Question

Illustration: Caterpillar Financial Services Corp. (a subsidiary of Caterpillar) and Sterling Construction Corp. sign a lease agreement dated January 1, Year 7, that calls for Caterpillar to lease a front-end loader to Sterling beginning January 1, Year 7. The terms and provisions of the lease agreement, and other pertinent data, are as follows.

•The term of the lease is five years. The lease agreement is noncancelable, requiring equal rental payments of $25,981.62 at the beginning of each year (annuity-due basis).

•The loader has a fair value at the inception of the lease of $100,000, an estimated economic life of five years, and no residual value.

•Sterling pays all of the executory costs directly to third parties except for the property taxes of $2,000 per year, which is included as part of its annual payments to Caterpillar.

•The lease contains no renewal options. The loader reverts to Caterpillar at the termination of the lease.

•Sterling’s incremental borrowing rate is 11 percent per year.

•Sterling depreciates, on a straight-line basis, similar equipment that it owns.

•Caterpillar sets the annual rental to earn a rate of return on its investment of 10 percent per year; Sterling knows this fact.

How do you find the minimum lease payment with financial calucator? btw the answer is 100,000

N=?

I/Y=?

PV=?

PMT=?

FV=?

Answer 1

Payment at beginning of each year = $ 25,981.62 ...(1)

property taxes (included in annual payments) per year = $ 2,000 ...(2)

minimum lease payment = (1) - (2) = 25,981.62 - 2,000 = 23,981.62 ...(3)

Above information also mentions residual value at 5th year = 0

Note: payments are made at beginning of each year, so beginning of year 1 would be t=0. So minimum lease payments would be:

at t=0: 23,981.62

at t=1: 23,981.62

at t=2: 23,981.62

at t=3: 23,981.62

at t=4: 23,981.62

PV(minimum lease payments) = 23,981.62 + PV(annuity, 4 years, payment of 23,981.62, 10% rate ) ...(4)

To calculate, PV(annuity, 4 years, payment of 23,981.62, 10% rate ) , in financial calculator,

N=4, PMT=23981.62, I/Y=10, FV=0 (as residual value is 0), PV=?

compute (CPT) PV, we get PV(annuity, 4 years, payment of 23,981.62, 10% rate ) = 76018.50859 ...(5)

Substituting value of equation (5) in equation (4), we get,

PV(minimum lease payments) = 23,981.62 + 76,018.50859 = 100,000.1286

{Note in above calculations my BA II Plus calculator was set in BGN mode value = END.}

You can also solve by setting your calculator to annuity-due mode with, BGN mode value = BGN.

To change modes - (2nd) (BGN) -> (2nd)(SET) -> (2nd)(QUIT)

If you set to BGN mode value = BGN,

N=5, PMT=23981.62, I/Y=10, FV=0 (as residual value is 0), PV=?

compute (CPT) PV, we get PV(minimum lease payments) = 100,000.1286.