calculate Tata's PV cost of leasing.
Lease payments are Tk. 10,000 per year, at the beginning of each year.
After-tax lease payment = Lease Payment $\times (1 - T_C) = 10,000 \times (1 - 0.40) = \text{Tk. } 6,000$
| Year | After-tax Lease Payment | PV Factor (6%) | PV of Payment |
|---|---|---|---|
| 0 | 6,000 | 1.0000 | 6,000 |
| 1 | 6,000 | 0.9434 | 5,660.40 |
| 2 | 6,000 | 0.8900 | 5,340.00 |
| 3 | 6,000 | 0.8396 | 5,037.60 |
| Total PV Cost of Leasing | Tk. 22,038.00 | ||
ii. Calculate Tata's PV cost of owning and make a decision.
The PV cost of owning is: Initial Outlay - PV of Depreciation Tax Shield - PV of After-tax Salvage Value + PV of After-tax Maint. Costs
Initial Outlay: Tk. 40,000
Depreciation: $\frac{40,000-10,000}{4} = \text{Tk. } 7,500$ per year.
Depreciation Tax Shield: $7,500 \times 0.40 = \text{Tk. } 3,000$ per year.
After-tax Salvage Value: $10,000 \times (1 - 0.40) = \text{Tk. } 6,000$
After-tax Maintenance Costs: $1,000 \times (1 - 0.40) = \text{Tk. } 600$
PV of Depreciation Tax Shield = $3,000 \times \frac{1-(1.06)^{-4}}{0.06} = 3,000 \times 3.4651 = \text{Tk. } 10,395.30$
PV of After-tax Salvage Value = $6,000 \times (1.06)^{-4} = 6,000 \times 0.7921 = \text{Tk. } 4,752.60$
PV of After-tax Maintenance Costs = $600 \times \frac{1-(1.06)^{-4}}{0.06} = 600 \times 3.4651 = \text{Tk. } 2,079.06$
PV Cost of Owning = $40,000 - 10,395.30 - 4,752.60 + 2,079.06 = \text{Tk. } 26,931.16$
Decision: Since the PV cost of leasing (**Tk. 22,038**) is less than the PV cost of owning (**Tk. 26,931.16**), Tata should **lease** the truck.
Problem Statement: Wolfson Corporation has decided to purchase a new machine that costs Tk.2.8 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 35 percent. The Sur Bank has offered Wolfson a four-year loan for Tk.2.8 million. The repayment schedule is four yearly principal repayments of Tk.700,000 and an interest charge of 9 percent on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolfson. Lease payments of Tk.830,000 per year are due at the beginning of each of the four years of the lease.
Required:
(i) Should Wolfson lease the machine or buy it with bank financing?
(ii) What is the annual lease payment that will make Wolfson indifferent to whether it leases the machine or purchases it?
Solution:
We will compare the Net Present Value of the cost of leasing (NPV of Lease) to the Net Present Value of the cost of owning (NPV of Buy). The appropriate discount rate is the after-tax cost of debt, which is $9\% \times (1 - 0.35) = 5.85\%$.
i. Lease vs. Buy Decision:
Let's calculate the NPV of the cost for both options.
PV of Leasing:
Lease payments are Tk. 830,000 at the beginning of each year. The after-tax cost is $830,000 \times (1 - 0.35) = \text{Tk. } 539,500$.
| Year | After-tax Lease Payment | PV Factor (5.85%) | PV of Cost |
|---|---|---|---|
| 0 | 539,500 | 1.0000 | 539,500.00 |
| 1 | 539,500 | 0.9447 | 509,697.15 |
| 2 | 539,500 | 0.8925 | 481,593.75 |
| 3 | 539,500 | 0.8432 | 454,954.40 |
| Total PV Cost of Leasing | Tk. 1,985,745.30 | ||
Note: The PV cost is the total of the discounted after-tax payments. Since payments are at the beginning of the year, Year 0 payment is not discounted.
PV of Buying:
This is the initial outlay minus the present value of the tax shield from depreciation and interest payments.
