Question

A manager needs to decide whether to purchase new equipment and sell it after 5 years, or, lease the equipment from a vendor for the same period. The upfront price of the equipment is P = #×$3 000, with additional annual insurance and maintenance costs amounting to $11 020 (payable at the end of each year). Rent for the same equipment is $2 500 per month, payable annually (at the end of each year). What must be the minimum resale value of the equipment (at the end of year 5) in order to justify buying it? Assume that the company’s cost of money is 8% compounded annually.

TIP: Use the PW of the rental alternative to determine the required resale price at the end of the period to make the two alternatives of equal value. Use cash flow diagrams

# = 50

Answer 1

Given Data

PURCHASE OPTION

Purchase Price = P = 50 * $3000 = $150000

Annual Insurance and maintenance = $11020

Resale value at the end of year 5 = S = ?

Interest rate = 8%

Useful life = 5 years

LEASE OPTION

Annual rent = $2500

Interest rate = 8%

Useful life = 5 years

In order to estimate the salvage value, we need to equate the Present worth of the purchase option to the Present worth of the lease option.

Present worth of Purchase option = Present worth of Lease option

150000+ 11020(P/A,8%,5) – S(P/F,8%,5) = 2500(P/A,8%,5)

Using DCIF Tables

150000+ 11020(3.993) – S(0.6806) = 2500(3.993)

(150000+ 11020(3.993) - 2500(3.993)) / (0.6806) = S

S = $270379.61