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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions Finance – Revision Exercise 2 (i) – Interest rates, bonds, forward rates & shares 1. How would you write the following expression: the two year forward rate starting in three years time? With the interest rate notation, a. the start date is the first number, so in this case that will be 3 b. the second number is the duration of the forward rate which is added to the start date, in this case the length of the forward rate is 2 years and this is added to the start date to give 5 c. the answer is 3f5 2. If the one, two, three, four year spot rates are 5%, 6%, 7%, 8% respectively, what is the one year forward rate starting in two years time? (1 + 2f3) = (1 + 0s3)3 (1 + 0s2)2 = (1.07)3 (1.06)2 = 1.09028 = 9.028% 3. A bond is priced at £96.45 in the market. It’s coupon rate is 4%, the bond has four years to redemption. What is the yield to maturity? Lay out your cash flow like this and make a guess at the interest rate that solves the equation. year 0 1 2 3 4 -96.45 + 4 + 4 + 4 + 104 = 0 ( 1 + r) (1 + r)^2 (1 + r)^3 (1 + r)^4 In this case the answer works out at 5% if you guess that first time. If you guess 4% and 6% you will get a positive and negative number, you get the YTM by interpolating from that point: YTM = r1 + ((N1/(N1+N2)) * ( r2 – r1)) src.doc - 1 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions 4. If the one, two, three, and four year spot rates are 4%, 4.5%, 5% and 5.25%, what will be the price of a four year bond with a 7% coupon? Layout the cash flows as below and discount by the appropriate discount rate (the spot rate for that year). year 1 2 3 4 Bond price = 7 + 7 + 7 + 107 1.04 1.045^2 1.05^3 1.0525^4 Bond price = £106.3835 5. There are three zero coupon government bonds, maturing in one, two and three years time. The prices are £93.50, £86.90, and £80.10 respectively. What are the spot rates that can be derived from these prices, and if there is a three year 9% coupon bond available in the market what will be its price? Given that price, what is the yield to maturity? Zero coupons Total Annualised Bond 100 return return cash flows disc c/f one year 93.5 1.069519 1.069519 6.95% 9 8.415 two year 86.9 1.150748 1.072729 7.27% 9 7.821 three year 80.1 1.248439 1.076769 7.68% 109 87.309 Price = 103.545 Bond price Bond cash flows YTM = -103.545 9 9 109 7.63% YTM 6. A company has dividends of 5.8p, 6p, 6.3p, 6.7p, 7.1p, 7.7p, 8.5p in 2006 through to 2012 respectively. If the cost of equity for the company is 14%, what is the share price if you base the growth of dividends on (i) the entire period, (ii) the last two years (2010 - 2012)? r = 0.14 Year Dividend 2006 5.8 2007 6.0 2008 6.3 2009 6.7 2010 7.1 2011 7.7 2012 8.5 Share price g (6) = 1.065774 0.065774 122p. g (2) = 1.094159 0.094159 203p. src.doc - 2 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions The growth rate for (i) takes the dividend paid this year (8.5p) and divides it by the first dividend (5.8p), this gives a growth factor of 1.4655, you need to take the root of 1/the number of returns (this is 6), the growth rate is 6.5774% (1+g = 1.065774). Then you plug this into the div growth formula. As you can see different assumptions about the div growth rate will have a dramatic impact on the share price. 7. How useful is the price-earnings ratio as a measure of value? List the advantages and disadvantages of its use. The p/e ratio is of limited use. It should only be used to compare similar companies, ie, companies from the same sector or business. The companies should have the same accounting conventions, so that the measures of earnings are based on the same calculations. For the measure to be useful there would need to be adjustments made to deliver a measure of earnings that is close to cash earnings rather than accounting earnings. P/e ratios should not be used across sectors, the comparison is meaningless, you are not comparing like with like. The accounting figures, despite continual changes to the accounting regulations are still subject to manipulation. 