Question

If a truck company ABC has an initial capital outlay of $22,500, WACC of 10%, and the following 5 possible cash flow patterns, depending upon the number of years it operates its truck business,

If operating for only one year: CF₀ = -22500, CF₁ = 23750

If operating for 2 years: CF₀ = -22500, CF₁ = 6250, CF₂ = 20250

If 3 years: CF₀ = -22500, CF₁ = 6250, CF₂ = 6250, CF₃ = 17250

If 4 years: CF₀ = -22500, CF₁ = 6250, CF2 = 6250, CF3 = 6250, CF₄ = 11250

If 5 years: CF₀ = -22500, 6250 each year for 5 years

In which year should the Company abandon its operation, so the company’s NPV will achieve the highest value?

Answer 1

NPV for operating for only one year = - Initial Outlay + Cash inflow per year/ (1 + interest rate)^period

NPV for operating for only one year = -$22,500 + $23,750 / (1 + 10%)¹

NPV for operating for only one year = -$909.09

NPV for operating for 2 years = - Initial Outlay + Cash inflow per year/ (1 + interest rate)^period

NPV for operating for 2 years = -$22,500 + $6250 / (1 + 10%)¹ + $20250 / (1 + 10%)²

NPV for operating for 2 years = -$82.64

NPV for operating for 3 years = - Initial Outlay + Cash inflow per year/ (1 + interest rate)^period

NPV for operating for 3 years = -$22,500 + $6250 / (1 + 10%)¹ + $6250 / (1 + 10%)² + $17250 / (1 + 10%)³

NPV for operating for 3 years = $1307.29

NPV for operating for 4 years = - Initial Outlay + Cash inflow per year/ (1 + interest rate)^period

NPV for operating for 4 years = -$22,500 + $6250 / (1 + 10%)¹ + $6250 / (1 + 10%)² + $6250 / (1 + 10%)³ + $11250 / (1 + 10%)⁴

NPV for operating for 4 years = $726.73

NPV for operating for 5 years = - Initial Outlay + Cash inflow per year/ (1 + interest rate)^period

NPV for operating for 5 years = -$22,500 + $6,250 / (1 + 10%)¹ + $6,250 / (1 + 10%)² + ...+ $6,250 / (1 + 10%)⁵

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value cash inflows

NPV for operating for 5 years = -$22,500 + $6,250 * (1 - (1 + 10%)^-5) / (10%)

NPV for operating for 5 years= -$22,500 + $23692.42

NPV for operating for 5 years = $1192.42

The company should abandon its operations after 3 years.