CH-8 Risk Analysis, Real Options, and Capital Budgeting – Corporate Finance : Book Guide

Chapter 8 Risk Analysis, Real Options, and Capital Budgeting 1. Though NPV is the best capital budgeting approach conceptually, it has been criticized in practice for giving managers a false sense of security. Sensitivity analysis, break even analysis, and scenario analysis shows NPV under varying assumptions, giving managers a better feel for the project’s risks. Unfortunately each methodology has its own drawbacks. Sensitivity analysis modifies only one variable at a time, but many variables are likely to vary together in the real world. Scenario analysis examines a project’s performance under different scenarios but not all scenarios. Break-even analysis calculates the sales figure at which the project breaks even. Though break-even analysis is frequently performed on an accounting profit basis, we suggest that a net present value basis is more appropriate. In essence, all capital budgeting techniques are tools and any tool in the wrong hands can cause damage. 2. Monte Carlo Analysis utilises the power of modern computing by allowing one to randomly simulate a very large number of scenarios based on a selection of pre-chosen inputs. With scenario analysis and sensitivity analysis, only a very small finite number of alternative outcomes can be examined. With Monte Carlo Analysis, many thousand alternatives are examined. The major weakness of the technique is that it relies on the analyst to provide distributions and estimates of the underlying inputs. Like NPV analysis, these can be wrong and yet they give the user a false sense of security. One way to improve on Monte Carlo Analysis is to use distributions based on empirical data instead of theoretical data. However, in real life, this can be difficult due to the lack of available data. 3. Traditional NPV analysis is often too conservative because it ignores profitable options such as the ability to expand the project if it is profitable, or abandon the project if it is unprofitable. The option to alter a project when it has already been accepted has a value, which increases the NPV of the project. 4. When the additional analysis has a negative NPV. Since the additional analysis is likely to occur almost immediately, this means when the benefits of the additional analysis outweigh the costs. The benefits of the additional analysis are the reduction in the possibility of making a bad decision. Of course, the additional benefits are often difficult, if not impossible, to measure; so much of this decision is based on experience. 5. To calculate the accounting breakeven, we first need to find the depreciation for each year. The depreciation is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £3,200,000 £640,000 £640,000 £2,560,000 2 £2,560,000 £512,000 £1,152,000 £2,048,000 3 £2,048,000 £409,600 £1,561,600 £1,638,400 4 £1,638,400 £327,680 £1,889,280 £1,310,720 5 £1,310,720 £1,310,720 £3,200,000 £0 To estimate the accounting breakeven, one must use Solver in Excel. The spreadsheet, which is shown below, shows the accounting profit when the number of units sold is 100,000. Sales Revenues Variable Costs Fixed Costs Dep. 20% EBT Tax Net Income 250000 £10.00 £2.50 £900,000 23% 0 1 250,000 £2,500,000 £625,000 £900,000 £640,000 £335,000 £77,050 £257,950 2 250,000 £2,500,000 £625,000 £900,000 £512,000 £463,000 £106,490 £356,510 3 250,000 £2,500,000 £625,000 £900,000 £409,600 £565,400 £130,042 £435,358 4 250,000 £2,500,000 £625,000 £900,000 £327,680 £647,320 £148,884 £498,436 5 250,000 £2,500,000 £625,000 £900,000 £1,310,720 -£335,720 -£77,216 -£258,504 Cum.Net Profit £1,289,750 Using Solver, the break-even number of units is: Sales Revenues Variable Costs Fixed Costs Depreciatio n 20% EBT Tax Net Income 205333 £10.00 £2.50 £900,000 23% 0 1 205,333 £2,053,333 £513,333 £900,000 £640,000 £0 £0 £0 2 205,333 £2,053,333 £513,333 £900,000 £512,000 £128,000 £29,440 £98,560 3 205,333 £2,053,333 £513,333 £900,000 £409,600 £230,400 £52,992 £177,408 4 205,333 £2,053,333 £513,333 £900,000 £327,680 £312,320 £71,834 £240,486 5 205,333 £2,053,333 £513,333 £900,000 £1,310,720 -£670,720 -£154,266 -£516,454 Cumulative Net Profit £0 And the accounting breakeven is 205,333 units. b. We add depreciation to net income to get operating cash flow: Year Net Income Depreciation Operating Cash Flow 1 £257,950 £640,000 £897,950 2 £356,510 £512,000 £868,510 3 £435,358 £409,600 £844,958 4 £498,436 £327,680 £826,116 5 -£258,504 £1,310,720 £1,052,216 Now we can calculate the NPV using our base-case projections. Year Investment OCF Net Cash Flow PV Cash Flows 0 -£3,200,000 -£3,200,000 -£3,200,000 1 £897,950 £897,950 £794,646 2 £868,510 £868,510 £680,171 3 £844,958 £844,958 £585,598 4 £826,116 £826,116 £506,673 5 £1,052,216 £1,052,216 £571,100 NPV = -£61,812 To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 300,000 units. The NPV at this sales level is: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 300000 £10.00 £2.50 £900,000 23% 0 1 300,000 £3,000,000 £750,000 £900,000 £640,000 £710,000 £163,300 £546,700 2 300,000 £3,000,000 £750,000 £900,000 £512,000 £838,000 £192,740 £645,260 3 300,000 £3,000,000 £750,000 £900,000 £409,600 £940,400 £216,292 £724,108 4 300,000 £3,000,000 £750,000 £900,000 £327,680 £1,022,320 £235,134 £787,186 5 300,000 £3,000,000 £750,000 £900,000 £1,310,720 £39,280 £9,034 £30,246 Year Net Income Depreciation Operating Cash Flow 1 £546,700 £640,000 £1,186,700 2 £645,260 £512,000 £1,157,260 3 £724,108 £409,600 £1,133,708 4 £787,186 £327,680 £1,114,866 5 £30,246 £1,310,720 £1,340,966 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£3,200,000 -£3,200,000 -£3,200,000 1 £1,186,700 £1,186,700 £1,050,177 2 £1,157,260 £1,157,260 £906,304 3 £1,133,708 £1,133,708 £785,717 4 £1,114,866 £1,114,866 £683,768 5 £1,340,966 £1,340,966 £727,822 And the NPV is £953,789. So, the change in NPV for every unit change in sales is: NPV/S = (£953,789 – (-£61,812)/(300,000 – 250,000) NPV/S = +£20.31 If sales were to drop by 500 units, then NPV would drop by: NPV drop = £20.31(500) = £10,156.01 You may wonder why we chose 300,000 units. Because it doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same. c. To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of £0.50. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one pound change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of £0.50 is: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 250000 £10.00 £0.50 £900,000 23% 0 1 250,000 £2,500,000 £125,000 £900,000 £640,000 £835,000 £192,050 £642,950 2 250,000 £2,500,000 £125,000 £900,000 £512,000 £963,000 £221,490 £741,510 3 250,000 £2,500,000 £125,000 £900,000 £409,600 £1,065,400 £245,042 £820,358 4 250,000 £2,500,000 £125,000 £900,000 £327,680 £1,147,320 £263,884 £883,436 5 250,000 £2,500,000 £125,000 £900,000 £1,310,720 £164,280 £37,784 £126,496 Year Net Income Depreciation Operating Cash Flow 1 £642,950 £640,000 £1,282,950 2 £741,510 £512,000 £1,253,510 3 £820,358 £409,600 £1,229,958 4 £883,436 £327,680 £1,211,116 5 £126,496 £1,310,720 £1,437,216 So, the change in OCF for a £1 change in variable costs is: Year OCF £3.50 OCF £2.50 Difference 0 £1,282,950 £897,950 £385,000 1 £1,253,510 £868,510 £385,000 2 £1,229,958 £844,958 £385,000 3 £1,211,116 £826,116 £385,000 7 £1,437,216 £1,052,216 £385,000 If variable costs decrease by £1 then, OCF would increase by £385,000. 