8. What are the problems with the dividend growth model as a means of valuing shares? The DGM can be manipulated to give different valuations if you use different spreads of years to calculate the growth rate of dividends. In seeking to place a high valuation on the company the best pairing of dividends might be used (eg, dividend growth from 05-10 was 6%, but div growth from 07-10 was only 4.5% - use 05-10 to maximise the valuation of the company). You need to be aware of this. You need to use the dividend growth period that most accurately reflects the company as it currently is, ie, if it has divested a large subsidiary two years ago, using the last five years as the growth period will not reflect the company accurately. There is the problem when g is equal or greater than r. In this case the DGM does not work. To overcome this we use the multi-stage valuation model. If the company does not pay any dividend – how do you value it? The company will have a valuation because there will be an expectation that the company will pay dividends at some time in the future. Microsoft only started paying dividends in 2003, yet by that time it was the most valuable company in the world. Microsoft may have only started paying dividends in 2003, but it was hugely cash generative, and the cash flows could be valued as what could potentially be paid out as dividends. Microsoft in the period before it started paying dividends regularly spent $billions on share repurchases (share repurchases are effectively dividends – they are cash that ends up in the shareholders hands). Apple does not pay any dividends, its earnings are ploughed back into the business, and the company has a stock market value of src.doc - 3 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions $240bn. It is better off using its earnings as a source of finance to grow the business, rather than paying out dividends to shareholders. 9. What features can a bond have that may help overcome the agency problems that bondholders have with managers and shareholders? Bondholders will have covenants in the bond contract, these can be positive or negative covenants. Positive covenants will be eg, the maintenance of certain financial ratios, there would have to be a certain level of operating profits divided by interest charges (fixed charge coverage) that would need to be at least met. Failure to do so would put the company in breach of the covenants and trigger action from bondholders. Negative covenants would be, eg restrictions on the amount that can be paid out as dividends or used to repurchase shares, restrictions on the amount and seniority of new debt that can be issued, or restrictions on disposal of assets. Put provisions can be built into the bond contract. This would enable the bondholder to demand repayment of the bond if the bondholders felt that the cash that had been lent to the company was in danger of not being repaid. The put can also be used to capture higher interest rates in the market ( ie, the company bond coupon is much lower than the current rate of interest, so the bondholder puts the bond back on to the company, and the bondholder can reinvest the proceeds at the higher rate in the market). If a company is in trouble in the markets and would face high borrowing costs from the debt markets and its shares have fallen sharply, so they don’t want to sell shares, a possible financing route is the convertible bond. This is a bond where the holder can convert into shares if the underlying shares rise in value passing a pre-set conversion price. The convertible bond helps solve agency problems in that bondholders would not normally lend to the company, but if the prospects are reasonable they could go down the route of a convertible. If the shares don’t recover, they get their coupon and principal back. If the shares recover, they can convert into equity and capture the upside. Because the convertibility option is attractive, the bonds can be sold with a much lower coupon than would normally be the case. From the equity point of view, the company is selling shares at a premium to the current value (about 50% higher and the sale will be in the future, conversion would not usually happen for a couple of years). The problem for equity is that there will be dilution of their holding when the bondholders convert. On conversion the bond liability disappears – the bondholders give up their bonds for equity. src.doc - 4 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions 10. If you have a 4 year bond with a 7% coupon, and the term structure of interest rates for the next four years is 4%, 5%, 6% and 6.5% respectively, what is the price of the bond and what is its duration? What does duration tell us (in general)? coupon: 7 A B C D E Spot int rate Years cash flow disc fact PV*cash flow PV c/f * time 1 7 0.9615 6.731 6.731 0.04 2 7 0.9070 6.349 12.698 0.05 3 7 0.8396 5.877 17.632 0.06 4 107 0.7773 83.174 332.694 0.065 bond price = 102.131 369.755 duration = 3.620 Column C is the discount factor for the set of