A young lady is trying to decide if she should attend university or not.
The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The hard work studying at school in her childhood should be classified as:
The lady's hard work studying and attending school during her childhood is a sunk cost since there's nothing she can do to get that time back. It's in the past, it's spent, she should forget about it. Her decision to attend university should ignore this sunk cost because regardless of her decision, this cost can't be recouped. Only the incremental benefits and costs should be included in her decision. Economists were the first to discover the importance of marginal changes, and the period is known as the Marginalist Revolution.
What is the net present value (NPV) of undertaking a full-time Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.
Assume the following:
- The degree takes 3 years to complete and all students pass all subjects.
- There are 2 semesters per year and 4 subjects per semester.
- University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to remain constant in real terms for the next 3 years.
- There are 52 weeks per year.
- The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
- The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
- The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
- Working full time at the grocery store instead of studying full-time pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week and are expected to remain constant in real terms.
- Full-time students can work full-time during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week.
- The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.
The NPV of costs from undertaking the university degree is:
Since most of the cash flows are weekly, it's easier to work with effective weekly rates than annual ones so convert the effective annual rate to an effective weekly rate:
###\begin{aligned} r_\text{eff wkly} &= (1+r_\text{eff yrly})^{1/52}-1 \\ &= (1+0.098)^{1/52}-1 \\ &= 0.001799508 \\ &\approx 0.0018 \\ \end{aligned} ###
Since all discount rates and cash flows are real, there is no need to do any conversions using inflation.
University fees will be ##4 \times $1,277 = $5,108## per semester, paid at t=0 for the first semester and again at t=19 weeks for the second semester.
The present value of university fees for one year is:
###\begin{aligned} V_\text{0, annual fee} &= (\text{First semester cost now}) + \frac{(\text{Second semester cost in 19 weeks})}{(1+0.001799508)^{19}} \\ &= 4 \times 1,277 + \frac{4 \times 1,277}{(1+0.001799508)^{19}} \\ &= 10,044.45768 \\ \end{aligned} ###
But as well as this explicit annual cost there is also the implicit opportunity cost which is that students can't work full-time while they are studying full-time. Students can still work during the summer holidays, but they can't work from t=0 to 38 weeks.
At $20/hr and 35hrs/wk they miss out on $700/wk paid in arrears. The present value of this annual opportunity cost is:
###\begin{aligned} V_\text{0, annual wages foregone} &= \frac{C_\text{wage 1,2,..38}}{r} \left(1-\frac{1}{(1+r)^{38}} \right) \\ &= \frac{700}{0.001799508} \left(1-\frac{1}{(1+0.001799508)^{38}} \right) \\ &= 25,688.58368 \\ \end{aligned} ###
Adding up the present value of the annual explicit and implicit costs:
###\begin{aligned} V_\text{0, annual cost} &= V_\text{0, annual fee} + V_\text{0, annual wages foregone} \\ &= 10,044.45768 + 25,688.58368 \\ &= 35,733.04136 \\ \end{aligned} ###
The annual costs are expected to be constant every year, so the present value of the costs over the whole 3 year degree is:
###\begin{aligned} V_\text{0, 3yr cost} &= \frac{V_\text{0,1,2, annual cost}}{r_\text{eff yrly}} \left(1-\frac{1}{(1+r_\text{eff yrly})^{3}} \right)(1+r_\text{eff yrly})^1 \\ &= \frac{35,733.04136}{0.098} \left(1-\frac{1}{(1+0.098)^{3}} \right)(1+0.098)^1 \\ &= $97,915.91465 \\ \end{aligned} ###
Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
| Sidebar Corp | ||
| Income Statement for | ||
| year ending 30th June 2013 | ||
| $m | ||
| Sales | 405 | |
| COGS | 100 | |
| Depreciation | 34 | |
| Rent expense | 22 | |
| Interest expense | 39 | |
| Taxable Income | 210 | |
| Taxes at 30% | 63 | |
| Net income | 147 | |
| Sidebar Corp | ||
| Balance Sheet | ||
| as at 30th June | 2013 | 2012 |
| $m | $m | |
| Cash | 0 | 0 |
| Inventory | 70 | 50 |
| Trade debtors | 11 | 16 |
| Rent paid in advance | 4 | 3 |
| PPE | 700 | 680 |
| Total assets | 785 | 749 |
| Trade creditors | 11 | 19 |
| Bond liabilities | 400 | 390 |
| Contributed equity | 220 | 220 |
| Retained profits | 154 | 120 |
| Total L and OE | 785 | 749 |
Note: All figures are given in millions of dollars ($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 \\ &= 700-680+34 \\ &= 54 \\ \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}) \\ &= (70+11+4-11) - (50+16+3-19) \\ &= 74 - 50 \\ &= 24 \\ \end{aligned}###
Now just substitute the values:
###\begin{aligned} CFFA &= NI + Depr - CapEx - \Delta NWC + IntExp \\ &= 147 + 34 - 54 - 24 + 39 \\ &= 142 \\ \end{aligned}###
Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?
