Question

Leases Worksheets Part 1: Economics of Leases-Setting Rental Payments suppose that a piece of machinery with a fair value of $40,000 will be leased for four years, with annual rental payments made at the beginning of each year, Determine the amount the lessor will charge for those annual payments under the following scenarios: a) Expected residual value = $8,000, and implicit interest rate = 6%. b) Expected residual value = $8,000, and implicit interest rate = 8%. c) Expected residual value = $0, and implicit interest rate = 8%.

Answer 1

Asset Value = 40000

a) Residual value = $8000 at 4th year end

IRR = 6%

Let Annual rent = x

IRR Value for 3 years as lease rents made at the begining of the year = 3.673

IRR Value at year 4 = 0.7921

So, 3.673(x)+8000*0.7921 = 40000

3.673x = 40000-6336.75

3.673x = 33663.25

x = $9165.05

Therefore,

Annual lease payments = $9165.05 per annum

b) Residual value = $8000 at 4th year end

IRR = 8%

Let Annual rent = x

IRR Value for 3 years as lease rents made at the begining of the year = 3.5771

IRR Value at year 4 = 0.7350

So, 3.5771(x)+8000*0.7350 = 40000

3.5771x = 40000-5880.24

3.5771x = 34119.76

x = $9538.39

Therefore,

Annual lease payments = $9538.39 per annum

c) Residual value = 0 at 4th year end

IRR = 8%

Let Annual rent = x

IRR Value for 3 years as lease rents made at the begining of the year = 3.5771

IRR Value at year 4 = 0.7350

So, 3.5771(x)+0 = 40000

3.5771x = 40000

    x = $11182.24

Therefore,

Annual lease payments = $11182.24 per annum