Question

Autonumerics, Inc. has just invested $600,000 in a manufacturing process that is estimated to generate an after-tax annual cash flow of $250,000 in each of the next five years. At the end of year 5, no further market for the product and no salvage value for the manufacturing process are expected. If a manufacturing problem delays plant start-up for one year (leaving only four years of process life), compute the revised annual cash flow to maintain the same internal rate of return as if no delay had occurred?

Answer 1

IRR is the rate at which NPV = 0

i.e. Present value of cash inflows = Present value of cash outflows

Let it be x%

= 600,000 = 250,000*PVAF(x%, 5 years)

PVAF(x%, 5 years) = 2.4

Using present value annuity factor table,

PVAF(30%, 5 years) = 2.4356

PVAF(31%, 5 years) = 2.3897

Using interpolation, x = 30% + (2.4356-2.4)/(2.4356-2.3897)

= 30.78%

Let Desired annual cash flow be y

y*PVAF(30.78%, 4 years) = 600,000

y*2.1382 = 600,000

y = $280,609.86

Hence, desired annual cash flows = $280,609.86