###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###
Capital expenditure (CapEx) is equal to 'net capital expenditure' which is the cash spent on (non-current) assets less the cash received from selling them. It is subtracted in the cash flow from assets (CFFA) equation to make up for how depreciation is added back. Since depreciation (Depr) is added back, no cost has been allocated to the assets bought such as land, buildings, factories and trucks, so it is subtracted in CFFA as CapEx.
The sum of the un-discounted Depr and CapEx amounts will cancel each other out, but there is a timing difference which is important. Depreciation allocates the asset cost over its life and this has nothing to do with cash flows, ignoring the time value of money. CapEx reflects when the money is actually spent, usually at the start when the asset is bought, taking the time value of money into account.
A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.
Buying less capital assets (non-current assets) such as land, buildings and trucks will decrease CapEx and increase CFFA.
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###There will be less depreciation and therefore a lower depreciation tax shield, causing a decrease in CFFA, but this is likely to be a small effect compared to the fall in CapEx.
###\begin{aligned} CFFA &= NI+Depr-CapEx - \varDelta NWC+IntExp \\ &= (Rev-COGS-FC-Depr-IntExp).(1-t_c)+Depr-CapEx - \varDelta NWC+IntExp \\ &= (Rev-COGS-FC).(1-t_c)+\mathbf{Depr.t_c} -CapEx - \varDelta NWC+IntExp.t_c \\ \end{aligned}###
Over the next year, the management of an unlevered company plans to:
- Achieve firm free cash flow (FFCF or CFFA) of $1m.
- Pay dividends of $1.8m
- Complete a $1.3m share buy-back.
- Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.
Assume that:
- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
Firm free cash flow (FFCF) should equal net payments to debt and equity holders.
Since the firm is unlevered, there are no cash flows to or from debt holders which makes it easier.
Note that the capital expenditure of $0.8m is a red herring since CapEx is already subtracted in FFCF, so the CapEx can be ignored.
###\begin{aligned} FFCF &= (\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}) \\ 1m &= 0 - 0 + (1.8m + 1.3m) - (\text{new equity raisings}) \\ \end{aligned} ### ###\begin{aligned} (\text{new equity raisings}) &= 0 - 0 + (1.8m + 1.3m) - 1m \\ &= 2.1m \\ \end{aligned} ###
Commentary regarding the retained profits
Since "the firm has sufficient retained profits to pay the dividend and complete the buy back", why does the firm need to raise money through equity financing?
Remember that all things on the liabilities (L) and owners' equity (OE) side of the balance sheet (L+OE), such as retained earnings, are just records of how the assets (A=L+OE) were funded.
These liabilities and owners' equity are not physical things such as cash on the assets side of the balance sheet.
So a firm can have lots of retained profits but no cash to pay things such as dividends. For example, the assets might be all property, plant and equipment (PPE) rather than cash.
Also, profit (on the income statement or P&L) does not necessarily correspond with cash flows. For example, depreciation (and often interest expense) are accruals that are non-cash items. So high profits doesn't necessarily mean high cash flow.
The note only mentions the sufficient retained earnings to afford the dividend and buyback due to the constraint on companies that most legal systems disallow firms from paying out equity through dividends and buybacks unless they have current or retained profits. This is designed to stop Ponzi schemes.
Over the next year, the management of an unlevered company plans to:
- Make $5m in sales, $1.9m in net income and $2m in equity free cash flow (EFCF).
- Pay dividends of $1m.
- Complete a $1.3m share buy-back.
Assume that:
- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
Equity free cash flow (EFCF) should equal net payments to equity holders (which is also equal to firm free cash flow (FFCF) less net payments to debt holders).
The sales and net income are irrelevant in this question. They are already included in the EFCF figure.
