Question

A company is considering producing long telephoto zoom lens, iLongLens, attachment for the iPhone 5. The initial investment for this project will be $3 million. This amount is for depreciable equipment, which will be depreciated over 5 years using the straight-line method to zero book value. The iLongLens is expected to generate Earnings before Depreciation and Taxes of $1.5 million per year for 6 years. At the end of the sixth year the equipment will be scrapped for $300,000. The company’s tax rate is 40% and the appropriate discount rate for this project is 15%. a) List all 7 after-tax cash flows for this project (0 is the initial investment).

b) Compute the NPV.

c) Compute the IRR and payback.

Answer 1

Tax rate		40%
Calculation of annual depreciation
Depreciation		Year-1	Year-2	Year-3	Year-4	Year-5	Year-6	Total
Cost		$        3,000,000	$       3,000,000	$        3,000,000	$        3,000,000	$       3,000,000	$        3,000,000
Dep Rate		20.00%	20.00%	20.00%	20.00%	20.00%	0.00%
Depreciation		$           600,000	$          600,000	$           600,000	$           600,000	$           600,000	$                      -	$       3,000,000
Calculation of after-tax salvage value
Cost of machine			$       3,000,000
Depreciation			$       3,000,000
WDV			$                     -
Sale price			$          300,000
Profit/(Loss)			$          300,000
Tax			$          120,000
Sale price after-tax			$          180,000
Calculation of annual operating cash flow
	Year-0	Year-1	Year-2	Year-3	Year-4	Year-5	Year-6
EBIT		$       1,500,000	$       1,500,000	$       1,500,000	$       1,500,000	$       1,500,000	$       1,500,000
Less: Depreciation as per table given above		$           600,000	$          600,000	$           600,000	$           600,000	$           600,000	$                      -
Profit before tax		$           900,000	$          900,000	$           900,000	$           900,000	$          900,000	$       1,500,000
Tax		$           360,000	$          360,000	$           360,000	$           360,000	$           360,000	$           600,000
Profit After Tax		$           540,000	$          540,000	$           540,000	$           540,000	$          540,000	$           900,000
Add Depreciation		$           600,000	$          600,000	$           600,000	$           600,000	$           600,000	$                      -
Cash Profit after-tax		$       1,140,000	$       1,140,000	$       1,140,000	$       1,140,000	$       1,140,000	$           900,000
Calculation of NPV
						15.00%
Year		Capital		Operating cash	Annual Cash flow	PV factor	Present values
0		$ (3,000,000.00)			$ (3,000,000.00)	1.0000	$ (3,000,000.00)
1				$ 1,140,000.00	$ 1,140,000.00	0.8696	$     991,304.35
2				$ 1,140,000.00	$ 1,140,000.00	0.7561	$     862,003.78
3				$ 1,140,000.00	$ 1,140,000.00	0.6575	$     749,568.50
4				$ 1,140,000.00	$ 1,140,000.00	0.5718	$     651,798.70
5				$ 1,140,000.00	$ 1,140,000.00	0.4972	$     566,781.48
6		$     180,000.00		$     900,000.00	$ 1,080,000.00	0.4323	$     466,913.80
					Net Present Value		$ 1,288,370.62
Calculation of the payback period
Year					Annual Cash flow	Cumulative cash flows
0					$      (3,000,000)	$      (3,000,000)
1					$        1,140,000	$      (1,860,000)
2					$        1,140,000	$         (720,000)
3					$        1,140,000	$           420,000
4					$        1,140,000	$       1,560,000
5					$        1,140,000	$       2,700,000
6					$        1,080,000	$       2,640,000
		So the payback period will be in 3rd year
		Payback period	=2+(720000/1140000)
		Year	2.63
Calculation of IRR
			30.00%		31.00%
Year		Total cash flow	PV factor @ 30%	Present values	PV factor @ 31%	Present values
0		$      (3,000,000)	1.000	$      (3,000,000)	1.000	$      (3,000,000)
1		$        1,140,000	0.769	$           876,923	0.763	$           870,229
2		$        1,140,000	0.592	$           674,556	0.583	$           664,297
3		$        1,140,000	0.455	$           518,889	0.445	$           507,097
4		$        1,140,000	0.350	$           399,146	0.340	$           387,097
5		$        1,140,000	0.269	$           307,035	0.259	$           295,494
6		$        1,080,000	0.207	$           223,750	0.198	$           213,696
				$                   300		$           (62,091)
		IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
		IRR	'=30%+ (31%-30%)*(299.825/(299.825-(-62090.)
			30.005%