6. For the best-case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. Doing so, we get: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 275000 £11.00 £1.35 £810,000 23% 0 1 275,000 £3,025,000 £371,250 £810,000 £640,000 £1,203,750 £276,863 £926,888 2 275,000 £3,025,000 £371,250 £810,000 £512,000 £1,331,750 £306,303 £1,025,448 3 275,000 £3,025,000 £371,250 £810,000 £409,600 £1,434,150 £329,855 £1,104,296 4 275,000 £3,025,000 £371,250 £810,000 £327,680 £1,516,070 £348,696 £1,167,374 5 275,000 £3,025,000 £371,250 £810,000 £1,310,720 £533,030 £122,597 £410,433 Year Net Income Depreciation Operating Cash Flow 1 £926,888 £640,000 £1,566,888 2 £1,025,448 £512,000 £1,537,448 3 £1,104,296 £409,600 £1,513,896 4 £1,167,374 £327,680 £1,495,054 5 £410,433 £1,310,720 £1,721,153 The best-case NPV is: Year Investment OCF Net Cash Flow PV Cash Flows 0 -£3,200,000 -£3,200,000 -£3,200,000 1 £1,566,888 £1,566,888 £1,386,626 2 £1,537,448 £1,537,448 £1,204,047 3 £1,513,896 £1,513,896 £1,049,206 4 £1,495,054 £1,495,054 £916,945 5 £1,721,153 £1,721,153 £934,173 NPVbest = £2,290,996 For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 225000 £9.00 £1.65 £990,000 23% 0 1 225,000 £2,025,000 £371,250 £990,000 £640,000 £23,750 £5,462 £18,287 2 225,000 £2,025,000 £371,250 £990,000 £512,000 £151,750 £34,902 £116,848 3 225,000 £2,025,000 £371,250 £990,000 £409,600 £254,150 £58,454 £195,696 4 225,000 £2,025,000 £371,250 £990,000 £327,680 £336,070 £77,296 £258,774 5 225,000 £2,025,000 £371,250 £990,000 £1,310,720 -£646,970 -£148,803 -£498,167 Year Net Income Depreciation Operating Cash Flow 1 £18,287 £640,000 £658,288 2 £116,848 £512,000 £628,848 3 £195,696 £409,600 £605,296 4 £258,774 £327,680 £586,454 5 -£498,167 £1,310,720 £812,553 The worst-case NPV is: Year Investment OCF Net Cash Flow PV Cash Flows 0 -£3,200,000 -£3,200,000 -£3,200,000 1 £658,288 £658,288 £582,555 2 £628,848 £628,848 £492,480 3 £605,296 £605,296 £419,500 4 £586,454 £586,454 £359,683 5 £812,553 £812,553 £441,021 NPVworst = -£904,760 7. In this question, we must carry out the full analysis in Excel and then use solver to determine the financial break even sales. If depreciation was applied using the straight line methodology, you could use the technique given in the chapter. However, when reducing balances are used, the depreciation that is charged each year will change and the method is not appropriate. The spreadsheet that is presented below shows the solution after Solver has been applied. (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £200,000 £40,000 £40,000 £160,000 2 £160,000 £32,000 £72,000 £128,000 3 £128,000 £25,600 £97,600 £102,400 4 £102,400 £20,480 £118,080 £81,920 5 £81,920 £81,920 £200,000 £0 Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 20,556 £25.00 £5.00 £350,000 25% 0 1 20,556 £513,910 £102,782 £350,000 £40,000 £21,128 £5,282 £15,846 2 20,556 £513,910 £102,782 £350,000 £32,000 £29,128 £7,282 £21,846 3 20,556 £513,910 £102,782 £350,000 £25,600 £35,528 £8,882 £26,646 4 20,556 £513,910 £102,782 £350,000 £20,480 £40,648 £10,162 £30,486 5 20,556 £513,910 £102,782 £350,000 £81,920 -£20,792 -£5,198 -£15,594 Year Net Income Depreciation Operating Cash Flow 1 £15,846 £40,000 £55,846 2 £21,846 £32,000 £53,846 3 £26,646 £25,600 £52,246 4 £30,486 £20,480 £50,966 5 -£15,594 £81,920 £66,326 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£200,000 -£200,000 -£200,000 1 £55,846 £55,846 £49,862 2 £53,846 £53,846 £42,926 3 £52,246 £52,246 £37,188 4 £50,966 £50,966 £32,390 5 £66,326 £66,326 £37,635 The NPV of these cash flows is equal to 0 and thus the breakeven point is 20,556 units sold. 8. Notice that there is no tax rate in this question, which means that depreciation has no cash flow effects. The only reason why we consider depreciation is to calculate the resale value in each year. (a) (b) (c) (d) Year Starting Value Depreciation Accumulated Depreciation Residual Value 25% (a)-(b) 1 €1,500,000 €375,000 €375,000 €1,125,000 2 €1,125,000 €281,250 €656,250 €843,750 3 €843,750 €210,938 €867,188 €632,813 4 €632,813 €158,203 €1,025,391 €474,609 5 €474,609 €118,652 €1,144,043 €355,957 6 €355,957 €88,989 €1,233,032 €266,968 7 €266,968 €66,742 €1,299,774 €200,226 8 €200,226 €50,056 €1,349,831 €150,169 9 €150,169 €37,542 €1,387,373 €112,627 10 €112,627 €28,157 €1,415,530 €84,470 The Cash Flow savings