Question

Problem 3: A construction firm must obtain a bulldozer to work on a long-term project. There are two options available to the firm – using a loan to purchase the bulldozer for $825,000, and leasing it from the equipment dealer. If the firm decides to purchase, it can finance the entire cost through a commercial bank for 8 years at an interest rate of 7.5% compounded annually. At the end of eight years, the firm will sell the bulldozer for a salvage value of $80,000.   If the firm decides to lease, it will pay the equipment dealer an up-front fee equal to 5% of the purchase price, followed by eight annual payments of $135,000. At the end of the lease, the firm will return the equipment to the dealer. The firm’s required rate of return is 10%.

1. Build an Excel worksheet to model the two options and help the firm decide which to choose. You can ignore depreciation or tax effects in your analysis (i.e., evaluate the options simply based on their respective cash flows).
2. Assuming that the equipment dealer is exactly indifferent between the construction firm purchasing or leasing, what is the dealer’s implied required rate of return? Note: the dealer retains the salvage value if the firm leases.

Answer 1

Under the purchase option

Annual payment of Loan (A) is given by

A/0.075*(1-1/1.075^8) = 825000

=> A = 140849.79

Net cost of bulldozer = 140849.79/1.1+140849.79/1.1^2+....+140849.79/1.1^8 - 80000/1.1^8

=140849.79/0.1*(1-1/1.1^8)-80000/1.1^8

=$714102.64

Under the Leasing option

Net cost of bulldozer = present value of payments

=5%*$825000 + 135000/1.1+135000/1.1^2+.....+135000/1.1^8

=$41250 + 135000/0.1*(1-1/1.1^8)

=$761465.04

So, in this case, the purchase option is better for the construction firm as the net cost is lesser in case of purchase

The dealer will spend $825000 today and receive 5% upfront fee as well as the annual lease payments and will also receive the salvage value at end of 8 years . So , the implied rate of return (r) to the dealer is given by

-825000+41250 + 135000/r*(1-1/(1+r)^8) + 80000/(1+r)^8 = 0

Solving r= 0.091176 or 9.12%

The dealer’s implied required rate of return is 9.12%