Initial Cost = Tk. 2,800,000
Annual Depreciation = $\frac{2,800,000}{4} = \text{Tk. } 700,000$
Depreciation Tax Shield = $700,000 \times 0.35 = \text{Tk. } 245,000$ per year.
| Year | Beginning Balance | Interest (9%) | Principal | Total Payment | Interest Tax Shield (35%) | Depreciation Tax Shield (35%) | PV Factor (5.85%) | PV of Inflows |
|---|---|---|---|---|---|---|---|---|
| 1 | 2,800,000 | 252,000 | 700,000 | 952,000 | 88,200 | 245,000 | 0.9447 | 314,640 |
| 2 | 2,100,000 | 189,000 | 700,000 | 889,000 | 66,150 | 245,000 | 0.8925 | 277,411 |
| 3 | 1,400,000 | 126,000 | 700,000 | 826,000 | 44,100 | 245,000 | 0.8432 | 243,962 |
| 4 | 700,000 | 63,000 | 700,000 | 763,000 | 22,050 | 245,000 | 0.7966 | 212,859 |
PV of all tax shields = $314,640 + 277,411 + 243,962 + 212,859 = \text{Tk. } 1,048,872$
PV cost of buying = Initial Cost - PV of Tax Shields
= $2,800,000 - 1,048,872 = \text{Tk. } 1,751,128$
Decision: Since the PV cost of buying (**Tk. 1,751,128**) is less than the PV cost of leasing (**Tk. 1,985,745.30**), Wolfson should **purchase** the machine with bank financing.
ii. Annual Lease Payment for Indifference:
For Wolfson to be indifferent, the PV cost of leasing must equal the PV cost of buying.
PV Cost of Buying = Tk. 1,751,128
Let $L$ be the annual lease payment. The PV cost of leasing is the present value of the after-tax lease payments. The payments are an annuity due.
PV factor for 4-year annuity due at 5.85% = $1 + \frac{1 - (1.0585)^{-3}}{0.0585} = 1 + \frac{1 - 0.8432}{0.0585} = 1 + \frac{0.1568}{0.0585} = 1 + 2.6803 = 3.6803$
$1,751,128 = L \times 0.65 \times 3.6803$
$1,751,128 = L \times 2.3922$
$L = \frac{1,751,128}{2.3922} = \text{Tk. } 732,019.23$
The annual lease payment that would make Wolfson indifferent is **Tk. 732,019.23**.
Problem Statement: The Locke Corporation has just leased a metal-bending machine that calls for annual lease payments of Tk. 30,000 payable in advance. The lease period is six years, and the lease is classified as a capital lease for accounting purposes. The company's incremental borrowing rate is 11 percent, whereas the lessor's implicit interest rate is 12 percent. Amortization of the lease in the first year amounts to Tk. 16,332. On the basis of this information, compute the following: (i) The accounting lease liability that will be shown on the balance sheet immediately after the first lease payment. (ii) The annual lease expense (amortization plus interest) in the first year as it will appear on the accounting income statement. (The interest expense is based on the accounting value determined in Part (i).)
Solution:
i. Accounting lease liability immediately after the first payment:
The initial value of the lease liability is the present value of all future lease payments, discounted at the company's incremental borrowing rate (11%) or the lessor's implicit rate (12%), whichever is lower. The problem is flawed in that it gives two different interest rates and doesn't clearly state which one to use. Let's use the standard method. The present value of the lease liability is the present value of the annuity payments. Since payments are in advance (annuity due), the formula is:
Let's use the company's incremental borrowing rate of 11% for the calculation. $n = 6$.
$PV = 30,000 + 30,000 \times \left[ \frac{1 - (1.11)^{-5}}{0.11} \right] = 30,000 + 30,000 \times 3.6959 = 30,000 + 110,877 = \text{Tk. } 140,877$
Initial lease liability = Tk. 140,877. The first payment is made immediately, so the liability is reduced by this amount.
Lease liability after first payment = $140,877 - 30,000 = \text{Tk. } 110,877$
The accounting lease liability immediately after the first payment is **Tk. 110,877**.
ii. Annual lease expense in the first year:
The annual lease expense on the income statement is the sum of the amortization (principal repayment) and the interest expense for that year.
Amortization in first year = Tk. 16,332 (given)
Interest expense in first year is based on the lease liability for the year.