of €280,000 is an annuity that can be calculated using the present value of an annuity formula. It is thus easy to estimate the NPV for each year the machine could be purchased. The NPV each year will be the present value of the increased cash savings minus cost. We must be careful, however. In order to make the correct decision, the NPV for each year must be taken to a common date. We will discount all of the NPVs to today. Doing so, we get: Year PV of outflow (a) Years Remaining PV of €280,000 per year ( c ) NPV (a) - ( c ) 0 € 1,500,000 10 € 1,582,062 € 82,062 1 € 1,500,000 9 € 1,332,062 -€ 167,938 2 € 1,500,000 8 € 1,108,848 -€ 391,152 3 € 1,500,000 7 € 909,550 -€ 590,450 4 € 1,500,000 6 € 731,605 -€ 768,395 5 € 1,500,000 5 € 572,725 -€ 927,275 6 € 1,500,000 4 € 430,868 -€ 1,069,132 7 € 1,500,000 3 € 304,211 -€ 1,195,789 8 € 1,500,000 2 € 191,123 -€ 1,308,877 9 € 1,500,000 1 € 90,153 -€ 1,409,847 The company should purchase the machine immediately, when the NPV is the highest. 9. We need to calculate the NPV of the two options, go directly to market now, or utilize test marketing first. The NPV of going directly to market now is: NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure) NPV = £20,000,000(0.50) + £5,000,000(0.50) NPV = £12,500,000 Now we can calculate the NPV of test marketing first. Test marketing requires a £2 million cash outlay. Choosing the test marketing option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0. NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]} / (1 + R)t NPV = –£2,000,000 + {[£20,000,000 (0.75)] + [£5,000,000 (0.25)]} / 1.15 NPV = £12,130,434.78 The company should go directly to market with the product since that option has the highest expected payoff. 10. We need to calculate the NPV of each option, and choose the option with the highest NPV. So, the NPV of going directly to market is: NPV = CSuccess (Prob. of Success) NPV = €1,200,000 (0.50) NPV = €600,000 The NPV of the focus group is: NPV = C0 + CSuccess (Prob. of Success) NPV = –€120,000 + €1,200,000 (0.70) NPV = €720,000 And the NPV of using the consulting firm is: NPV = C0 + CSuccess (Prob. of Success) NPV = –€400,000 + €1,200,000 (0.90) NPV = €680,000 The firm should conduct a focus group since that option has the highest NPV. 11. The company should analyze both options, and choose the option with the greatest NPV. So, if the company goes to market immediately, the NPV is: NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure) NPV = €30,000,000(.55) + €3,000,000(.45) NPV = €17,850,000 Customer segment research requires a €1 million cash outlay. Choosing the research option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0. So, the NPV of the customer segment research is: NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]} / (1 + R)t NPV = –€1,000,000 + {[€30,000,000 (0.70)] + [€3,000,000 (0.30)]} / 1.15 NPV = €18,043,478 Graphically, the decision tree for the project is: The company should undertake the market segment research since it has a higher NPV. 12. a. The accounting breakeven is the after-tax sum of the fixed costs and depreciation charge divided by the after-tax contribution margin (selling price minus variable cost). So, the accounting breakeven level of sales is: QA = [(FC + Depreciation)(1 – tC)] / [(P – VC)(1 – tC)] QA = [(£340,000 + £20,000) (1 – 0.35)] / [(£2.00 – £0.72) (1 – 0.35)] QA = 281,250.00 units Start Research No Research €18.0435 million at t = 0 €17.85 million at t = 0 Success Failure Success Failure €30 million at t = 1 (€26.087 million at t = 0) €3 million at t = 1 (€2.6087 million at t = 0) €30 million at t = 0 €3 million at t = 0 b. When calculating the financial breakeven point, we express the initial investment as an equivalent annual cost (EAC). Dividing the in initial investment by the seven-year annuity factor, discounted at 15 percent. We can do this because depreciation is calculated on a