###\begin{aligned} EFCF &= FFCF - (\text{net payments to debt holders}) \\ &= (\text{net payments to equity holders}) \\ &= (\text{payments to equity holders}) - (\text{receipts from equity holders}) \\ &= (\text{dividend and buyback payments}) - (\text{new equity raisings}) \\ 2m &= (1m + 1.3m) - (\text{new equity raisings}) \\ \end{aligned} ### ###\begin{aligned} (\text{new equity raisings}) &= (1m + 1.3m) - 2m \\ &= 0.3m \\ \end{aligned} ###
Find the cash flow from assets (CFFA) of the following project.
| Project Data | ||
| Project life | 2 years | |
| Initial investment in equipment | $6m | |
| Depreciation of equipment per year for tax purposes | $1m | |
| Unit sales per year | 4m | |
| Sale price per unit | $8 | |
| Variable cost per unit | $3 | |
| Fixed costs per year, paid at the end of each year | $1.5m | |
| Tax rate | 30% | |
Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch $0.9 million when it is sold at t=2.
Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another $0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.
Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).
Initially at time zero, no time has elapsed so there is zero revenue, expenses, income, depreciation and so on. But there is an initial change in net working capital due to the inventory purchase.
###\begin{aligned} \Delta NWC_0 &= \Delta NWC_\text{now} - \Delta NWC_\text{before} \\ &= CA_\text{now} - CL_\text{now} - (CA_\text{before} - CL_\text{before}) \\ &= 0.8m - 0 - (0 - 0) \\ &= 0.8m \\ \end{aligned}###There is CapEx, which is the $6m cost of the equipment. Using the Cash Flow From Assets equation:
###\begin{aligned} CFFA_0 &= NI_0 + Depr_0 - CapEx_0 - \Delta NWC_0 + IntExp_0 \\ &= 0 + 0 - 6m - 0.8m + 0 \\ &= -6.8m \\ \end{aligned}###At time one the Net Income, CapEx and change in NWC must be calculated and then substituted into the CFFA equation.
###\begin{aligned} \Delta NWC_1 &= CA_\text{now} - CL_\text{now} - (CA_\text{before} - CL_\text{before}) \\ &= 0.8m - 0 - (0.8m - 0) \\ &= 0 \\ \end{aligned}### ###\begin{aligned} NI_1 &= (Rev_1 - COGS_1 - FC_1 - Depr_1 - IntExp_1)(1-t_c) \\ &= (4m \times 8 - 4m \times 3 - 1.5m - 1m)(1-0.3) \\ &= 12.25m \\ \end{aligned}###Note that CapEx is zero since no equipment was bought or sold.
###\begin{aligned} CFFA_1 &= NI_1 + Depr_1 - CapEx_1 - \Delta NWC_1 + IntExp_1 \\ &= 12.25m + 1m - 0 - 0 + 0 \\ &= 13.25m \\ \end{aligned}### For the final cash flow at time 2, the Net Income will be the same but the CapEx and change in NWC must be calculated. ###\begin{aligned} \Delta NWC_2 &= CA_\text{now} - CL_\text{now} - (CA_\text{before} - CL_\text{before}) \\ &= 0 - 0 - (0.8m - 0) \\ &= -0.8m \\ \end{aligned}### ###\begin{aligned} CapEx_2 &= -(P_\text{mkt} - \text{CapitalGainsTax}) \\ &= -(P_\text{mkt} - (P_\text{mkt} - P_\text{book}).t_c) \\ &= -(0.9m - (0.9m - 4m) \times 0.3) \\ &= -1.83m \\ \end{aligned}###Note that change in NWC and CapEx are both negative, so net cash was gained rather than spent from selling the inventory (NWC) and selling the equipment (CapEx).
###\begin{aligned} CFFA_2 &= NI_2 + Depr_2 - CapEx_2 - \Delta NWC_2 + IntExp_2 \\ &= 12.25m + 1m - (-1.83m) - (-0.8m) + 0 \\ &= 15.88m \\ \end{aligned}###Value the following business project to manufacture a new product.
| Project Data | ||
| Project life | 2 yrs | |
| Initial investment in equipment | $6m | |
| Depreciation of equipment per year | $3m | |
| Expected sale price of equipment at end of project | $0.6m | |
| Unit sales per year | 4m | |
| Sale price per unit | $8 | |
| Variable cost per unit | $5 | |
| Fixed costs per year, paid at the end of each year | $1m | |
| Interest expense per year | 0 | |
| Tax rate | 30% | |
| Weighted average cost of capital after tax per annum | 10% | |
Notes
- The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).
Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).
At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought. - The project cost $0.5m to research which was incurred one year ago.
Assumptions
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 3% pa.
- All rates are given as effective annual rates.
- The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.
What is the expected net present value (NPV) of the project?
Since all cash flows are real and the and the discount rate is real, there is no need to convert rates or cash flows which is a relief.
About note 1. The firm's current assets and liabilities are irrelevant for evaluating our project since they will not change if we go ahead with the project or not. They are not incremental cash flows. But the increase in current assets and liabilities are incremental cash flows and will lead to a change in net working capital. Here is the general equation for calculating the change (or increase) in net working capital:
###\begin{aligned} \varDelta NWC &= NWC_\text{now} - NWC_\text{before} \\ &= (CA_\text{now} - CL_\text{now}) - (CA_\text{before} - CL_\text{before}) \\ &= \varDelta CA - \varDelta CL \\ \end{aligned}###
The increases in NWC at each time will be:
###\begin{aligned} \varDelta NWC_0 &= \varDelta CA - \varDelta CL \\ &= 2m - 0 \\ &= 2m \\ \varDelta NWC_\text{1} &= \varDelta CA - \varDelta CL \\ &= 0.2m - 0.1m \\ &= 0.1m \\ \varDelta NWC_\text{2} &= \varDelta CA - \varDelta CL \\ &= (-2m-0.2m) - (-0.1m) \\ &= -2.1m \\ \end{aligned}###
Note that ##\varDelta NWC_\text{2}## is negative because at the end of the project all of the working capital (which is probably mostly inventory) is sold. This is stated at the end of note 1. The lower inventory means current assets falls, which is a negative change.
About note 2. The research and development cost is a sunk cost so it should be ignored. It can not be recovered and it has to be paid whether we go ahead with the project or not, so it's irrelevant to our decision and evaluation.
When the equipment is sold at t=2 for $0.6m there will be negative capital expenditure (CapEx). Complicating matters is the capital gains tax (CGT) effect since the book carrying value (original cost less accumulated depreciation) of the equipment will be 0, so there will be a capital gain of $0.6m on which we have to pay CGT. Since the 50% CGT discount applies we can reduce the corporate tax rate so the CGT will be less. The capital expenditure will be:
###\begin{aligned} CapEx &= -(P_\text{mkt} - CGT) \\ &= -(P_\text{mkt} - (P_\text{mkt}-P_\text{book}).(1-\text{CGTDiscount}).t_c) \\ &=-(0.6m - (0.6m-0) \times(1-0.5) \times 0.3) \\ &=-0.51m \\ \end{aligned}###
Note that selling a capital asset is a negative capital expenditure (CapEx), that's why the figure is negative (-0.51m).
To find the Net Income (NI) which will be paid at the end of each year (t=1 and 2),
###\begin{aligned} NI &= (Rev-COGS-FC-Depr-IntExp).(1-t_c) \\ &= (Q(P-VC)-FC-Depr-IntExp).(1-t_c) \\ &= (4m(8-5)-1m-3m-0).(1-0.3) \\ &= 5.6m \end{aligned}###
To find the CFFA at each time period.
###\begin{aligned} CFFA_0 &= NI+Depr-CapEx - \varDelta NWC+IntExp \\ &= 0 +0 -6m - 2m +0 \\ &= -8m \\ CFFA_1 &= NI+Depr-CapEx - \varDelta NWC+IntExp \\ &= 5.6m +3m -0 - 0.1m +0 \\ &= 8.5m \\ CFFA_2 &= NI+Depr-CapEx - \varDelta NWC+IntExp \\ &= 5.6m +3m -(-0.51m) - (-2.1m) +0 \\ &= 11.21m \\ \end{aligned}###
The project value is the present value of the CFFA.
###\begin{aligned} V_\text{0, project} &= CFFA_0 + \frac{CFFA_1}{(1+r)^1} + \frac{CFFA_2}{(1+r)^2} \\ &= -8m + \frac{8.5m}{(1+0.1)^1} + \frac{11.21m}{(1+0.1)^2} \\ &= -8m + 7.72727273m + 9.26446281m \\ &= 8.99173553m \\ \end{aligned}###
Since the net present value is positive, the project should be accepted. The project will increase the value of the firm's assets by $8.99m.