Jones llc is purchasing a new machine for 180000 the new mac

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

Solution

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