Question

Jones llc is purchasing a new machine for $180000 the new machine would generate cash flow 100000 for each of the next three years. Jones uses a discount rate of 15% what is the benefit cost ratio ?

show me the steps on how to get "PVIF" and the formulas you used to get it

Answer 1

First, we need to compute the present value of each of the future cash inflows. Present value of an amount can be computed as -

PV = Amount / (1 + r)ⁿ

where, r is the discount rate, n is year to which the cash flow belongs

The above formula can also be written as -

PV = Amount x 1 / (1 + r)ⁿ

or, PV = Amount x PVIF (r, n)

so, PVIF (Present value interest factor of $1) = 1 / (1 + r)ⁿ

Therefore, you either mulitply the amount by the PVIF of the respective year or, you can divide amount by (1 + r)ⁿ. Both will net the same result.

Present value of cash inflows = [ $100,000 / (1 + 0.15)¹ ] + [ $100,000 / (1 + 0.15)² ] + [ $100,000 / (1 + 0.15)³ ] = $228,322.511711

Benefit cost ratio = Present value of cash inflows / Initial cost = $228,322.511711 / $180,000 = 1.268458398 or 1.27