# Determining Present Worth w/ Interest

• Sep 20th 2012, 09:00 AM
jegues
Determining Present Worth w/ Interest
A bakery is thinking of purchasing a small delivery truck that has a first cost of $18,000 and its to be kept in service for 6 years, at which time the salvage value is expected to be$2500. Maintenance and operating costs are estimated at $2500 the first year and will increase at a rate of$200 per year. Determine the present worth of this vehicle, using an interest rate of 12 percent.

My attempt:

Finding the regular annuity for such an arithmetic series,

$\displaystyle A^{''} = 2500 + 200(\frac{A}{G}, 12\%, 6) = \$2934.41$Finding the present worth of maintenance costs given such an annuity, (NOTE: A here is A'' found previously)$\displaystyle P = 2934.41(\frac{A}{P},12\%,6) = \$12064.56$

Finding the present worth of the future salvage value,

$\displaystyle P = 2500(\frac{P}{F},12\%,6) =$1266.58$Thus the overall present worth of the vehicle is,$\displaystyle \$18000 + \$12064.56 - \$1266.58 = \$28797.98$Is this correct? • Sep 20th 2012, 11:17 PM MaxJasper Re: Determining Present Worth w/ Interest$28797.97 is correct !
• Sep 21st 2012, 10:34 AM
Wilmer
Re: Determining Present Worth w/ Interest
Quote:

Originally Posted by jegues
.....that has a first cost of $18,000... Can you explain what that means? This style of problem usually states a purchase price, then the positive and negative subsequent flows resulting from this purchase; then, is the purchase price advantageous? • Sep 23rd 2012, 06:39 AM jegues Re: Determining Present Worth w/ Interest Quote: Originally Posted by Wilmer Can you explain what that means? This style of problem usually states a purchase price, then the positive and negative subsequent flows resulting from this purchase; then, is the purchase price advantageous? I'm assuming it means the purchase price. • Sep 23rd 2012, 08:58 AM Wilmer Re: Determining Present Worth w/ Interest Quote: Originally Posted by jegues I'm assuming it means the purchase price. Ok; then 28797.97 is definitely correct. Can you calculate this: if$K is the savings each year due to the purchase, what is K in order to break even ?