A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.
What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?
The opportunity to meet a desirable future spouse should be classified as:
The higher chance of meeting a clever spouse is a positive side effect that should be included in the decision to go to university. It's not a sunk cost since the chance of meeting a clever young man depends on her decision to go to university or not. Also, it's not an opportunity cost since it's actually a benefit from going to university.
It's funny how the word 'opportunity' in the last sentence of the question makes people sub-consciously think opportunity cost, even though it is clearly not a cost.
A man is thinking about taking a day off from his casual painting job to relax.
He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.
But he's thinking about the hours that he could work today (in the future) which are:
The hours that he could work in the future are an opportunity cost of his decision to take a day off and relax, assuming that working is the 'next best alternative' to relaxing. The hours that he could spend working are not a sunk cost yet because they are in the future, they are an incremental cost of staying home to relax.
A man has taken a day off from his casual painting job to relax.
It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:
The hours that he took off from work are now a sunk cost because they are in the past and there is nothing that he can do to get them back, he should forget about them. As the saying goes, "don't cry over spilt milk".
Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
| Candys Corp | ||
| Income Statement for | ||
| year ending 30th June 2013 | ||
| $m | ||
| Sales | 200 | |
| COGS | 50 | |
| Operating expense | 10 | |
| Depreciation | 20 | |
| Interest expense | 10 | |
| Income before tax | 110 | |
| Tax at 30% | 33 | |
| Net income | 77 | |
| Candys Corp | ||
| Balance Sheet | ||
| as at 30th June | 2013 | 2012 |
| $m | $m | |
| Assets | ||
| Current assets | 220 | 180 |
| PPE | ||
| Cost | 300 | 340 |
| Accumul. depr. | 60 | 40 |
| Carrying amount | 240 | 300 |
| Total assets | 460 | 480 |
| Liabilities | ||
| Current liabilities | 175 | 190 |
| Non-current liabilities | 135 | 130 |
| Owners' equity | ||
| Retained earnings | 50 | 60 |
| Contributed equity | 100 | 100 |
| Total L and OE | 460 | 480 |
Note: all figures are given in millions of dollars ($m).
Using the Cash Flow From Assets equation,
### CFFA = NI + Depr - CapEx - \Delta NWC + IntExp ###Capital expenditure (CapEx) can be calculated as the change in Net Fixed Assets (NFA) plus depreciation. Note that NFA is the same thing as the carrying amount of property, plant and equipment (PPE).
###\begin{aligned} CapEx &= NFA_\text{now} - NFA_\text{before} + Depr \\ &= 240 - 300 + 20 \\ &= -40 \\ \end{aligned}###
Note that CapEx is negative. This means that the firm must have sold more capital assets than it bought.
Another way to calculate CapEx is to look at the difference in the undepreciated cost:
###\begin{aligned} CapEx &= FA_\text{now} - FA_\text{before} \\ &= 300 - 340 \\ &= -40 \\ \end{aligned}###
To find the change in net working capital (##\Delta NWC##), take the difference between the NWC now and before:
###\begin{aligned} \Delta NWC &= CA_\text{now} - CL_\text{now} - (CA_\text{before} - CL_\text{before}) \\ &= 220-175 - (180-190) \\ &= 45 - (-10) \\ &= 55 \\ \end{aligned}###
Now just substitute the values:
###\begin{aligned} CFFA &= NI + Depr - CapEx - \Delta NWC + IntExp \\ &= 77 + 20 - (-40) - (55) + 10 \\ &= 77 + 20 + 40 - 55 + 10 \\ &= 92 \\ \end{aligned}###
Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
| Ching-A-Lings Corp | ||
| Income Statement for | ||
| year ending 30th June 2013 | ||
| $m | ||
| Sales | 100 | |
| COGS | 20 | |
| Depreciation | 20 | |
| Rent expense | 11 | |
| Interest expense | 19 | |
| Taxable Income | 30 | |
| Taxes at 30% | 9 | |
| Net income | 21 | |
| Ching-A-Lings Corp | ||
| Balance Sheet | ||
| as at 30th June | 2013 | 2012 |
| $m | $m | |
| Inventory | 49 | 38 |
| Trade debtors | 14 | 2 |
| Rent paid in advance | 5 | 5 |
| PPE | 400 | 400 |
| Total assets | 468 | 445 |
| Trade creditors | 4 | 10 |
| Bond liabilities | 200 | 190 |
| Contributed equity | 145 | 145 |
| Retained profits | 119 | 100 |
| Total L and OE | 468 | 445 |
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Using the Cash Flow From Assets Equation,
### CFFA = NI + Depr - CapEx - \Delta NWC + IntExp ###Capital expenditure (CapEx) can be calculated as the change in Net Fixed Assets (NFA) plus depreciation. Note that NFA is the same thing as the carrying amount of property, plant and equipment (PPE).
