36 What is the Benefit to Cost ratio for a project costing 2

#36 What is the Benefit to Cost ratio for a project costing $200K in the first year (no discount) that produces a net benefit of $50K per year for five years when the discount rate is 5%?

Solution

Benefit to cost ratio = Total discounted values of benefit / total discounted values of cast

Total discounted value of benefit = Annuity * [ 1 - 1 / ( 1 + R)ⁿ] / R

Total discounted value of benefit = 50,000 * [ 1 - 1 / ( 1 + 0.05)⁵] / 0.05

Total discounted value of benefit = 50,000 * 4.329477

Total discounted value of benefit = $216,473.8335

Benefit to cost ratio = 216,473.8335 / 200,000

Benefit to cost ratio = 1.0824