spot interest rates (1/(1 + r)n) Column D is the discount factor * the bond cash flow. This is then multiplied by time. Columns D and E are summed. Divide the total of column D (the bond price) into column E (the time weighted present value cash flows), this gives you the Duration measure. Duration is a measure of the riskiness of the bond. The higher the duration the more risky the bond is. This means that its value will be more volatile than bonds with lower duration measures. The highest measure for duration is the term of the bond, eg, if you had a 5 year bond, the highest value for duration would be 5. This would be the case if it was a zero coupon bond. With the zero coupon bond all the cash flows are at the end of the bond’s life. This makes it the riskiest bond to hold, because changes in interest rates will affect the distant cash flows most. The more a bond pays out during its life the lower its duration will be. So, if you had two four year bonds; a 10% bond and a 3% bond, the 10% bond would have the lower duration measure, because it will have paid out more of its cash flows (the 10% coupon cash flows) during its life. src.doc - 5 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions Finance – Revision Exercise 2 (ii) – Capital budgeting - solutions 1. An asset has a book value of £100,000 having cost £200,000 originally, the company faces a tax rate of 30%. Show the cash flow implications of the following: (a) The asset is sold for £130,000. There is a taxable gain (sale value – book value) * tax rate (130 – 100) * 0.3 = £9,000 tax payable Cash inflow of £130,000 from the sale of machinery Cash outflow of £9,000 in tax payable (b) The asset is sold for £40,000. Tax loss (40 – 100) * 0.3 = £18,000 tax saving Cash inflow of £40,000 from sale of machinery Cash inflow of £18,000 saving (reduction) in taxes – you do not get £18,000 in cash, you save by paying £18,000 less in taxes. (c) The asset is sold for £100,000 Sale at book value – no tax effects Cash inflow of £100,000 from sale. 2. NYS wants to buy new machinery for £550,000 which will be depreciated straight-line to zero over 5 years. It requires £100,000 set up, installation and shipping costs. Their will be a requirement for an additional £30,000 in inventory for the new machine. The new machine replaces an old machine bought and installed for £350,000 two years ago. It was being depreciated straight line to zero over its seven year life. The old equipment can be sold today for £200,000. The company faces a 30% tax rate. What is the initial investment? Year 0 initial investment: £ ’000. Machinery (550) Installation (100) src.doc - 6 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions Working capital (30) Sale of old machine 200 Tax saving 15 Net investment (465) The sale of the old machinery creates a loss of £50k which will produce a reduction in taxes of £15k (£50 * 0.3). The net investment will include any cost of new machinery, any shipping or installation costs, any investment in working capital as a result of the project and any sale of old equipment with the associated tax effects of that sale. 3. Using the company NYS in Q.2, the new machine will generate revenues of £290,000 and have cash operating costs of £80,000 for years 1 through 5. The old machine has revenues of £170,000 and cash costs of £90,000. Assume the new machine will have zero value at the end of the project. What are the after tax cash flows? To identify all the cash flows associated with the project it is best to set these out in the form of: cash flows with the project – cash flows without the project. Do this for revenues, for operating costs and you need to look at the change in depreciation as that will have an effect on the tax cash flows. CF = [(Rw – Rwo) – (Ow – Owo) – (Dw – Dwo)] * (1 – t) then add back the change in depreciation + (Dw – Dwo) Where Rw = revenues with the project Owo= operating costs without the project Dw = depreciation with the project etc. t = tax rate Depreciation basis for new machine is on cost + installation straight line to zero. = 550 + 100 – 0 5 = £130k per annum Old machine £350k/ 7 = £50k per annum CF = [(290 – 170) – (80 – 90) – (130 – 50)] * (1 – 0.3) + (130 – 50) src.doc - 7 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions = ([120 – (-10) –80] * 0.7) + 80 = (50 * 0.7) + 80 = £115k OR in the cash flow framework layout; Cash flows yr 1- 4 Revenues 120 Costs 10 Tax -15 FCF* 115 Tax calc Revenues 120 Costs 10 Depreciation -80 pre-tax 50 tax -15 Cash flows will be £115k per annum for years 1-4, year 5 will have £30k return of working capital in addition to the £115k. Final year cash flows would also include any winding down costs and revenues for the project eg. Any sale and tax effect from the new machinery, any removal or clear up costs, and any opportunity cost cash flows. 