###\begin{aligned} CapEx &= PPE_\text{now} - PPE_\text{before} + Depr \\ &= 400 - 400 + 20 \\ &= 20 \\ \end{aligned}###
CapEx is positive, so the firm must have bought more capital assets than it sold.
To find the change in net working capital (##\Delta NWC##), take the difference between the NWC now and before. Note that current assets includes inventory, trade debtors and rent paid in advance. Current liabilities only includes trade creditors in this instance.
###\begin{aligned} \Delta NWC &= CA_\text{now} - CL_\text{now} - (CA_\text{before} - CL_\text{before}) \\ &= (49+14+5-4) - (38+2+5-10) \\ &= 64 - 35 \\ &= 29 \\ \end{aligned}###
Now just substitute the values:
###\begin{aligned} CFFA &= NI + Depr - CapEx - \Delta NWC + IntExp \\ &= 21 + 20 - 20 - 29 + 19 \\ &= 11\\ \end{aligned}###
To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.
Current assets and current liabilities are needed to find the change in net working capital, an input into the firm's free cash flow equation. These two quantities are found in the balance sheet.
Capital expenditure is needed in the firm's free cash flow equation, and the CapEx can be found using the balance sheet's change in net fixed assets (usually property, plant and equipment (PPE)) plus depreciation. Net fixed assets is found in the balance sheet.
Thanks to Shahzada for assisting with this question.
Cash Flow From Assets (CFFA) can be defined as:
Cash flow from assets (CFFA), also known as free cash flow to the firm (FCFF), is the cash generated from the firm's assets. It is the income component of the total dollar return from the assets, in the same way as shares, bonds and land have income returns called dividends, coupons and rent respectively. The idea is that the value of a project or business is the present value of its cash flow from assets in the same way that the value of a stock is the present value of its dividends.
Because a firm's assets (V) are owned by the debt (D) and equity (E) holders who fund it (V=D+E), the CFFA is indirectly owed to debt and equity holders. CFFA is the cash available to distribute to the debt and equity holders. CFFA is equal to the debt's coupon and principal payments less new debt raisings plus the equity's dividend and buy back payments less new equity raisings. The CFFA must equal the net payments to the debt and equity holders who fund the assets because if the CFFA is not paid out, the cash must have been kept by the business and thus increases net working capital, making CFFA zero. Here are some other examples which also hinge on the way the increase in net working capital (NWC) is subtracted from CFFA.
- If a firm pays a dividend to shareholders then the firm's cash will fall, causing a decrease in NWC which will increase CFFA. This increase is exactly equal to the dividend payment to shareholders.
- If a firm raises equity in an initial public offering (IPO), then the cash raised will increase current assets (cash) and will be subtracted in the CFFA equation as an increase in net working capital. The cash payment by the shareholders to the company for the shares in the IPO is a negative cash flow from the company to the shareholders, and this is equal to the negative CFFA due to the large increase in NWC.
- A firm earns positive net income and generates excess cash but no debt or equity is raised or paid out. It seems like there is a positive CFFA and it is not equal to the zero payments to debt or equity holders. But in fact, if no cash flows are paid to or received from debt or equity holders, then the excess cash will just sit in the bank account, increasing net working capital, and causing CFFA to be zero, which is equal to the zero payments to debt and equity holders. So actually CFFA was not positive, it was zero. We just overlooked that the excess cash increases NWC.