straight line basis. If Depreciation was determined using reducing balances, you would have to calculate the Financial Breakeven using a spreadsheet and Solver. The EAC of the initial investment is: EAC = Initial Investment / PVIFA15%,7 EAC = £140,000 / 4.1604 EAC = £33,650.45 Note that this calculation solves for the annuity payment with the initial investment as the present value of the annuity. In other words: PVA = C({1 – [1/(1 + R)]t } / R) £140,000 = C{[1 – (1/1.15)7 ] / .15} C = £33,650.45 Now we can calculate the financial breakeven point. The financial breakeven point for this project is: QF = [EAC + FC(1 – tC) – Depreciation(tC)] / [(P – VC)(1 – tC)] QF = [£33,650.45 + £340,000(.65) – £20,000(.35)] / [(£2 – £0.72) (.65)] QF = 297,656.79 or about 297,657 units 13. The Net Income of the base case scenario is given below: Revenues €44,000,000,000 Variable Costs €39,600,000,000 Fixed Costs €2,000,000,000 Net Income €2,400,000,000 We arrive at the figures as follows: Revenues = Market Size * Market Share * Price per Unit = 1.1 million * 10% * €400,000 = €44 billion Variable Costs = 90% of Revenues = €39.6 billion We now consider the scenarios as envisioned by the three directors. Director A Director B Director C Revenues €9,600,000,000 €37,500,000,000 €76,800,000,000 Variable Costs €11,136,000,000 €30,000,000,000 €53,760,000,000 Fixed Costs €5,000,000,000 €3,000,000,000 €1,000,000,000 Net Income €6,536,000,000 €4,500,000,000 €22,040,000,000 The main uncertainties in the project are clearly Revenues and Variable Costs. 14. a. At the accounting breakeven, the IRR is zero percent since the project recovers the initial investment. The payback period is N years, the length of the project since the initial investment is exactly recovered over the project life. The NPV at the accounting breakeven is: NPV = I [(1/N)(PVIFAR%,N) – 1] b. At the cash breakeven level, the IRR is –100 percent, the payback period is negative, and the NPV is negative and equal to the initial cash outlay. c. The definition of the financial breakeven is where the NPV of the project is zero. If this is true, then the IRR of the project is equal to the required return. It is impossible to state the payback period, except to say that the payback period must be less than the length of the project. Since the discounted cash flows are equal to the initial investment, the undiscounted cash flows are greater than the initial investment, so the payback must be less than the project life. 15. The base-case, best-case, and worst-case values are shown below. Remember that in the best-case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease, and costs increase. Scenario Unit sales Variable cost Fixed costs Base 150 £18,000 £200,000 Best 165 £16,200 £180,000 Worst 135 £19,800 £220,000 Using the tax shield approach, the OCF and NPV for the base case estimate are: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 1 £460,000 £92,000 £92,000 £368,000 2 £368,000 £73,600 £165,600 £294,400 3 £294,400 £58,880 £224,480 £235,520 4 £235,520 £235,520 £460,000 £0 Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 150 £24,000.00 £18,000.00 £200,000 24% 1 150 £3,600,000 £2,700,000 £200,000 £92,000 £608,000 £145,920 £462,080 2 150 £3,600,000 £2,700,000 £200,000 £73,600 £626,400 £150,336 £476,064 3 150 £3,600,000 £2,700,000 £200,000 £58,880 £641,120 £153,869 £487,251 4 150 £3,600,000 £2,700,000 £200,000 £235,520 £464,480 £111,475 £353,005 Year Net Income Depreciation Operating Cash Flow 1 £462,080 £92,000 £554,080 2 £476,064 £73,600 £549,664 3 £487,251 £58,880 £546,131 4 £353,005 £235,520 £588,525 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£460,000 -£460,000 -£460,000 1 £554,080 £554,080 £481,809 2 £549,664 £549,664 £415,625 3 £546,131 £546,131 £359,090 4 £588,525 £588,525 £336,491 NPVbase = £1,133,015 The OCF and NPV for the best case estimate are: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 