4. Using the NYS example, layout all the relevant cash flows and calculate the NPV if the cost of capital is 9%. Year 0 1 2 3 4 5 Machinery -550 Installation -100 wking capital -30 30 sale of old machinery 200 revenues 120 120 120 120 120 costs 10 10 10 10 10 tax 15 -15 -15 -15 -15 -15 Cash flows -465 115 115 115 115 145 Disc at 9% 0.09 1 0.917 0.842 0.772 0.708 0.650 NPV -465 105.50 96.79 88.80 81.47 94.24 1.81 src.doc - 8 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions Tax calculation operating profits 130 depreciation -80 pre tax 50 tax at 0.3 -15 5. A company is buying a new machine, it costs £230,000 plus £20,000 to install. Working capital will increase by £25,000 as a result of the new machine. Taking each of the examples in Q.1 (a), (b) and (c), as the machine it is replacing, work out the year 0 cash flow (net investment). (a) (b) (c) new mach -230 -230 -230 install -20 -20 -20 wking cap -25 -25 -25 sale of old 130 40 100 tax effect -9 18 net inv. -154 -217 -175 With (a) there is the £9,000 tax payable to be included in the initial investment, with (b) there is the tax saving of £18,000 and there is no tax impact with the sale at £100,000. 6. A company has sales of £80m and expenses (excluding depreciation) of £50m. The company’s assets have a book value of £60m and 5 years of life remaining – they are depreciated straight line to zero. The company faces a 30% tax rate. Assume no change in working capital. What is the annual cash flow of the company? Sales 80 Expenses (50) Op profits 30 Tax (5.4) Cash flow 24.6 Tax calculation Op profits 30 Depn (12) Pre tax 18 Tax @ 30% (5.4) src.doc - 9 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions 7. A company has the opportunity of buying one machine for £400,000 that will replace three older machines. The older machines can be sold for £10,000, £20,000 and £15,000, they have respective book values of £40,000, £40,000 and £35,000. The new machine will reduce the need for so much stock so there will be a saving of £15,000 per annum on stock levels. The new machine will require shipping and installation charges of £30,000. Tax rate is 30%. What is the year 0 cash flow (net investment)? New machines (400) Installation (30) Wking cap 15 Sale of old mach 45 Tax saving 21 Net investment (349) Total book value of old machines = £115k, sale value = £45k, loss = £70k, tax saving at 30% tax rate = £21k. 8. Explain how you would treat each of the following for project capital budgeting cash flow analysis: - interest payments not included these are payments to capital suppliers. This effect is caught in the discount rate (WACC) - project overheads if they are directly related to the project they would be included, otherwise overheads are excluded - general company fixed costs these would be incurred anyway whether the project went ahead or not, so they would be excluded - working capital Initial investment in working capital is a year 0 cash flow, they any change in working capital year on year would be included in the cash flow, and working capital would be returned at the end of the project. 9. You own a large industrial site, part of which has been developed but isn’t used. To use up this extra space you decide to run a single five year project on it. Explain if there are any capital budgeting concerns regarding the use of this company owned land. The land is not free, there is an opportunity cost to using it – it could be used for another project or it could be sold. You would enter an opportunity cost in year 0 for the land, being the value of its best alternative use, for example being sold. src.doc - 10 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions If you ran the project, at the end you would have an opportunity cash flow in the form of the revenue you could get if you sold the land at the end of the project. 10. Two companies plan new product launches: Samsung plan to launch a new mobile phone to replace their current best seller; Sky decides to launch a new dedicated sports channel – this time offering ‘live chess’ on TV. What are the associated cash flow costs of these two ventures? Explain how you would decide on the relevant cash flows in decisions like this? These are associated costs – potential product cannibalisation costs. In the case of Samsung they would lose sales if they did not launch a new product – rivals would – it is an intensely competitive sector. For Sky there would be a small drop in their original product cash flows – no-one else would launch a channel like this and they would probably take away some (small amount) of their own sales from other channels. 