Question

A project has annual cash flow of $8000 for first 10 years and $11000 for next 10 years. The company’s WACC is 10% and IRR is 14%. What is project’s payback and NPV?

Please show formula. Thanks

Answer 1

1]	IRR is that discount rate for which NPV is 0.When NPV is 0,
	PV of cash inflows = Initial investment
	Hence, here, initial investment is given by:
	The PV of cash inflows can be calculated as the PV of the
	two different annuities; $8,000 for years 1 to 10 and $11,000
	for the years 11 to 20.
	PV of the first stream [using the formula for PV of annuity] = 10000*(1.14^10-1)/(0.14*1.14^10) =	$         52,161
	[Formula for PV of annuity = A*((1+r)^n-1)/((r*(1+r)^n)
	where, r = the rate of interest and n = number of years]
	Discounted value of the second stream at t10 = 11000*(1.14^10-1)/(0.14*1.14^10) =		$    57,377
	PV of the above lump sum at t0 = 57377/1.14^10 =	$         15,477
	Initial investment = PV of the cash inflows of years 1 to 20 = 52161+15477 =	$         67,638
	So, the Initial investment = $67,638
2]	Payback period:
	Payback period is the number of years taken for the cash flows
	to recoup the initial investment of $67,658.
	As the cash inflow is $10000 for the first 10 years, the payback
	will occur within those years.
	Payback period = Initital investment/Annual cash inflow = 67638/10000 =	6.76	Years
2]	Calculation of NPV:
	NPV = PV of cash inflows at WACC of 10%-Initial investment.
	PV of cash inflows:
	PV of the first stream [using the formula for PV of annuity] = 10000*(1.1^10-1)/(0.1*1.1^10) =	$         61,446
	Discounted value of the second stream at t10 = 11000*(1.1^10-1)/(0.1*1.1^10) =		$    67,590
	PV of the above lump sum at t0 = 67590/1.1^10 =	$         26,059
	Initial investment = PV of the cash inflows of years 1 to 20 = 61446+26059 =	$         87,505
	Less: Initial investment	$         67,638
	NPV	$         19,866