Question

Karen Wilson Construction Company is considering the acquisition of a new bulldozer. Big Tools, Inc. has offered to lease the equipment to Wilson Company for all 12 years of its useful life at annual year-end lease payments of $24,500. Each payment will include 9% interest. At the end of 12 years of lease payments, Big Tools, Inc. will allow Wilson to keep the bulldozer.
Required:
a. At what amount should the bulldozer and lease obligation be capitalized on Wilson’s balance sheet?
b. Prepare an amortization table for the lease.
c. Explain why a $24,500 lease payment doesn’t cause the amount owed to decrease by $24,500.
d. Explain why Wilson’s interest expense gets smaller for each successive year of the lease.

Answer 1

Answer:

a) 175,437.77

b)

$\left[\begin{array}{ccccc}Year&Beg Principal&Interest&Installment&Ending\\1&175437.77&15789.4&-24500&166727.17\\2&166727.17&15005.45&-24500&157232.62\\3&157232.62&14150.94&-24500&146883.56\\4&146883.56&13219.52&-24500&135603.08\\5&135603.08&12204.28&-24500&123307.36\\6&123307.36&11097.66&-24500&109905.02\\7&109905.02&9891.45&-24500&95296.47\\8&95296.47&8576.68&-24500&79373.15\\9&79373.15&7143.58&-24500&62016.73\\10&62016.73&5581.51&-24500&43098.24\\\end{array}\right]$

$\left[\begin{array}{ccccc}11&43098.24&3878.84&-24500&22477.08\\12&22477.08&2022.94&-24500&0.02\\\end{array}\right]$

(I split into two arrays as I couldn't put  the entire information into one)

c) because of the time value of money the principal generates interest over time making the installment pay up both concept principal and interest.

d) they decrease as the principal decreases over time as the lease payment exceeds the interest accrued over the year.

Explanation:

a) it will record at the present value of the lease payment annuity

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 24,500

time 12

rate 0.09

$24500 \times \frac{1-(1+0.09)^{-12} }{0.09} = PV$

PV $175,437.7693

b)

we build the table starting withthe beginning lease value

calcualte the interest accrued over the year and subtract the lease payment

this makes a new balance of the loan principal which start the process again until it is fully paid.