11. Taking two investment decisions from the last couple of years; Apple launching its ‘i-pad’, and Carphone Warehouse taking over AOL’s European operations. Carphone Warehouse already had an internet offering to the UK household market, then added AOL to it. Discuss what you think the associated cash flow considerations would be in these cases? What about Apple’s earlier products like the ipod and iphone? Can you think of other examples like this? Is the ipad a new segment of the market that won’t steal sales away from existing Apple products or is it a substitute ipod for some people? In which case the ipad would steal sales away from ipod products. The ipad is unlikely to make many people go out and buy an ipod, but buyers who would be making a computer purchase decision, may buy an Apple computer as a result of buying the ipad. So there may be a mixture of revenue enhancement and revenue cannibalisation from the introduction of the ipad. Earlier Apple product launches had similar impacts. It was argued that the ‘i-phone’ might steal sales from the existing i-pods that were available, but an alternative view was that Apple was extending the range into a new segment of the market, if Apple didn’t do this the mobile phone manufacturers would encroach more and more into the main i-pod market and steal sales away from Apple. Carphone Warehouse with the takeover have become the No.3 operator in broadband in the UK. AOL is being maintained as a separate company and they have to pay a royalty to the US AOL parent company. So Carphone’s AOL unit is in competition with its main broadband unit for new customers. AOL originally offered a free laptop or a Sony PS3 to new customers (including existing Carphone customers) if they signed up for a 2 year contract. They were stealing sales from themselves. src.doc - 11 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions 12. What are mutually exclusive projects and can you give some examples? You must choose either one or the other of the projects on offer, you cannot undertake both projects. Company has a plot of land, it can build an office development or a leisure complex, but not both, on that plot of land. 13. (a) What is the net impact of the following increases in the year 0 investment in a project: Inventory £50,000 Accounts payable £30,000 Accounts receivable £80,000 Inventory and a/c receivable are cash outflows – they are a use of funds Accounts payable is a cash inflow – it is a source of funds. The net effect is (50) + (80) + 30 = (100) outflow in the cash flows. (b) What would be the working capital entry for the final year? Cash inflow of £100k 14. Why is cash flow used instead of accounting earnings in capital budgeting analysis? Cash flows pays for capital expenditure, it pays the capital suppliers, accounting earnings are not cash, they are open to manipulation. 15. What impact do the following have on project cash flows – describe the likely impact on either the initial investment cash flows, or the operating cash flows of the project. Assume a tax rate of 30%. (a) An old machine is sold for £10,000 to be replaced by a new one, the old machine having a book value of £25,000. Sale of old machine £10k Tax saving £4.5 Both cash inflows, the machine is sold at a loss so there will be a tax credit. There may be further cash flow effects depending on the annual level of depreciation on the old machine – there will be an effect on the depreciation tax shield in future years if there is still depreciation to be taken off the existing machine (see the effects in Q.2 and 3 with the change in depreciation as a result of changing a machine). (b) A new machine producing cost savings of £50,000 per year from replacing an old machine src.doc - 12 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions Cash inflow of £50k After tax cash flow of £35k (this is how much it would contribute to your final after tax cash flows.) (c) Ongoing marketing analysis into project’s product popularity. This is taking place during the project so it is a relevant cash flow. (d) Extension of credit to new customers (that is taken up by customers) i) at the start of the project This is a use of funds, so it is a cash outflow and would show up in the initial year 0 working capital. ii) during