Respuesta :
Answer:
NPV = $3,013,537.02
IRR = 20.15%
Explanation:
initial investment $19,500,000
sales revenue per year:
year 1 = 76,000 x $420 = $31,920,000
year 2 = 89,000 x $420 = $37,380,000
year 3 = 108,750 x $420 = $45,675,000
year 4 = 101,500 x $420 = $42,630,000
year 5 = 68,800 x $420 = $28,896,000
change in net working capital:
year 0 = $2,250,000
year 1 = ($37,380,000 - $31,920,000) x 0.2 = $1,092,000
year 2 = ($45,675,000 - $37,380,000) x 0.2 = $1,659,000
year 3 = ($42,630,000 - $45,675,000) x 0.2 = -$609,000
year 4 = ($28,896,000 - $42,630,000) x 0.2 = -$2,746,800
year 5 = -$1,646,000
fixed costs = $4,700,000
contribution margin per unit = $420 - $270 = $150 per unit
resale value at the end of year 5 = $3,900,000
MACRS depreciation 7 year property:
year % depreciation expense
1 14.29% $2,786,550
2 24.49% $4,775,550
3 17.49% $3,410,550
4 12.29% $2,396,550
5 6.44%* $1,255,800*
*net of resale value
net cash flow year 0 = -$19,500,000 - $2,250,000 = -$21,750,000
net cash flow year 1 = [($11,400,000 - $4,700,000 - $2,786,550) x 0.75] + $2,786,550 - $1,092,000 = $4,629,637.50
net cash flow year 2 = [($13,350,000 - $4,700,000 - $4,775,550) x 0.75] + $4,775,550 - $1,659,000 = $6,022,387.50
net cash flow year 3 = [($16,312,500 - $4,700,000 - $3,410,550) x 0.75] + $3,410,550 + $609,000 = $10,171,012.50
net cash flow year 4 = [($15,225,000 - $4,700,000 - $2,396,550) x 0.75] + $2,396,550 + $2,746,800 = $11,239,687.50
net cash flow year 5 = [($10,320,000 - $4,700,000 - $1,255,800) x 0.75] + $1,255,800 + $1,646,000 = $6,174,950
NPV = $3,013,537.02
IRR = 20.15%
In this exercise we will use our knowledge of finance to calculate interest, so we find that:
- [tex]NPV = \$3,013,537.02[/tex]
- [tex]IRR = 20.15\%[/tex]
So knowing that from the initial investment we will obtain the following values per year:
[tex]year 1 = 76,000 * \$420 = \$31,920,000[/tex]
[tex]year 2 = 89,000 * \$420 = \$37,380,000[/tex]
[tex]year 3 = 108,750* \$420 = \$45,675,000[/tex]
[tex]year 4 = 101,500 * \$420 = \$42,630,000[/tex]
[tex]year 5 = 68,800 * \$420 = \$28,896,000[/tex]
So knowing that from the net working capital we will obtain the following values per year:
[tex]year 0 = \$2,250,000\\year 1 = (\$37,380,000 - \$31,920,000) * 0.2 = \$1,092,000\\year 2 = (\$45,675,000 - \$37,380,000) * 0.2 = \$1,659,000\\year 3 = (\$42,630,000 - \$45,675,000) * 0.2 = -\$609,000\\year 4 = (\$28,896,000 - \$42,630,000) * 0.2 = -\$2,746,800\\year 5 = -\$1,646,000[/tex]
Then from the values previously informed we can calculate the cash flow, as:
[tex]year 0 = -\$19,500,000 - \$2,250,000 = -\$21,750,000\\year 1 = [(\$11,400,000 - \$4,700,000 - \$2,786,550) * 0.75] + \$2,786,550 - \$1,092,000 = \$4,629,637.50\\year 2 =\$6,022,387.50\\year 3 = \$10,171,012.50\\year 4 = \$11,239[/tex]
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