Question

A project requires an initial investment of $950,000 depreciated straight-line to $0 in 10 years. The investment is expected to generate annual sales of $600,000 with annual costs of $250,000 for 10 years. Assume a tax rate of 30% and the NPV of $300,000. What is a discount rate of the project?

Answer 1

Initial Investment = $950,000
Salvage Value = $0
Useful Life = 10 years

Annual Depreciation = (Initial Investment - Salvage Value) / Useful Life
Annual Depreciation = ($950,000 - $0) / 10
Annual Depreciation = $95,000

Annual Sales = $600,000
Annual Costs = $250,000

Annual OCF = (Annual Sales - Annual Costs) * (1 - Tax Rate) + Tax Rate * Annual Depreciation
Annual OCF = ($600,000 - $250,000) * (1 - 0.30) + 0.30 * $95,000
Annual OCF = $350,000 * 0.70 + 0.30 * $95,000
Annual OCF = $273,500

Let Discount Rate be i%

Net Present Value = - Initial Investment + Annual OCF * PVA of $1 (Discount Rate, Useful Life)
$300,000 = -$950,000 + $273,500 * PVA of $1 (i%, 10)
$1,250,000 = $273,500 * PVA of $1 (i%, 10)
PVA of $1 (i%, 10) = 4.57084

Using table values or financial calculator, i = 17.53%

Discount Rate = 17.53%

So, the discount rate of the project is 17.53% or 18%