Question

ure, Heavy Highway and Equipment Spring 2019 Homework 1 Equipment Economics Instruction: Use the Interest Table to calculate values. Show your calculations and procedures for a full credit including a cash flow diagram. Otherwise, the deduction will be applied. A contractor has purchased a new truck for $125,000 and plans to use the truck for 6 years After 6 years of use, the estimated salvage value for the truck will be $30,000. What is the contractor's annual cost (annual uniform series) for the truck at an interest rate of 10%? (20 Points)

Answer 1

We are given following parameters

Cost of Truck=Co=-$125,000 (Negative sign indicates the cash outflow)

Future value of Salvage =FV=$30,000

Rate of interest=i=10%

Useful life=n=6 years

Firstly we can calculate the present worth (PW1) of salvage value to be received after 6 years

PW1=FV*(P/F,10%,6)=30000*(P/F,10%,6)

(P/F,10%,6)=1/(1+i)^n=1/(1+10%)^6=0.564474

So,

PW1= 30000*0.564474=$16,934.22

Present Worth of cash flows associated with project

PW=C0+PW1=-125000+16934.22=-108065.78

We can drop negative sign as it indicates cost. It is not required in further calculations.

Now, we are required to find uniform annual series which is equivalent to calculated present worth (PW)

Uniform annual cost=PW*(A/P,10%,6)

Plug in the various value, we get

(A/P,10%,6)=1/(P/A,10%,6)=1/4.355261=0.229607

Uniform annual cost=PW*(A/P,10%,6)= 108065.78*0.229607=$24,812.70

Uniform annual cost= $24,812.70