Interest = (Initial Liability - First Payment) $\times$ Interest Rate = $110,877 \times 0.11 = \text{Tk. } 12,196.47$
Lease expense = Amortization + Interest = $16,332 + 12,196.47 = \text{Tk. } 28,528.47$
The annual lease expense in the first year is approximately **Tk. 28,528**.
Problem Statement: Wolfson Corporation has decided to purchase a new machine that costs Tk.2.8 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 35 percent. The Sur Bank has offered Wolfson a four-year loan for Tk.2.8 million. The repayment schedule is four yearly principal repayments of Tk.700,000 and an interest charge of 9 percent on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolfson. Lease payments of Tk.830,000 per year are due at the beginning of each of the four years of the lease.
Required:
(i) Should Wolfson lease the machine or buy it with bank financing?
(ii) What is the annual lease payment that will make Wolfson indifferent to whether it leases the machine or purchases it?
Solution:
We will compare the two options (Lease vs. Buy) by calculating the Net Present Value of the cost of leasing (NPV of Lease) to the Net Present Value of the cost of owning (NPV of Buy). The appropriate discount rate is the after-tax cost of debt, which is $9\% \times (1 - 0.35) = 5.85\%$.
i. Lease vs. Buy Decision:
Let's calculate the NPV of the cost for both options.
PV of Leasing:
Lease payments are Tk. 830,000 at the beginning of each year. The after-tax cost is $830,000 \times (1 - 0.35) = \text{Tk. } 539,500$.
| Year | After-tax Lease Payment | PV Factor (5.85%) | PV of Cost |
|---|---|---|---|
| 0 | 539,500 | 1.0000 | 539,500.00 |
| 1 | 539,500 | 0.9447 | 509,697.15 |
| 2 | 539,500 | 0.8925 | 481,593.75 |
| 3 | 539,500 | 0.8432 | 454,954.40 |
| Total PV Cost of Leasing | Tk. 1,985,745.30 | ||
Note: The PV cost is the total of the discounted after-tax payments. Since payments are at the beginning of the year, Year 0 payment is not discounted.
PV of Buying:
This is the initial outlay minus the present value of the tax shield from depreciation and interest payments.
Initial Cost = Tk. 2,800,000
Annual Depreciation = $\frac{2,800,000}{4} = \text{Tk. } 700,000$
Depreciation Tax Shield = $700,000 \times 0.35 = \text{Tk. } 245,000$ per year.
| Year | Beginning Balance | Interest (9%) | Principal | Total Payment | Interest Tax Shield (35%) | Depreciation Tax Shield (35%) | PV Factor (5.85%) | PV of Inflows |
|---|---|---|---|---|---|---|---|---|
| 1 | 2,800,000 | 252,000 | 700,000 | 952,000 | 88,200 | 245,000 | 0.9447 | 314,640 |
| 2 | 2,100,000 | 189,000 | 700,000 | 889,000 | 66,150 | 245,000 | 0.8925 | 277,411 |
| 3 | 1,400,000 | 126,000 | 700,000 | 826,000 | 44,100 | 245,000 | 0.8432 | 243,962 |
| 4 | 700,000 | 63,000 | 700,000 | 763,000 | 22,050 | 245,000 | 0.7966 | 212,859 |
PV of all tax shields = $314,640 + 277,411 + 243,962 + 212,859 = \text{Tk. } 1,048,872$
PV cost of buying = Initial Cost - PV of Tax Shields
= $2,800,000 - 1,048,872 = \text{Tk. } 1,751,128$
Decision: Since the PV cost of buying (**Tk. 1,751,128**) is less than the PV cost of leasing (**Tk. 1,985,745.30**), Wolfson should **purchase** the machine with bank financing.
ii. Annual Lease Payment for Indifference:
For Wolfson to be indifferent, the PV cost of leasing must equal the PV cost of buying.
PV Cost of Buying = Tk. 1,751,128
Let $L$ be the annual lease payment. The PV cost of leasing is the present value of the after-tax lease payments. The payments are an annuity due.
PV factor for 4-year annuity due at 5.85% = $1 + \frac{1 - (1.0585)^{-3}}{0.0585} = 1 + \frac{1 - 0.8432}{0.0585} = 1 + \frac{0.1568}{0.0585} = 1 + 2.6803 = 3.6803$
$1,751,128 = L \times 0.65 \times 3.6803$
$1,751,128 = L \times 2.3922$
$L = \frac{1,751,128}{2.3922} = \text{Tk. } 732,019.23$
The annual lease payment that would make Wolfson indifferent is **Tk. 732,019.23**.
