Question

Marin Inc. wishes to lease machinery to Thiensville Company. Thiensville wants the machinery for 4 years, although it has a useful life of 10 years. The machinery has a fair value at the commencement of the lease of $49,000, and Marin expects the machinery to have a residual value at the end of the lease term of $25,000. However, Thiensville does not guarantee any part of the residual value. Thiensville does expect that the residual value will be $47,000 instead of $25,000. What would be the amount of the annual rental payments Marin demands of Thiensville, assuming each payment will be made at the end of each year and Marin wishes to earn a rate of return on the lease of 6%?

*Please show how to do the calculation on a financial calculator without a factor table*

Answer 1

Answer -

Step - ( 1 ) - Information Given -

Marin Inc. wishes to lease machinery to Thiensville Company.

The machinery has a fair value at the commencement of the lease of $49000.

Lease term = 4 years.

Unguaranteed residual value of machinery at the end of the lease term = $25000.

Rate of return on the lease = 6%

.

Step - ( 2 ) - Calculation of Present Value of Unguaranteed residual value of machinery at the end of the lease term -

Formula =

Present Value = UGRV / ( 1 + r )n

Here,

UGRV = Unguaranteed residual value of machinery = $25000.

r = Rate of return on the lease = 6%

n = Time period = 4 year

Putting the values in the above formula we get -

Present Value of Unguaranteed residual value =

= $25000 / ( 1 + 0.06 )⁴

= $25000 / 1.26247696

= $19802 [ Rounded off to zero decimal places ]

.

Step - ( 3 ) - Calculation of Present Value of Annual rental payments -

= Fair value of machinery on lease - Present Value of Unguaranteed residual value

= $49000 - $19802 [ Refer step - (2) for calculations ]

= $29198

.

Step - ( 4 ) - Calculation of Annual rental payments -

Formula =

PV / [ 1 - ( 1 + r )-n / r ]

Here,

PV = Present Value of Annual rental payments = $29198 [ Refer step - (3) for calculations ]

r = Rate of return on the lease = 6%

n = Time period = 4 year

Putting the values in the above formula we get -

Annual rental payments =

= $29198 / [ 1 - ( 1 + 0.06 )^-4 / 0.06 ]

= $29198 / 3.46510561283

= $8426 [ Rounded off to zero decimal places ]