Question

Conch Republic spent $750,000 to develop a prototype for a new smart phone that has all the features of the existing one but adds new features such as wifi tethering. The company has spent a further $200,000 for a marketing study to determine the expected sales figures for the new smart phone. Conch Republic can manufacture the new smart phone for $205 each in variable costs. Fixed costs for the operation are estimated to run $5.1 million per year. The estimated sales volume is 64,000, 106,000, 87,000, 78,000, and 54,000 per year for the next five years, respectively. The unit price of the new smart phone will be $485. The necessary equipment can be purchased for $34.5 million and will be depreciated on a seven-year MACRS schedule. It is believed the value of the equipment in five years will be $5.5 million. Net working capital for the smart phones will be 20 percent of sales and will occur with the timing of the cash flows for the year (i.e., there is no initial out-lay for NWC). Changes in NWC will thus first occur in Year 1 with the first year's sales. Conch Republic has a 35 percent corporate tax rate and a required return of 12 percent. questions: a. What is the payback period of the project?

b. What is the profitability index of the project?

c. What is the IRR of the project?

d. What is the NPV of the project?

Answer 1

Amount spent on prototype				$              (750,000.00)
Amount spent on study				$              (200,000.00)
Variable Cost per Unit				$                         205.00
Fixed Costs				$             5,100,000.00
Sales Price per phone				$                         485.00
Equipment				$           34,500,000.00
Equipment Salvage Value				$             5,500,000.00
Net Working Capital				20%
Corportate Tax Rate				35%
Required Return				12%
Estimating sales Volume
Year	amount sold	price	Total Sales
1	$                64,000.00	$                        485.00	$                    31,040,000.00
2	$              106,000.00	$                        485.00	$                    51,410,000.00
3	$                87,000.00	$                        485.00	$                    42,195,000.00
4	$                78,000.00	$                        485.00	$                    37,830,000.00
5	$                54,000.00	$                        485.00	$                    26,190,000.00
Sales based on MACRS Depreciation
Year	Beggin Book Value	Decreciation %	Depreciation	Ending Book Value
1	$        34,500,000.00	14%	$                      4,930,050.00	$           29,569,950.00
2	$        29,569,950.00	24%	$                      8,380,050.00	$           21,189,900.00
3	$        21,189,900.00	17%	$                      6,034,050.00	$           15,155,850.00
4	$        15,155,850.00	12%	$                      4,309,050.00	$           10,846,800.00
5	$        10,846,800.00	9%	$                      3,080,850.00	$             7,765,950.00
6	$          7,765,950.00	9%	$                      3,077,400.00	$             4,688,550.00
7	$          4,688,550.00	9%	$                      3,080,850.00	$             1,607,700.00
8	$          1,607,700.00	4%	$                      1,538,700.00	$                   69,000.00
Income Statement
	Year 1	Year 2	Year 3	Year 4	Year 5
Sales	$        31,040,000.00	$          51,410,000.00	$                    42,195,000.00	$           37,830,000.00	$            26,190,000.00
Variable Cost	$        13,120,000.00	$          21,730,000.00	$                    17,835,000.00	$           15,990,000.00	$            11,070,000.00
Fixed Costs	$          5,100,000.00	$            5,100,000.00	$                      5,100,000.00	$             5,100,000.00	$               5,100,000.00
Depreciation	$          4,930,050.00	$            8,380,050.00	$                      6,034,050.00	$             4,309,050.00	$               3,080,850.00
EBIT	$          7,889,950.00	$          16,199,950.00	$                    13,225,950.00	$           12,430,950.00	$               6,939,150.00
Taxes	$          2,761,482.50	$            5,669,982.50	$                      4,629,082.50	$             4,350,832.50	$               2,428,702.50
Net Income	$          5,128,467.50	$          10,529,967.50	$                      8,596,867.50	$             8,080,117.50	$               4,510,447.50
Changes Net Working Capital
	Year 1	Year 2	Year 3	Year 4	Year 5
Beginning	$                               -	$            6,208,000.00	$                    10,282,000.00	$             8,439,000.00	$               7,566,000.00
Ending	$          6,208,000.00	$          10,282,000.00	$                      8,439,000.00	$             7,566,000.00	$               5,238,000.00
NWC Cash Flow	$        (6,208,000.00)	$          (4,074,000.00)	$                      1,843,000.00	$                 873,000.00	$               2,328,000.00
Opperating Cash Flow
	Year 1	Year 2	Year 3	Year 4	Year 5
Opperating Cash Flow	$        10,058,517.50	$          18,910,017.50	$                    14,630,917.50	$           12,389,167.50	$               7,591,297.50
After Tax Salvage Value
Macrs depreciation value	$          7,765,950.00
Actual Salvage Value	$          5,500,000.00
The difference	$          2,265,950.00	Since positive the company depreciated too slow
Taxes	$              793,082.50
Taxed Salvage value	$          1,472,867.50
Projected Total Cash Flow
	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Operating Cash Flow		$          10,058,517.50	$                    18,910,017.50	$           14,630,917.50	$            12,389,167.50	$    7,591,297.50
Changes in NWC		$          (6,208,000.00)	$                    (4,074,000.00)	$             1,843,000.00	$                  873,000.00	$    2,328,000.00
Capital spending	$     (34,500,000.00)					$    1,472,867.50
Total Projected Cash Flows	$     (34,500,000.00)	$            3,850,517.50	$                    14,836,017.50	$           16,473,917.50	$            13,262,167.50	$ 11,392,165.00
Cumulative cash flow	$     (34,500,000.00)	$       (30,649,482.50)	$                 (15,813,465.00)	$                 660,452.50	$            13,922,620.00	$ 25,314,785.00
Total Projected Cash Flows
	Year	Amount	PRESENT VALUE FACTOR	PRESENT VALUE
	0	$       (34,500,000.00)	1	$        (34,500,000.00)
	1	$            3,850,517.50	0.8929	$             3,438,127.08
	2	$          14,836,017.50	0.7972	$           11,827,273.15
	3	$          16,473,917.50	0.7118	$           11,726,134.48
	4	$          13,262,167.50	0.6355	$             8,428,107.45
	5	$          11,392,165.00	0.5674	$             6,463,914.42
			NPV	$             7,383,556.57
			IRR	6.6375%
			PROFITABILITY INDEX	0.21402
A. PAYBACK PERIOD	=	Years before full recovery+ (uncovered cost at the start of the year /cash flow during the year)
	=	3+(1581346.5/16473917.50)
	=	3.96 YEARS
B. PROFITABILITY INDEX	=	NET PRESENT VALUE OF CASH INFLOWS
		INITIAL CASH OUTFLOW
C. IRR	=	LOWER RATE + ( NPV AT LOWER RATE/(NPV AT LOWER RATE - NPV AT HIGHER RATE ))*(HIGHER RATE - LOWER RATE )
D. NPV	=	PRESENT VALUE OF CASH INFLOWS - PRESENT VALUE OF CASH OUTFLOW