Problem Statement: The Locke Corporation has just leased a metal-bending machine that calls for annual lease payments of Tk. 30,000 payable in advance. The lease period is six years, and the lease is classified as a capital lease for accounting purposes. The company's incremental borrowing rate is 11 percent, whereas the lessor's implicit interest rate is 12 percent. Amortization of the lease in the first year amounts to Tk. 16,332. On the basis of this information, compute the following: (i) The accounting lease liability that will be shown on the balance sheet immediately after the first lease payment. (ii) The annual lease expense (amortization plus interest) in the first year as it will appear on the accounting income statement. (The interest expense is based on the accounting value determined in Part (i).)
Solution:
i. Accounting lease liability immediately after the first payment:
The initial value of the lease liability is the present value of all future lease payments, discounted at the company's incremental borrowing rate (11%) or the lessor's implicit rate (12%), whichever is lower. The problem is flawed in that it gives two different interest rates and doesn't clearly state which one to use. Let's use the standard method. The present value of the lease liability is the present value of the annuity payments. Since payments are in advance (annuity due), the formula is:
Let's use the company's incremental borrowing rate of 11% for the calculation. $n = 6$.
$PV = 30,000 + 30,000 \times \left[ \frac{1 - (1.11)^{-5}}{0.11} \right] = 30,000 + 30,000 \times 3.6959 = 30,000 + 110,877 = \text{Tk. } 140,877$
Initial lease liability = Tk. 140,877. The first payment is made immediately, so the liability is reduced by this amount.
Lease liability after first payment = $140,877 - 30,000 = \text{Tk. } 110,877$
The accounting lease liability immediately after the first payment is **Tk. 110,877**.
ii. Annual lease expense in the first year:
The annual lease expense on the income statement is the sum of the amortization (principal repayment) and the interest expense for that year.
Amortization in first year = Tk. 16,332 (given)
Interest expense in first year is based on the lease liability for the year.
Interest = (Initial Liability - First Payment) $\times$ Interest Rate = $110,877 \times 0.11 = \text{Tk. } 12,196.47$
Lease expense = Amortization + Interest = $16,332 + 12,196.47 = \text{Tk. } 28,528.47$
The annual lease expense in the first year is approximately **Tk. 28,528**.
Problem Statement: Wolfson Corporation has decided to purchase a new machine that costs Tk.2.8 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 35 percent. The Sur Bank has offered Wolfson a four-year loan for Tk.2.8 million. The repayment schedule is four yearly principal repayments of Tk.700,000 and an interest charge of 9 percent on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolfson. Lease payments of Tk.830,000 per year are due at the beginning of each of the four years of the lease.
Required:
(i) Should Wolfson lease the machine or buy it with bank financing?
(ii) What is the annual lease payment that will make Wolfson indifferent to whether it leases the machine or purchases it?
Solution:
We will compare the two options (Lease vs. Buy) by calculating the Net Present Value of the cost of leasing (NPV of Lease) to the Net Present Value of the cost of owning (NPV of Buy). The appropriate discount rate is the after-tax cost of debt, which is $9\% \times (1 - 0.35) = 5.85\%$.
i. Lease vs. Buy Decision:
Let's calculate the NPV of the cost for both options.
PV of Leasing:
Lease payments are Tk. 830,000 at the beginning of each year. The after-tax cost is $830,000 \times (1 - 0.35) = \text{Tk. } 539,500$.
| Year | After-tax Lease Payment | PV Factor (5.85%) | PV of Cost |
|---|---|---|---|
| 0 | 539,500 | 1.0000 | 539,500.00 |
| 1 | 539,500 | 0.9447 | 509,697.15 |
| 2 | 539,500 | 0.8925 | 481,593.75 |
| 3 | 539,500 | 0.8432 | 454,954.40 |
| Total PV Cost of Leasing | Tk. 1,985,745.30 | ||
Note: The PV cost is the total of the discounted after-tax payments. Since payments are at the beginning of the year, Year 0 payment is not discounted.
PV of Buying:
This is the initial outlay minus the present value of the tax shield from depreciation and interest payments.