Summarizing with an equation,
###\begin{aligned} CFFA &= (\text{net payments to debt holders}) + (\text{net payments to equity holders}) \\ &= (\text{payments to debt holders}) - (\text{receipts from debt holders}) + (\text{payments to equity holders}) - (\text{receipts from equity holders}) \\ &= (\text{coupon and principal payments}) - (\text{new debt raisings}) + (\text{dividend and buyback payments}) - (\text{new equity raisings}) \\ \end{aligned} ###
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###The net income (NI) equation and cash flow from assets (CFFA) equations are:
###NI=(Rev-COGS-FC-\mathbf{Depr}-IntExp).(1-t_c)###
###CFFA=NI+\mathbf{Depr}-CapEx - \varDelta NWC+IntExp###
Substituting NI into CFFA and then expanding and collecting like terms,
###\begin{aligned} CFFA &= (Rev-COGS-FC-\mathbf{Depr}-IntExp).(1-t_c)+\mathbf{Depr}-CapEx - \varDelta NWC+IntExp \\ &= (Rev-COGS-FC).(1-t_c)+\mathbf{Depr.t_c} -CapEx - \varDelta NWC+IntExp.t_c \\ \end{aligned}###
The bold term is called the depreciation tax shield (##Depr.t_c##) which is the tax saving per year. This is because higher depreciation results in lower tax payments to the government since before-tax NI is lower. Depreciation is added to CFFA since depreciation is not a cash flow, it's an accrual item made up by accountants who attempt to allocate the lumpy capital expenditure (CapEx) smoothly through time. But CFFA is only supposed to include cash items, so depreciation is added back. The only effect of depreciation on CFFA is the depreciation tax-shield effect.
It's quite surprising that higherdepreciation expense actually leads to a CFFA increase and at the same time a NI decrease. It shows how CFFA (or better, the net present value of CFFA) can give quite a different picture of firm value compared with NI.
Note that the interest tax shield (##IntExp.t_c##) is also shown in the above equation. It's the tax saving per year from paying less tax to the government due to interest expense.
Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###An increase in inventories will have no effect on net income because accountants only expense inventory when it is sold. In other words, buying a billion dollars of inventory and leaving it in a warehouse all year will have no impact on net income. The billion dollar cost of the inventory will only affect net income through the account 'cost of goods sold' (COGS) when the inventory is sold, or when the inventory is written down if it becomes old, out-dated or out of fashion and the accountant decides to re-value it.
Obviously any purchase of inventory will have a negative effect on cash flow, and the opportunity cost of having money tied up in inventory rather than in the bank is a cost that must be taken into account. This is why CFFA subtracts the increase in net working capital ##ΔNWC##, which is the increase in current assets less the increase in current liabilities.
Find the cash flow from assets (CFFA) of the following project.
| One Year Mining Project Data | ||
| Project life | 1 year | |
| Initial investment in building mine and equipment | $9m | |
| Depreciation of mine and equipment over the year | $8m | |
| Kilograms of gold mined at end of year | 1,000 | |
| Sale price per kilogram | $0.05m | |
| Variable cost per kilogram | $0.03m | |
| Before-tax cost of closing mine at end of year | $4m | |
| Tax rate | 30% | |
Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.
Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.
Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.
Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.
Initially at time zero, no time has elapsed so there is zero revenue, expenses, income, depreciation and so on. But there is CapEx, which is the $9m cost of building the mine as well as the $3m opportunity cost of foregoing the eco-resort. Using the Cash Flow From Assets equation:
###\begin{aligned} CFFA_0 &= NI_0 + Depr_0 - CapEx_0 - \Delta NWC_0 + IntExp_0 \\ &= 0 + 0 - (9m+3m) - 0 + 0 \\ &= -12m \\ \end{aligned}###At time one the Net Income and CapEx must be calculated and then substituted into the CFFA equation. Note that revenue at time one includes the 1,000 kilograms of gold as well as the $1m of diamonds mentioned in note 1 which is a side benefit.
###\begin{aligned} NI_1 &= (Rev_1 - COGS_1 - FC_1 - Depr_1 - IntExp_1)(1-t_c) \\ &= ((1,000 \times 0.05m + 1m) - (1,000 \times 0.03m) - 4m - 8m - 0)(1-0.3) \\ &= (51m - 30m - 4m - 8m - 0)(1-0.3) \\ &= 9m \times 0.7 \\ &= 6.3m \\ \end{aligned}### ###\begin{aligned} CapEx_1 &= -(P_\text{mkt} - \text{CapitalGainsTax}) \\ &= -(P_\text{mkt} - (P_\text{mkt} - P_\text{book}).t_c) \\ &= -(2.5m - (2.5m - 1m) \times 0.3) \\ &= -2.05m \\ \end{aligned}###Note that CapEx is actually negative, so net cash was gained not spent.
###\begin{aligned} CFFA_1 &= NI_1 + Depr_1 - CapEx_1 - \Delta NWC_1 + IntExp_1 \\ &= 6.3m + 8m - (-2.05m) - 0 + 0 \\ &= 16.35m \\ \end{aligned}###