Question

National Widgets Incorporated is buying a new delivery vehicle that they believe will increase their profits. Vehicle A will cost $28,000 in Year 0, and the profits will be $5,600 in Year 1, increasing by 2% each year after that (a geometric gradient). Vehicle B will cost $29,500 in Year O, and the profits will be $5,400 in Year 1, increasing by 4% each year after that (another geometric gradient). If the useful life of both vehicles is 10 years and the MARR is 10%, what is the present worth of each vehicle? Which vehicle, if any, should you choose? What is the present worth of Vehicle A? $ (Round to the nearest dollar - no decimal places. If you get a negative number, include the negative sign.) What is the present worth of Vehicle B? $ (Round to the nearest dollar - no decimal places. If you get a negative number, include the negative sign.) Which vehicle, if any, should you choose? O A. Vehicle A O B. Vehicle B O C. Neither

Answer 1

Vehicle A

Present worth = Present worth of benefits -Present worth of costs

Present worth = 5600{1- [(1+g)/(1+i)]^n / i-g } - 28000

Here i = 10%; g = 2%; n =10 years

Present worth = 5600{1- [(1+0.02)/(1+0.1)]^10 / 0.1-0.02 } - 28000

Present worth = 37101.74 - 28000

Present worth = $ 9101.7

Vehicle B

Present worth = Present worth of benefits -Present worth of costs

Present worth = 5400{1- [(1+g)/(1+i)]^n / i-g } - 29500

Here i = 10%; g = 4%; n =10 years

Present worth = 5400{1- [(1+0.04)/(1+0.1)]^10 / 0.1-0.04 } - 28000

Present worth = 38637.15 - 29500

Present worth = $ 9137.15

Since the PW of Vehicle B is higher the same is to be choosen