the project If everything else remained the same this would represent a use of funds, a cash outflow and would show up as a change in working capital. The relevant entry would be the change year on year. (e) A fully depreciated asset is sold for £20,000 at the start of the project. There is a £20k gain on the book value of the asset, so this is a taxable gain – there would be a £20k cash inflow and a £6k tax cash outflow (30% tax on the gain). (f) A new asset has an estimated salvage value of £40,000 If the depreciation basis had been to depreciate down to the expected salvage value, then in the final year the sale of the equipment for £40k would have no tax consequences. If depreciation had been down to zero the £40k salvage value would be taxable. The final year sale is a cash inflow. (g) The firm has borrowed £200,000 at 8% interest. These would not appear in the cash flows. The interest rate impact is captured in the cost of capital. (h) As a result of introducing a new product, sales of the existing product fell by £15,000. This would be an associated cost and a cash outflow of £15k, unless the product was in a very competitive market and the sales would have been lost anyway even if the new product wasn’t launched. (i) Between year 2 and 3, accounts payable increases by £20,000. This is a source of funds and would reduce working capital (assuming all other items remained the same) this would be a cash inflow. (j) Marketing costs incurred before the project started are paid at the end of year 2. These are irrelevant, they have to be paid whether the project goes ahead or not – sunk cost. src.doc - 13 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions (k) There is a net increase in depreciation of £35,000 a year in years 1 to 5, and then a net increase of £55,000 a year from years 6- 10. Depreciation itself is not a cash flow – the machine has been bought and paid for, but there is a tax shield associated with depreciation. Depreciation is added back on to accounting profits to give cash flow. The value of the tax shield in years 1-5 will be £35k * 0.3 = £10.5k, and £16.5k in years 6-10. This means that tax will be lower in those years by £10.5k and £16.5k as a result of the depreciation tax shield. [eg. Cash flow exercises (separate handout) Q.4, health club in Edinburgh: Depreciation = £6k per annum Tax with depreciation = £4.8k (0.30 * £16k) Tax without depreciation = £6.6k (0.30 * £22k) Difference = £1.8k Depreciation tax shield = Depreciation * tax rate = £6k * 0.30 = £1.8k Tax paid is lower by £1.8k because of the depreciation tax shield. 16. You are examining the viability of a capital investment project that your firm is interested in. The project will require an initial investment of £800,000 and the projected revenues are £640,000 a year for five years. The projected cost-of-goods- sold is 40% of revenues and the company faces a tax rate of 30%. The initial investment is primarily in plant and equipment which would be depreciated straight line over 5 years to zero salvage value. The project makes use of other resources that your firm already owns: Two employees of the firm, each with a salary of £64,000 a year, who are currently employed by another division will be transferred to work on this project. The other division has no alternative use for them, but they are covered by a union contract, which will prevent them from being fired for three years (during which time they would be paid their current salary). The project will use excess capacity in the current packaging plant. While this excess capacity has no alternative use now, it is estimated that the firm will have to invest £400,000 in a new packaging plant in year 4 as a consequence of this project using up excess capacity (instead of year 8 as originally planned). The project will use a van currently owned by the firm. While the van is not currently used, it can be rented out for £4,800 a year for the next five years. The book value of the van is £16,000 and it is being depreciated on a straight line basis to zero (with five years still to be depreciated). The discount rate for the project is 12%. src.doc - 14 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions What is the NPV of the project? Q.16 Opportunity costs showing two routes to get to the npv init investment 800 tax 30% annuity sales 640 disc rt 12% factor 3.6048 cost of sales 40% years 5 depn 160 Cash flows Year 0 1 2 3 4 5 initial investment -800 sales 640 640 640 640 640 costs -256 -256 -256 -256 -256 two managers -128 -128 van -4.8 -4.8 -4.8 -4.8 -4.8 op prof 379.2 