165 £24,000.00 £16,200.00 £180,000 24% 1 165 £3,960,000 £2,673,000 £180,000 £92,000 £1,015,000 £243,600 £771,400 2 165 £3,960,000 £2,673,000 £180,000 £73,600 £1,033,400 £248,016 £785,384 3 165 £3,960,000 £2,673,000 £180,000 £58,880 £1,048,120 £251,549 £796,571 4 165 £3,960,000 £2,673,000 £180,000 £235,520 £871,480 £209,155 £662,325 Year Net Income Depreciation Operating Cash Flow 1 £771,400 £92,000 £863,400 2 £785,384 £73,600 £858,984 3 £796,571 £58,880 £855,451 4 £662,325 £235,520 £897,845 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£460,000 -£460,000 -£460,000 1 £863,400 £863,400 £750,783 2 £858,984 £858,984 £649,515 3 £855,451 £855,451 £562,473 4 £897,845 £897,845 £513,346 NPVbest = £2,016,117 And the OCF and NPV for the worst case estimate are: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 135 £24,000.00 £19,800.00 £220,000 24% 1 135 £3,240,000 £2,673,000 £220,000 £92,000 £255,000 £61,200 £193,800 2 135 £3,240,000 £2,673,000 £220,000 £73,600 £273,400 £65,616 £207,784 3 135 £3,240,000 £2,673,000 £220,000 £58,880 £288,120 £69,149 £218,971 4 135 £3,240,000 £2,673,000 £220,000 £235,520 £111,480 £26,755 £84,725 Year Net Income Depreciation Operating Cash Flow 1 £193,800 £92,000 £285,800 2 £207,784 £73,600 £281,384 3 £218,971 £58,880 £277,851 4 £84,725 £235,520 £320,245 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£460,000 -£460,000 -£460,000 1 £285,800 £285,800 £248,522 2 £281,384 £281,384 £212,767 3 £277,851 £277,851 £182,692 4 £320,245 £320,245 £183,101 NPVworst = £367,081 b. To calculate the sensitivity of the NPV to changes in fixed costs, we choose another level of fixed costs. We will use fixed costs of £210,000. The OCF using this level of fixed costs and the other base case values, we get: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 150 £24,000.00 £18,000.00 £210,000 24% 1 150 £3,600,000 £2,700,000 £210,000 £92,000 £598,000 £143,520 £454,480 2 150 £3,600,000 £2,700,000 £210,000 £73,600 £616,400 £147,936 £468,464 3 150 £3,600,000 £2,700,000 £210,000 £58,880 £631,120 £151,469 £479,651 4 150 £3,600,000 £2,700,000 £210,000 £235,520 £454,480 £109,075 £345,405 Year Net Income Depreciation Operating Cash Flow 1 £454,480 £92,000 £546,480 2 £468,464 £73,600 £542,064 3 £479,651 £58,880 £538,531 4 £345,405 £235,520 £580,925 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£460,000 -£460,000 -£460,000 1 £546,480 £546,480 £475,200 2 £542,064 £542,064 £409,878 3 £538,531 £538,531 £354,093 4 £580,925 £580,925 £332,146 NPV = £1,111,317 The sensitivity of NPV to changes in fixed costs is: NPV/FC = (£1,111,317 – £1,133,015)/(£210,000 – 200,000) NPV/FC = -£2.1698 For every pound FC increase, NPV falls by £2.1698. c. The accounting breakeven is determined in this example using Solver. The spreadsheet below gives the level of units sold that result in a zero profit over the four years. Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 52.5 £24,000.00 £18,000.00 £200,000 24% 0 53 £1,260,000 £945,000 £200,000 £92,000 £23,000 £5,520 £17,480 1 53 £1,260,000 £945,000 £200,000 £73,600 £41,400 £9,936 £31,464 2 53 £1,260,000 £945,000 £200,000 £58,880 £56,120 £13,469 £42,651 3 53 £1,260,000 £945,000 £200,000 £235,520 -£120,520 -£28,925 -£91,595 4 52.5 £24,000.00 £18,000.00 £200,000 24% Total £0 As can be seen, this figure is 52.5 units. 16. The marketing study and the research and development are both sunk costs and should be ignored. We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be: Sales New clubs £700  55,000 = £38,500,000 Exp. clubs £1,100  (–13,000) = –14,300,000 Cheap clubs £400  10,000 = 4,000,000 £28,200,000 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the clubs any more, we will save these variable costs, which is an inflow. So: Var. costs New clubs –£320  55,000 = –£17,600,000 Exp. Clubs –£600  (–13,000) = 7,800,000 Cheap clubs –£180  10,000 = –1,800,000 –£11,600,000 We now determine the depreciation schedule