Homework Answers
a.
The initial outlay associated with the project consists of the following:
- Initial expenditure associated with the purchase of new production equipment = $1,200,000
- One time initial investment in net working capital = $30,000
So, Initial outlay associated with the project = $1,200,000 + $30,000
= $1,230,000
b.
The project annual Free Cash Flows from Year-1 through Year-9 is calculated in the table below:
The table shows the calculation of Free Cash Flow for all three sales forecast options
| Sales Forecast Option | ||||||
| With 9000 Units sold per year | With 5000 Units sold per year | With 14000 Units sold per year | ||||
| Description | Legend | Formula | Year 1 through 9 | Year 1 through 9 | Year 1 through 9 | |
| Initial Investment for new Equipment | I | $1,200,000 | ||||
| Equipment Life | n | 10 | ||||
| No of Units sold per Year | S | 9000 | 5000 | 14000 | ||
| Price per unit sold | P | $ 100 | $ 100 | $ 100 | ||
| Revenue | R | =P*S | $ 900,000 | $ 500,000 | $ 1,400,000 | |
| Variable Cost per Unit | VC | $ 30.0 | $ 30.0 | $ 30.0 | ||
| Total Variable Cost per Year | V | =VC*S | $ 270,000 | $ 150,000 | $ 420,000 | |
| Fixed Cost per Year | FC | $ 140,000 | $ 140,000 | $ 140,000 | ||
| Depreciation Cost per Year | D | =I/n | $ 120,000 | $ 120,000 | $ 120,000 | |
| Income before Taxes per Year | EBIT | =R-V-FC-D | $ 370,000 | $ 90,000 | $ 720,000 | |
| Taxes @ 32% | T | =EBIT*0.32 | $ 118,400 | $ 28,800 | $ 230,400 | |
| Net Income | PAT | =EBIT-T | $ 251,600 | $ 61,200 | $ 489,600 | |
| Depreciation | D | $ 120,000 | $ 120,000 | $ 120,000 | ||
| Change in Net Working Capital | NWC | $ - | $ - | $ - | ||
| Free Cash Flow | FCF | =PAT-NWC+D | $ 371,600 | $ 181,200 | $ 609,600 |
Now,
The probability of selling 9,000 units per year is 70%
The probability of selling 5,000 units per year is 15%
The probability of selling 14,000 units per year is 15%
So,
The probability of annual Free Cash Flow of $ 371,600 from Year-1 through 9 is 70%
The probability of annual Free Cash Flow of $ 181,200 from Year-1 through 9 is 15%
The probability of annual Free Cash Flow of $ 609,600 from Year-1 through 9 is 15%
Hence, the expected annual Free Cash Flows from Year-1 through 9 is
= ($371,600 * 70%) + ($181,200 * 15%) + ($609,600 * 15%)
= $378,740
c.
Using the expected cash flow = $378,740 as derived in part (b) we can calculate the Free Cash Flow of the project in year 10 i.e.. the Terminal Cash Flow:
The calculation is shown in the table below:
| Description | Legend | Formula | Year-10 |
| Income before Taxes per Year | EBIT | $ 378,740.0 | |
| Taxes @ 32% | T | =EBIT*0.32 | $ 121,196.8 |
| Net Income | PAT | =EBIT-T | $ 257,543.2 |
| Depreciation | D | $ 120,000 | |
| Change in Net Working Capital | NWC | $ 30,000.0 | |
| Free Cash Flow | FCF | =PAT+D+NWC | $ 407,543.2 |
So, from the above table we can see that the Terminal Cash Flow of the project in Year 10 is $407,543.20.
d.
Now we will calculate the expected NPV of the project.
To calculate the expected NPV we consider the following:
Expected future cash flow from Year-1 through Year-9 is = $378,740
Expected Terminal Cash Flow in Year-10 is = $407,543.20
Required Rate of Return = 11%
| Legend | Formula | ||||||||||||
| Year | n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Initial Investment | I | $1,230,000.00 | |||||||||||
| Free Cash Flow | FCF | $378,740.00 | $378,740.00 | $378,740.00 | $378,740.00 | $378,740.00 | $378,740.00 | $378,740.00 | $378,740.00 | $378,740.00 | $407,543.20 | ||
| Cost of Capital | K | 11% | |||||||||||
| Present Value of Future Cash Flows | PV | = FCF / ((1+K)^n) | $341,207.21 | $307,393.88 | $276,931.42 | $249,487.77 | $224,763.76 | $202,489.87 | $182,423.31 | $164,345.32 | $148,058.85 | $143,530.39 | |
| Sum of Present Values of all Future Cash Flows | ∑ PV | $ ,240,631.77 | |||||||||||
| Net Present Value | NPV | = ∑ PV - I | $1,010,631.77 |
So, the NPV of the project is $1,010,632
If 9000 skateboards are sold then,
Expected future cash flow from Year-1 through Year-9 is = $371,600
Expected Terminal Cash Flow in Year-10 is = $402,688
Required Rate of Return = 11%
| Legend | Formula | ||||||||||||
| Year | n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Initial Investment | I | $ 1,230,000.00 |
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