Question

Sage Hill Company is negotiating to lease a piece of equipment to MTBA, Inc. MTBA requests that the lease be for 9 years. The equipment has a useful life of 10 years. Sage Hill wants a guarantee that the residual value of the equipment at the end of the lease is at least $4,000. MTBA agrees to guarantee a residual value of this amount though it expects the residual value of the equipment to be only $2,500 at the end of the lease term.

If the fair value of the equipment at lease commencement is $100,000, what would be the amount of the annual rental payments Sage Hill demands of MTBA, assuming each payment will be made at the beginning of each year and Sage Hill wishes to earn a rate of return on the lease of 8%?

Answer 1

The lease will be classified as financial lease because the term of lease is 9 years which covers the major part of the economic life of the asset which is 10 years. This implies that the present value of annual lease rentals and guaranteed residual value will be equal to the fair of the leased asset.

Fair Value of the equipment = $100,000

Lease Term = 9 years

Rate of Interest = 8%

Guaranteed Residual Value = $2,500

Annuity factor of 8% for 9 years = 6.74664

Discounting factor of 8% at beginning of 9 years = 0.54027

Let annual lease payments = X

Fair Value of equipment = (Annual lease rentals * Annuity factor of 8% for 9 years) + (Guaranteed Residual Value * Discounting factor of 8% at 9 years)

$100,000 = (X * 6.74664) + ($2,500 * 0.54027)

$100,000 = (X * 6.74664) + $1350.675

(X * 6.74664) = $100,000 - 1,350.675

X = 98,649.325 / 6.74664

X = $14,621.99

Therefore, Annual lease payments shall be $14,621.99 at the beginning of each year.

Note: The present value factors are rounded off to five decimal places. If discounting factors are specifically stated in you question, then please use the discounting factors given with your question.