379.2 379.2 251.2 251.2 tax -65.76 -65.76 -65.76 -27.36 -27.36 cash flows -800 313.44 313.44 313.44 223.84 223.84 disc factor 1 0.893 0.797 0.712 0.636 0.567 disc c/ flows -800 279.86 249.87 223.10 142.25 127.01 222.10 less opportunity cost of building 4 yrs early = -92.65 npv = 129.44 Taxation calculation Year 0 1 2 3 4 5 op prof 379.2 379.2 379.2 251.2 251.2 depn -160 -160 -160 -160 -160 pre tax 219.2 219.2 219.2 91.2 91.2 tax @ 30% -65.76 -65.76 -65.76 -27.36 -27.36 alternatively: yr0 yr 1-5 init inv -800 sales 640 cost of sales -256 op profit 384 tax -67.2 cash flow 316.8 PV of cash flows = 1141.99 (316.8 * 5yr annuity at 10%) Taxation calculation op profit 384 src.doc - 15 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions depn -160 pre tax profit 224 tax -67.2 Opportunity costs: < This method separates out each of the opportunity costs and subtracts them at the end salary after tax PV employees yr 4 128 89.6 56.94 first 3 yrs irrelevant yr 5 128 89.6 50.84 107.78 opportunity cost yr 4 yr 8 difference new factory 400 254.21 161.55 92.65 opportunity cost can do either way: rent 5 yr annuity after tax i) van 4.8 3.6048 17.303 12.11 after rent tax 5 yr annty PV ii) van 4.8 3.36 3.604776 12.11 opportunity cost NPV = -800 + 1141.99 - 107.78 -92.65 -12.11 NPV = 129.44 The depreciation on the van is irrelevant as a project cash flow because the firm would have the depreciation whether they did the project or not 17. A company has a dividend today of 10p. The share price is 220p, the rate of growth of the dividend is 4%. What is the cost of equity capital? r = D1 + g P0 D0 = 10p D1 = 10p * 1.04 = 10.4 = 10.4 + 0.04 220 = 0.08727 = 8.73% src.doc - 16 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions 18. A company has a dividend in 2007 of 16p and a dividend of 23.5p in 2012 (just paid). The share price is 380p. What is the cost of equity? r = D1 + g P0 D0 = 23.5 g = (FV/PV)1/n = (23.5 / 16)0.2 = 1.079915 dividend growth rate = 7.99% D1 = 23.5 * 1.079915 = 25.378 r = 25.378 + 0.0799 380 = 0.06678 + 0.0799 = 0.14668 = 14.668% 19. If the risk free rate of interest is 4% and the beta of company X is 0.9 and the return on the stock market is 12%, what is the cost of equity for company X? E(r ) = Rf + (rm – rf) = 4 + 0.9(12 – 4 ) = 11.2% 20. If the market risk premium is 7% and company Y has a beta of 1.2, what is the cost of equity for Y given a risk free rate of 4.5%? E(r ) = Rf + (rm – rf) src.doc - 17 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions = 4.5 + 1.2(7) = 12.9% With these calculations watch out for the different labels ‘ return on the stockmarket’ (rm) and the ‘stockmarket risk premium’ (rm – rf). The second term has already worked out the expression in the brackets. 21. If XYZ is made up of one part debt to three parts equity, and the required rate of return on debt is 6%, the cost of equity is 15%, tax is 30%, what is the weighted average cost of capital? WACC = ( E * ke) + ( D * kd*(1 – t)) E + D E + D = (0.75 * 0.15) + (0.25 * 0.06 *0.7) = 0.1125 + 0.0105 = 0.1230 = 12.3% 22. A company has just paid a dividend of 10p, this is up from 8.5p two years ago. The company has 70% equity in its capital structure. The risk free rate of interest is 4%, the equity risk premium is 6%. The company has a bond in issue with a coupon of 7%. The bond is priced at £106.25 in the market, the share price is 250p. The bond has three years to maturity. The tax rate is 30%. What is the WACC? For debt we need to calculate the yield to maturity, this is the IRR of the bond from its price today to maturity. This is the replacement cost of debt for the company. For equity we have; for the CAPM, the risk free rate and the market risk premium, but no beta, for the dividend growth model, we have the share price, D0 and the dividend 2 years ago, so we can calculate the growth rate and obtain D1. So we have enough information to use the dividend growth model. The calculations are shown below; With the dividends we need to work out the growth rate (10/8.5)0.5 = 1.0847, so the growth rate is 8.47%. For the YTM we need to find the rate that solves the following expression; -106.25 + 7/(1+YTM) + 7/(1+YTM)2 + 107/(1+YTM)3 = 0. You solve by trial and error. The bond has a coupon of £7, but will lose just over £6 over 3 years. Buying the bond at this price will lose slightly over £2 per year through to maturity. A rough and ready guess at the YTM would take the £7 of income and subtract the slightly more than £2 in capital losses to give a YTM slightly less than src.doc - 18 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions 5. Using trial and error, 5% and 4% would be a good place to start (this rough and ready calc works OK for bonds with short lives, it works less well for longer dated bonds, but it gives you a reasonable indication of where to start with the trial and error). Bond cash flows: YTM -106.25 7 7 107 4.72% required rate on debt (rd) d0 10 tax = 30% d-2 8.5 g = 1.0847 D1 = 10.8465 P0 = 250 r = 0.128038 12.80% cost of equity (re) weights: equity 70% debt = 30% WACC= 0.089627 + 0.009906 = 0.099533 9.95% 23. If a project has a different risk to the parent company how would you work out a WACC for the project? You need to construct a tailor made WACC that reflects the risk of the project. One route to achieving this can be (if the figures are given for this method) to ungear the parent company beta. The ungeared beta is just the weighted average of the company’s debt and equity betas. Once you have the company ungeared beta (or asset beta) you would adjust for project – company differences in revenue volatility and operational gearing. The revenue volatility adjustment is to multiply the company ungeared beta by Project revenue volatility divided by company revenue volatility. The multiply the resulting beta by 1+project fixed costs divided by 1+company fixed costs. This will give you the project ungeared beta. If the project is funded 100% by equity, then you would just use this beta directly in the capm calculation; re = rf + β(rm – rf). This would be the cost of capital for the project. If the project was part funded with debt, then you would need a debt beta and an equity beta. If this was a question you would be given the debt beta and debt or equity weighting and you would work out the equity beta from that information src.doc - 19 -
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Finance Revision Exercise 2 – Interest rates & Capital budgeting - solutions (the project ungeared beta would just be the weighted average of the debt and equity betas and the only missing item would be the equity beta, so you could rearrange the formula to solve for the missing equity beta). Once you have the equity and debt betas, they can be used in the capm formula to calculate the costs of equity and debt and then these put into a WACC calculation. Another route to get a project cost of capital if it is in a different line of business to the parent company, is to use a proxy company. There may be a company listed on the stockmarket that only does what the project is going to do (eg parent company is a games software company and launches a project in retailing – this has a different risk profile to the parent company. Look to the quoted games retailers for a cost of capital). The beta of the proxy company would be ungeared by multiplying the equity and debt betas by their weights in the capital structure and adding together. What you have then is the ungeared beta for a project of that risk. In capital budgeting you have to use a discount rate that reflects the risk of the project being undertaken – the parent WACC doesn’t do this, but using a proxy company in that area allows you to establish an ungeared beta that represents the riskiness of the project. That would then be adjusted to match the capital structure of the project (you would follow the process outlined in the paragraph above if the project is not 100% equity funded.). So two methods have been outlined; one is to adjust the parent ungeared beta for the different risk profile of the project, and the second is to use a proxy company, ungear its beta and adjust for funding that is being used for the project. 24. You have been hired as a capital budgeting analyst by a sports goods firm. It manufactures running shoes and has gained 10% of the overall shoe market (total market worth £100 million a year). The fixed costs associated with manufacturing these shoes is £2 million a year and variable costs are 45% of revenues. The tax rate is 30%. The discount rate is 8%. The company believes that it can increase its market share to 20% (of the £100m market) by investing £15 million in a new distribution system (which will be depreciated straight line over its 10 year life to a scrap and salvage value of zero) and spending £1 million a year in additional advertising. The company proposes to continue to maintain working capital at 10% of annual revenues. (a) What is the initial investment for this project? (b) What is the annual operating cash flow from this project? (c) What is the NPV of the project? src.doc - 20 -
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