MINIMUM ASSET LIFE TO JUSTIFY
A HIGHER INVESTMENT
The timber floor of a bridge is to be replaced, and consideration is being given to treating
the timber to prolong its life and reduce maintenance costs. An untreated timber floor
costs $5000 and has an annual maintenance cost of $500 and a life of 10 years. A treated
timber floor costs $8500 and has an annual maintenance cost of $300. How long should
the treated timber last to make it more economical than the untreated timber? Use an in-
terest rate of 5 percent.
Calculation Procedure:- Compute the annual cost of the untreated timber floor
Using the capital-recovery factor, we see the annual cost is $5000(0.12950) + $500 =
$1147.50. - Set up an expression for the annual cost of the
treated timber floor
The annual cost is $8500(CR) + $300. - Compute the minimum life required to justify
treating the timber
Equate the annual costs, giving $8500(CR) + $300 = $1147.50, or CR = 0.09971. Interpo-
lating in the compound-interest table for 5 percent, we find N= 14.3 years. The life of the
treated timber floor must exceed 14.3 years to make it more economical.
COMPARISON OF EQUIPMENT COST
AND INCOME GENERATED
A firm is considering purchasing equipment that will reduce annual labor costs by $4000.
The equipment costs $30,000 and has a salvage value of $5000 and a life of 7 years. The
annual maintenance cost is $600. While not in use by the firm, the equipment can be rent-
ed to others to generate an income of $1000 per year. If money can be invested for an 8
percent return, is the firm justified in buying the equipment?
Calculation Procedure:- Compute the annual cost of using the equipment
Using the capital-recovery-factor annual cost, we get A = ($30,000 - $5000)(0.19207) +
$5000(0.08) + $600 = $5802. - Compute the annual cost of not purchasing the equipment
If the equipment is not purchased, the firm will incur an extra labor cost of $4000 over
that with the equipment. Also, the rental income that would be obtained from the equip-
ment will be lost. Hence, the total annual cost without the equipment would be A = $4000
- $1000 = $5000.
Since the annual cost with the equipment would be $5802, the firm should not pur-
chase the equipment because without it the annual cost is only $5000.