Question

The physician's office that you manage wants to buy equipment for $20,000, with projected cash flows of $3,000 per year over the equipment's ten-year useful life. Calculate the NPV/IRR at 10 percent.

Answer 1

NPV :-

present value of cash outflow = $20000 * PVAF(10%,10years)

= $20000 * 1

= $20000

Present value of cash inflow = $3000 * PVAF(10%,10years)

= $3000* 6.145

= $18435

NPV = $18435- $20000

= -$1565

IRR:-

Since the cash inflow are equal , a rough approximation may be made with the reference to the payback period. The payabck period will be;

payback period = $20000 / $3000

= 6.667 year

Now , serach for a value nearest to 4 in the 10th year row of the PVAF table, the closest figure are given in the rate 8% (6.710) and 9% (6.418). This means that the IRR of the proposal is expected to lie between 8% and 9%.

At 8%, NPV = $3000 * PVAF(8%,10years) - 20000

= (6.710 *3000)- 20000

= 20130 - 20000

=130

At 9%, NPV =$3000 *  PVAF(9%,10years) -  20000

= (3000*6.418) - 20000

= 19254-20000

= - 746

IRR = 8% + 130 / (130- (-746) * ( 9% - 8%)

= 8% + 130 / 876 * 1%

= 8% + 0.15%

= 8.15%