Initial Cost = Tk. 2,800,000
Annual Depreciation = $\frac{2,800,000}{4} = \text{Tk. } 700,000$
Depreciation Tax Shield = $700,000 \times 0.35 = \text{Tk. } 245,000$ per year.
| Year | Beginning Balance | Interest (9%) | Principal | Total Payment | Interest Tax Shield (35%) | Depreciation Tax Shield (35%) | PV Factor (5.85%) | PV of Inflows |
|---|---|---|---|---|---|---|---|---|
| 1 | 2,800,000 | 252,000 | 700,000 | 952,000 | 88,200 | 245,000 | 0.9447 | 314,640 |
| 2 | 2,100,000 | 189,000 | 700,000 | 889,000 | 66,150 | 245,000 | 0.8925 | 277,411 |
| 3 | 1,400,000 | 126,000 | 700,000 | 826,000 | 44,100 | 245,000 | 0.8432 | 243,962 |
| 4 | 700,000 | 63,000 | 700,000 | 763,000 | 22,050 | 245,000 | 0.7966 | 212,859 |
PV of all tax shields = $314,640 + 277,411 + 243,962 + 212,859 = \text{Tk. } 1,048,872$
PV cost of buying = Initial Cost - PV of Tax Shields
= $2,800,000 - 1,048,872 = \text{Tk. } 1,751,128$
Decision: Since the PV cost of buying (**Tk. 1,751,128**) is less than the PV cost of leasing (**Tk. 1,985,745.30**), Wolfson should **purchase** the machine with bank financing.
ii. Annual Lease Payment for Indifference:
For Wolfson to be indifferent, the PV cost of leasing must equal the PV cost of buying.
PV Cost of Buying = Tk. 1,751,128
Let $L$ be the annual lease payment. The PV cost of leasing is the present value of the after-tax lease payments. The payments are an annuity due.
PV factor for 4-year annuity due at 5.85% = $1 + \frac{1 - (1.0585)^{-3}}{0.0585} = 1 + \frac{1 - 0.8432}{0.0585} = 1 + \frac{0.1568}{0.0585} = 1 + 2.6803 = 3.6803$
$1,751,128 = L \times 0.65 \times 3.6803$
$1,751,128 = L \times 2.3922$
$L = \frac{1,751,128}{2.3922} = \text{Tk. } 732,019.23$
The annual lease payment that would make Wolfson indifferent is **Tk. 732,019.23**.
Problem Statement: The Locke Corporation has just leased a metal-bending machine that calls for annual lease payments of Tk. 30,000 payable in advance. The lease period is six years, and the lease is classified as a capital lease for accounting purposes. The company's incremental borrowing rate is 11 percent, whereas the lessor's implicit interest rate is 12 percent. Amortization of the lease in the first year amounts to Tk. 16,332. On the basis of this information, compute the following: (i) The accounting lease liability that will be shown on the balance sheet immediately after the first lease payment. (ii) The annual lease expense (amortization plus interest) in the first year as it will appear on the accounting income statement. (The interest expense is based on the accounting value determined in Part (i).)
Solution:
i. Accounting lease liability immediately after the first payment:
The initial value of the lease liability is the present value of all future lease payments, discounted at the company's incremental borrowing rate (11%) or the lessor's implicit rate (12%), whichever is lower. The problem is flawed in that it gives two different interest rates and doesn't clearly state which one to use. Let's use the standard method. The present value of the lease liability is the present value of the annuity payments. Since payments are in advance (annuity due), the formula is:
Let's use the company's incremental borrowing rate of 11% for the calculation. $n = 6$.
$PV = 30,000 + 30,000 \times \left[ \frac{1 - (1.11)^{-5}}{0.11} \right] = 30,000 + 30,000 \times 3.6959 = 30,000 + 110,877 = \text{Tk. } 140,877$
Initial lease liability = Tk. 140,877. The first payment is made immediately, so the liability is reduced by this amount.
Lease liability after first payment = $140,877 - 30,000 = \text{Tk. } 110,877$
The accounting lease liability immediately after the first payment is **Tk. 110,877**.
ii. Annual lease expense in the first year:
The annual lease expense on the income statement is the sum of the amortization (principal repayment) and the interest expense for that year.
