Question

In your construction business, you are planning to purchase a truck which costs $45,000 and have a variable cost that starts at $15,000 the first year and increases by $2,000 per year. Assume that the estimated market value at the end of five years is $9,000 and the interest rate is %10. What is the equivalent annual cost of owning and operating the truck? a) Between $22,000 and $22.400 b) None of the answers are correct Od Between $30,600 and $40,000 d) Between $32,000 and $32,400 e) Between $12,000 and $12,400

Answer 1

Answer: Option B: None of the answer is correct

Given

Price of Truck P=45000

Variable cost for 1st year V1=15000

Variable cost for 2nd year V2=15000+2000=17000

Variable cost for 3rd year V3=17000+2000=19000

Variable cost for 4th year V4=19000+2000=21000

Variable cost for 5th year V5=21000+2000=23000

Salvage value after five years S=9000

r=10%

So PV of Variable cost V=V1/(1+r)^1+V2/(1+r)^2+V3/(1+r)^3+V4/(1+r)^4+V5/(1+r)^5

V=15000/(1+10%)^1+17000/(1+10%)^2+19000/(1+10%)^3+21000/(1+10%)^4+23000/(1+10%)^5

V=$70585.4

PV of Salvage value S1=S/(1+r)^5=9000/(1+10%)^5

S1=$5588.29

NPV=P+V-S1 =45000+70585.4-5588.29=109997.1

So Equivalent annual cost = NPV*r/(1-(1+r)^-5) =109997.1*10%/(1-(1+10%)^-5)=$29016.96