Question

A project requires an initial investment of $320,000 depreciated straight-line to $0 in 24 years. The investment is expected to generate annual sales of $90,000 with annual costs of $45,000 for 30 years. Assume a tax rate of 30% and a discount rate of 20%. What is the NPV of the project?

Answer 1

Sol :

Given,

Initail investment = -$320,000

Tax rate = 30%

Discount rate -= 20%

Annual sales = $90,000

Annual cost = $45,000 for 30 years

Year 0 cash flow

Initial investment = -$320000

Present value is same in year 0

Year 1-24 years

Depreciation tax benefit

(320000/24)*30% = 4000

Number of years (n) = 24

Discount rate = 20%

Present value of Annuity will be used to calculate PV of Depreciation tax benefit. Tax benefit is cash inflow.

Present value of Annual Cash inflows = Annual amount x (1-(1/(1+r)^n) / r

Present value of Annual Cash inflows = 4000 x (1-(1/(1+20%)^24))/20%

Present value of Annual Cash inflows = 19748.4177

Year 1-30 years

Operating profit excluding Depreciation = 90000-45000 = 45000

Cash flow after tax = 45000 x (1-30%) =31500

Number of years (n) = 30

Discount rate = 20%

Present value of Annuity will be used to calculate PV of cash flows. Tax benefit is cash inflow.

Present value of Annual Cash inflows = Annual amount x (1-(1/(1+r)^n) / r

Present value of Annual Cash inflows = 31500 x (1-(1/(1+20%)^30))/20%

Present value of Annual Cash inflows = 156836.4966

NPV = Sum of all of cash flows present values.

NPV = (-320000 + 156836.4966 + 19748.4177)

NPV = -143415.0857

NPV of the project is -143415.09, therefore the project should not be accepted.