Amortization in first year = Tk. 16,332 (given)
Interest expense in first year is based on the lease liability for the year.
Interest = (Initial Liability - First Payment) $\times$ Interest Rate = $110,877 \times 0.11 = \text{Tk. } 12,196.47$
Lease expense = Amortization + Interest = $16,332 + 12,196.47 = \text{Tk. } 28,528.47$
The annual lease expense in the first year is approximately **Tk. 28,528**.
Problem Statement: Wolfson Corporation has decided to purchase a new machine that costs Tk.2.8 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 35 percent. The Sur Bank has offered Wolfson a four-year loan for Tk.2.8 million. The repayment schedule is four yearly principal repayments of Tk.700,000 and an interest charge of 9 percent on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolfson. Lease payments of Tk.830,000 per year are due at the beginning of each of the four years of the lease.
Required:
(i) Should Wolfson lease the machine or buy it with bank financing?
(ii) What is the annual lease payment that will make Wolfson indifferent to whether it leases the machine or purchases it?
Solution:
We will compare the two options (Lease vs. Buy) by calculating the Net Present Value of the cost of leasing (NPV of Lease) to the Net Present Value of the cost of owning (NPV of Buy). The appropriate discount rate is the after-tax cost of debt, which is $9\% \times (1 - 0.35) = 5.85\%$.
i. Lease vs. Buy Decision:
Let's calculate the NPV of the cost for both options.
PV of Leasing:
Lease payments are Tk. 830,000 at the beginning of each year. The after-tax cost is $830,000 \times (1 - 0.35) = \text{Tk. } 539,500$.
| Year | After-tax Lease Payment | PV Factor (5.85%) | PV of Cost |
|---|---|---|---|
| 0 | 539,500 | 1.0000 | 539,500.00 |
| 1 | 539,500 | 0.9447 | 509,697.15 |
| 2 | 539,500 | 0.8925 | 481,593.75 |
| 3 | 539,500 | 0.8432 | 454,954.40 |
| Total PV Cost of Leasing | Tk. 1,985,745.30 | ||
Note: The PV cost is the total of the discounted after-tax payments. Since payments are at the beginning of the year, Year 0 payment is not discounted.
PV of Buying:
This is the initial outlay minus the present value of the tax shield from depreciation and interest payments.
Initial Cost = Tk. 2,800,000
Annual Depreciation = $\frac{2,800,000}{4} = \text{Tk. } 700,000$
Depreciation Tax Shield = $700,000 \times 0.35 = \text{Tk. } 245,000$ per year.
| Year | Beginning Balance | Interest (9%) | Principal | Total Payment | Interest Tax Shield (35%) | Depreciation Tax Shield (35%) | PV Factor (5.85%) | PV of Inflows |
|---|---|---|---|---|---|---|---|---|
| 1 | 2,800,000 | 252,000 | 700,000 | 952,000 | 88,200 | 245,000 | 0.9447 | 314,640 |
| 2 | 2,100,000 | 189,000 | 700,000 | 889,000 | 66,150 | 245,000 | 0.8925 | 277,411 |
| 3 | 1,400,000 | 126,000 | 700,000 | 826,000 | 44,100 | 245,000 | 0.8432 | 243,962 |
| 4 | 700,000 | 63,000 | 700,000 | 763,000 | 22,050 | 245,000 | 0.7966 | 212,859 |
PV of all tax shields = $314,640 + 277,411 + 243,962 + 212,859 = \text{Tk. } 1,048,872$
PV cost of buying = Initial Cost - PV of Tax Shields
= $2,800,000 - 1,048,872 = \text{Tk. } 1,751,128$
Decision: Since the PV cost of buying (**Tk. 1,751,128**) is less than the PV cost of leasing (**Tk. 1,985,745.30**), Wolfson should **purchase** the machine with bank financing.
ii. Annual Lease Payment for Indifference:
For Wolfson to be indifferent, the PV cost of leasing must equal the PV cost of buying.
PV Cost of Buying = Tk. 1,751,128
Let $L$ be the annual lease payment. The PV cost of leasing is the present value of the after-tax lease payments. The payments are an annuity due.
