Question

3. (16) Find and report the standard or traditional B/C ratio for each project below using an interest rate of 7.0% if required. Projects are not substitutes for each other so no comparison analysis is required. Project Purchase/Investment Life yrs 12 Recurring Costs 40,000 (Present Worth) 4000 annually 13,500 annually Benefits of Project 140,000 (Present Worth) 8,800 years 1 thru 5, 7,000 year 6 Dis benefits 1 79,000 8000 (Present Worth) 2 24,000 15,000 6 3 15 136,000 (Present Worth) 0 32,000 annually 5,000 8 150,000(Present Worth) 2000 annually

Answer 1

B/C ratio = present value of benefits / present value of costs

Project 1 :

Net PV of benefits = PV of benefits - PV of disbenefits = 140,000 - 8,000 = 132,000

PV of costs = PV of recurring costs + Investment = 40,000 + 79,000 = 119,000

B/C ratio = 132,000 / 119,000 = 1.11

Project 2 :

PV of benefits = 8,800 * PVAF(7%,5) + 7000 / 1.07⁶ = 40,746

PV of costs = PV of recurring costs + Investment = 4000 * PVAF(7%,6) + 24,000 = 43,066

B/C ratio = 40,746 / 43,066 = 0.95

Project 3 :

PV of benefits = 136,000

PV of costs =  PV of recurring costs + Investment = 13,500 * PVAF(7%,15) + 15,000 = 137,957

B/C ratio = 136,000 / 137,957 = 0.99

Project 4 :

PV of benefits = 30,000 * PVAF(7%,8) = 179,139

PV of costs = PV of recurring costs + Investment = 150,000 + 5,000 = 155,000

B/C ratio = 179,139 / 155,000 = 1.16