Question

Koss Leasing requires a 15 percent return on its investments. It is prepared to lease you a truck for two years, provided that it can achieve this return. The lease payments are to be made at the beginning of the year. The truck, which has a useful economic life of six years, cost Koss $60,000. Its estimated value in two years is $17,000. The CCA rate is 30 percent, and Koss’s tax rate is 25 percent.

Calculate the annual lease payment required by Koss Leasing. (Do not round intermediate calculations. Round the final answer to the nearest whole dollar.)

Annual lease payment      

Numeric Response

Answer 1

Solution:

Let the annual lease payment to be received by Koss Leasing at the beginning of each year be L.

1st Lease Payment at beginning of year 1, i.e. point of time 0:

The Capital Cost Allowance (CCA) rate is 30%. However, this being beginning of 1st year i.e. point of time 0 at which the truck is acquired no CCA applies until the end of the year.

Tax rate is 25% or 0.25 and residual income is 1 - 0.25 = 0.75

So cash inflow from lease rental net of tax = 0.75L

2nd Lease Payment at end of year 1:

CCA of 30% applied to the cost of the truck is 30% of $60,000

= $18,000

So, rental net of CCA = L - 18,000

Rental net of tax = 0.75 x (L - 18000)

= 0.75L - 13,500

Adding back the CCA allowance as it is a non-cash deduction, the cash inflow from lease rental net of tax is = 0.75L - 13,500 + 18,000

= 0.75L + 4,500

This has to be discounted to point of time 0 at required return on investment of 15%

So discounted cash inflow = CI (1+r)ⁿ

= (0.75L + 4,500) (1+0.15)¹

= (0.75L + 4,500) 1.15

Estimated value of the truck at end of year 2:

The estimated value at end of year 2 is $17,000. Assuming it is saleable at this value this would be an inflow which is to be discounted to point of time 0.

So discounted cash inflow CI (1+r)ⁿ

= 17000 1.15²

Now the present value of the above 3 cash flows has to be equated with the cost of the truck of $60,000, then only we can solve and find the value of L in the equation

0.75L + [(0.75L + 4,500) 1.15] + [ 17000 1.15² ] = 60,000

Multiplying and dividing 0.75L by 1.15² and [(0.75L + 4,500) 1.15] by 1.15:

[(0.75L x 1.15² ) 1.15² ] + [1.15 x(0.75L + 4,500) 1.15²] + [ 17000 1.15² ] = 60,000

Since all 3 additives on the LHS are divided by 1.15² we can now multiply both LHS and RHS by 1.15² to get:

1.15² x { [(0.75L x 1.15²) 1.15² ] + [1.15 x(0.75L + 4,500) 1.15²] + [ 17000 1.15² ] } = 1.15² x 60,000

(0.75L x 1.15²) + [1.15 x(0.75L + 4,500)] +17000 = 1.15² x 60,000

(0.75L x 1.15²) + [1.15 x(0.75L + 4,500)] +17000 = 79,350

(0.75L x 1.15²) + [1.15 x(0.75L + 4,500)] = 79,350 - 17000

(0.75L x 1.15²) + [1.15 x(0.75L + 4,500)] = 62,350

0.991875L + 0.8625L + 5,175 = 62,350

0.991875L + 0.8625L = - 5,175 + 62,350

1.854375L = 57,175

L = 57,175 1.854375

L = 30,832.49 or 30,832 (rounded down to nearest dollar)

Hence, the annual lease payment required by Koss Leasing for a 15 percent return on its investment in the truck of $60,000 is $30,832.