PV factor for 4-year annuity due at 5.85% = $1 + \frac{1 - (1.0585)^{-3}}{0.0585} = 1 + \frac{1 - 0.8432}{0.0585} = 1 + \frac{0.1568}{0.0585} = 1 + 2.6803 = 3.6803$
$1,751,128 = L \times 0.65 \times 3.6803$
$1,751,128 = L \times 2.3922$
$L = \frac{1,751,128}{2.3922} = \text{Tk. } 732,019.23$
The annual lease payment that would make Wolfson indifferent is **Tk. 732,019.23**.
Problem Statement: The principal reason for the existence of leasing is that:
a) Intermediate-term loans are difficult to obtain
b) Companies, financial institutions, and individuals derive different benefits from owning assets
c) Leasing is a renewable source of intermediate-term funds
d) This is a type of financing unaffected by changes in tax law
e) It never appears as a liability on the balance sheet
Solution:
The correct answer is **(b) Companies, financial institutions, and individuals derive different benefits from owning assets**. The primary reason for leasing is that it allows the party who can most effectively use the tax benefits of asset ownership (e.g., depreciation) to claim them, while still allowing another party to use the asset. This often results in a lower effective cost of financing for the lessee and a more efficient allocation of capital.
Problem Statement: The management of a company has decided to acquire Machine X which costs \$63,000 and has an operational life of four years. The expected scrap value would be zero. Tax is payable at 30% on operating cash flows one year in arrears. Tax allowable depreciation is available at 25% a year on a reducing balance basis. Suppose that the company has the opportunity either to purchase the machine or to lease it under a finance lease arrangement, at an annual rent of \$20,000 for four years, payable at the end of each year. The company can borrow to finance the acquisition at 10%. Should the company lease or buy the machine?
Solution:
To decide whether to lease or buy, we need to compare the present value of the cost of leasing (PV of Lease) with the present value of the cost of buying (PV of Buy). The appropriate discount rate for this analysis is the after-tax cost of debt: $10\% \times (1 - 0.30) = 7\%$.
PV of Buying (Net Cost of Owning):
PV of Buy = Initial Outlay - PV of Depreciation Tax Shield.
Initial Outlay = \$63,000.
We need to calculate the depreciation tax shield for each year.
| Year | Opening NBV | Depreciation (25%) | Tax Shield (30%) | PV Factor (7%) | PV of Tax Shield |
|---|---|---|---|---|---|
| 1 | 63,000 | 15,750 | 4,725 | 0.9346 | 4,416 |
| 2 | 47,250 | 11,813 | 3,544 | 0.8734 | 3,095 |
| 3 | 35,437 | 8,859 | 2,658 | 0.8163 | 2,169 |
| 4 | 26,578 | 6,645 | 1,994 | 0.7629 | 1,521 |
PV of Depreciation Tax Shield (total) = $4,416 + 3,095 + 2,169 + 1,521 = \text{Tk. } 11,201$
PV of Buy = Initial Outlay - PV of Tax Shield = $63,000 - 11,201 = \text{Tk. } 51,799$
PV of Leasing (Net Cost of Leasing):
The cash flows for leasing are the after-tax lease payments. The lease payments are \$20,000 at the end of each year. The tax shield on the lease payments is realized one year later.
PV of after-tax lease payments = PV of Lease Payments - PV of Tax Shield
PV of Lease Payments = $20,000 \times \frac{1-(1.07)^{-4}}{0.07} = 20,000 \times 3.3872 \approx \text{Tk. } 67,744$
PV of Tax Shield on Lease Payments = $(20,000 \times 0.30) \times \frac{1-(1.07)^{-4}}{0.07} \times \frac{1}{1.07}$
$= 6,000 \times 3.3872 \times 0.9346 \approx \text{Tk. } 18,989$
PV Cost of Leasing = $67,744 - 18,989 = \text{Tk. } 48,755$
Decision: Since the cost of leasing (**Tk. 48,755**) is less than the cost of buying (**Tk. 51,799**), the company should **lease** the machine.
Problem Statement: In a sale and leaseback arrangement, the seller is the lessee and the buyer is the lessor.
Solution:
True. In a sale and leaseback arrangement, a firm sells an asset it owns to another party and immediately leases it back. The original owner of the asset is the **seller** and now becomes the **lessee** (the user of the asset). The party that buys the asset is the **buyer** and becomes the **lessor** (the owner who receives lease payments).