Question

2. Complete problems: NPV, IRR, MIRR, Profitability Index, Payback, Discounted Payback
   
   A project has an initial cost of $60,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 12%. Show your work.

• What is the project’s NPV? (Hint: Begin by constructing a timeline).
• What is the project’s IRR?
• What is the project’s MIRR?
• What is the project’s PI?
• What is the project’s payback period?
• What is the project’s discounted payback period?

Answer 1

Calculating payback

Year	Cash flows
1	$10,000
2	$10,000
3	$10,000
4	$10,000
5	$10,000
6	$10,000
7	$10,000
8	$10,000

The initial cash outlay is $60,000.The pay back period is the time it takes to recover the initial cash outlay

• Payback period = Total initial capital investment / Annual expected net cash flows

= $60,000 / $10,000

= 6 years

Hence, the payback period for the project is 6 years.

• Discounted pay back period

  Year	cash flows	PV at 12%	Present value of cash flows
  1	$10,000	0.892	$8,920
  2	$10,000	0.797	$7,970
  3	$10,000	0.711	$7,110
  4	$10,000	0.635	$6,350
  5	$10,000	0.567	$5,670
  6	$10,000	0.506	$5,060
  7	$10,000	0.452	$4,520
  8	$10,000	0.403	$4,030

  Total present value of cash inflows is = $49,630.

Initial cost is = $60,000

Here total present value of cash inflows is less than the initial cost. The initial cost is not recovered in 8 years.

Calculation of net present value

year	cash flows	PV at 12%	present value of cash flows
0	($60,000)	1.000	($60,000)
1	$10,000	0.892	$8,920
2	$10,000	0.797	$7,970
3	$10,000	0.711	$7,110
4	$10,000	0.635	$6,350
5	$10,000	0.567	$5,670
6	$10,000	0.506	$5,060
7	$10,000	0.452	$4,520
8	$10,000	0.403	$4,030
			($10,370)

present value of inflows is less than the present value of outflows.i.e -$10,370.