Question

What the NPV of purchasing a new plant for £70m that will turn its first profit of £10m in year

4, after which cash flow will grow at a 2% rate per year, if the cost of capital is 8%?

Answer 1

NPV = sum of all future cash flows

Cash flow at Year 4 = profit of 10m + terminal value

Terminal value = Cash flow in Year 5/(k-g) = CF4*(1+g)/(k-g) where

CF4 = profit of 10m; k = cost of capital = 8%; g = perpetual growth rate = 2%

Terminal value = 10*(1+2%)/(8%-2%) = 170m

Cash flow at Year 4 = 10 + 170 = 180m

PV of cash flow at Year 4 = 180/(1+8%)^4 = 132.31m

NPV = PV of cash flow - initial investment

= 132.31 - 70 = 62.31m (Answer)