of the investment asset. (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 £18,200,000 £3,640,000 £3,640,000 £14,560,000 2 £14,560,000 £2,912,000 £6,552,000 £11,648,000 3 £11,648,000 £2,329,600 £8,881,600 £9,318,400 4 £9,318,400 £1,863,680 £10,745,280 £7,454,720 5 £7,454,720 £1,490,944 £12,236,224 £5,963,776 6 £5,963,776 £1,192,755 £13,428,979 £4,771,021 7 £4,771,021 £954,204 £14,383,183 £3,816,817 The pro forma income statement will be: Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income £28,200,000.00 £11,600,000.00 £7,500,000 28% 1 £28,200,000 £11,600,000 £7,500,000 £3,640,000 £5,460,000 £1,528,800 £3,931,200 2 £28,200,000 £11,600,000 £7,500,000 £2,912,000 £6,188,000 £1,732,640 £4,455,360 3 £28,200,000 £11,600,000 £7,500,000 £2,329,600 £6,770,400 £1,895,712 £4,874,688 4 £28,200,000 £11,600,000 £7,500,000 £1,863,680 £7,236,320 £2,026,170 £5,210,150 5 £28,200,000 £11,600,000 £7,500,000 £1,490,944 £7,609,056 £2,130,536 £5,478,520 6 £28,200,000 £11,600,000 £7,500,000 £1,192,755 £7,907,245 £2,214,029 £5,693,216 7 £28,200,000 £11,600,000 £7,500,000 £954,204 £8,145,796 £2,280,823 £5,864,973 Using the bottom up OCF calculation, we get: Year Net Income Depreciation Operating Cash Flow 1 £3,931,200 £3,640,000 £7,571,200 2 £4,455,360 £2,912,000 £7,367,360 3 £4,874,688 £2,329,600 £7,204,288 4 £5,210,150 £1,863,680 £7,073,830 5 £5,478,520 £1,490,944 £6,969,464 6 £5,693,216 £1,192,755 £6,885,971 7 £5,864,973 £954,204 £6,819,177 The Cash Flow analysis is given below: Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -£18,200,000 -£950,000 -£19,150,000 -£19,150,000 1 £7,571,200 £7,571,200 £6,641,404 2 £7,367,360 £7,367,360 £5,668,944 3 £7,204,288 £7,204,288 £4,862,689 4 £7,073,830 £7,073,830 £4,188,275 5 £6,969,464 £6,969,464 £3,619,721 6 £6,885,971 £6,885,971 £3,137,156 7 £3,816,817 £6,819,177 £950,000 £11,585,994 £4,630,196 So, the payback period is: Payback period = 2 + £4,211,440/£7,204,288 Payback period = 2.585 years The NPV is £13,598,385 IRR = 17.72% b. The upper and lower bounds for the variables are: Base Case Lower Bound Upper Bound Unit sales (new) 55,000 49,500 60,500 Price (new) £700 £630 £770 VC (new) £320 £288 £352 Fixed costs £7,500,000 £6,750,000 £8,250,000 Sales lost (expensive) 13,000 11,700 14,300 Sales gained (cheap) 10,000 9,000 11,000 Best-case We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be: Sales New clubs £770  60,500 = £46,585,000 Exp. Clubs £1,100  (–11,700) = – 12,870,000 Cheap clubs £400  11,000 = 4,400,000 £38,115,000 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the clubs any more, we will save these variable costs, which is an inflow. So: Var. costs New clubs £288  60,500 = £17,424,000 Exp. clubs £600  (–11,700) = – 7,020,000 Cheap clubs £180  11,000 = 1,980,000 £12,384,000 The pro forma income statement will be: Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income £38,115,000 £12,384,000.00 £6,750,000 28% 1 £38,115,000 £12,384,000 £6,750,000 £3,640,000 £15,341,000 £4,295,480 £11,045,520 2 £38,115,000 £12,384,000 £6,750,000 £2,912,000 £16,069,000 £4,499,320 £11,569,680 3 £38,115,000 £12,384,000 £6,750,000 £2,329,600 £16,651,400 £4,662,392 £11,989,008 4 £38,115,000 £12,384,000 £6,750,000 £1,863,680 £17,117,320 £4,792,850 £12,324,470 5 £38,115,000 £12,384,000 £6,750,000 £1,490,944 £17,490,056 £4,897,216 £12,592,840 6 £38,115,000 £12,384,000 £6,750,000 £1,192,755 £17,788,245 £4,980,709 £12,807,536 7 £38,115,000 £12,384,000 £6,750,000 £954,204 £18,026,796 £5,047,503 £12,979,293 Year Net Income Depreciation Operating Cash Flow 1 £11,045,520 £3,640,000 £14,685,520 2 £11,569,680 £2,912,000 £14,481,680 3 £11,989,008 £2,329,600 £14,318,608 4 £12,324,470 £1,863,680 £14,188,150 5 £12,592,840 £1,490,944 £14,083,784 6 £12,807,536 £1,192,755 £14,000,291 7 £12,979,293 £954,204 £13,933,497 Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -£18,200,000 -£950,000 -£19,150,000 -£19,150,000 1 £14,685,520 £14,685,520 £12,882,035 2 £14,481,680 £14,481,680 £11,143,183 3 £14,318,608 £14,318,608 £9,664,653 4 £14,188,150 £14,188,150 £8,400,524 5 £14,083,784 £14,083,784 £7,314,676 6 £14,000,291 £14,000,291 £6,378,344 7 £3,816,817 £13,933,497 £950,000 £18,700,314 £7,473,343 NPV = £44,106,758 Worst-case We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be: Sales New clubs £630  49,500 = £31,185,000 Exp. Clubs £1,100  (– 14,300) = – 15,730,000 Cheap clubs £400  9,000 = 3,600,000 £19,055,000 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the pairs any more, we will save these variable costs, which is an inflow. So: Var. costs New clubs £352  49,500 = £17,424,000 Exp. Clubs £600  (– 14,300) = – 8,580,000 Cheap clubs £180  9,000 = 1,620,000 £10,464,000 The pro forma income statement will be: Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income £19,055,000 £10,464,000.00 £8,250,000 28% 1 £19,055,000 £10,464,000 £8,250,000 £3,640,000 -£3,299,000 -£923,720* -£2,375,280 2 £19,055,000 £10,464,000 £8,250,000 £2,912,000 -£2,571,000 -£719,880* -£1,851,120 3 £19,055,000 £10,464,000 £8,250,000 £2,329,600 -£1,988,600 -£556,808* -£1,431,792 4 £19,055,000 £10,464,000 £8,250,000 £1,863,680 -£1,522,680 -£426,350* -£1,096,330 5 £19,055,000 £10,464,000 £8,250,000 £1,490,944 -£1,149,944 -£321,984* -£827,960 6 £19,055,000 £10,464,000 £8,250,000 £1,192,755 -£851,755 -£238,491* -£613,264 7 £19,055,000 £10,464,000 £8,250,000 £954,204 -£613,204 -£171,697* -£441,507 * Assumes a tax credit Using the bottom up OCF calculation: Year Net Income Depreciation Operating Cash Flow 1 -£2,375,280 £3,640,000 £1,264,720 2 -£1,851,120 £2,912,000 £1,060,880 3 -£1,431,792 £2,329,600 £897,808 4 -£1,096,330 £1,863,680 £767,350 5 -£827,960 £1,490,944 £662,984 6 -£613,264 £1,192,755 £579,491 7 -£441,507 £954,204 £512,697 And the worst-case NPV is: Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -£18,200,000 -£950,000 -£19,150,000 -£19,150,000 1 £1,264,720 £1,264,720 £1,109,404 2 £1,060,880 £1,060,880 £816,313 3 £897,808 £897,808 £605,995 4 £767,350 £767,350 £454,333 5 £662,984 £662,984 £344,333 6 £579,491 £579,491 £264,009 7 £3,816,817 £512,697 £950,000 £5,279,514 £2,109,891 NPV = –£13,445,723 c. To calculate the sensitivity of the NPV to changes in the price of the new clubs, we simply need to change the price of the new club. We will choose £750, but the choice is irrelevant as the sensitivity will be the same no matter what price we choose. We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be: Sales New clubs £750  55,000 = £41,250,000 Exp. Clubs £1,100  (– 13,000) = –14,300,000 Cheap clubs £400  10,000 = 4,000,000 £30,950,000 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the pairs any more, we will save these variable costs, which is an inflow. So: Var. costs New clubs £320  55,000 = £17,600,000 Exp. Clubs £600  (–13,000) = –7,800,000 Cheap clubs £180  10,000 = 1,800,000 £11,600,000 The pro forma income statement will be: Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income £30,950,000 £11,600,000.00 £7,500,000 28% 1 £30,950,000 £11,600,000 £7,500,000 £3,640,000 £8,210,000 £2,298,800 £5,911,200 2 £30,950,000 £11,600,000 £7,500,000 £2,912,000 £8,938,000 £2,502,640 £6,435,360 3 £30,950,000 £11,600,000 £7,500,000 £2,329,600 £9,520,400 £2,665,712 £6,854,688 4 £30,950,000 £11,600,000 £7,500,000 £1,863,680 £9,986,320 £2,796,170 £7,190,150 5 £30,950,000 £11,600,000 £7,500,000 £1,490,944 £10,359,056 £2,900,536 £7,458,520 6 £30,950,000 £11,600,000 £7,500,000 £1,192,755 £10,657,245 £2,984,029 £7,673,216 7 £30,950,000 £11,600,000 £7,500,000 £954,204 £10,895,796 £3,050,823 £7,844,973 Using the bottom up OCF calculation, we get: Year Net Income Depreciation Operating Cash Flow 1 £5,911,200 £3,640,000 £9,551,200 2 £6,435,360 £2,912,000 £9,347,360 3 £6,854,688 £2,329,600 £9,184,288 4 £7,190,150 £1,863,680 £9,053,830 5 £7,458,520 £1,490,944 £8,949,464 6 £7,673,216 £1,192,755 £8,865,971 7 £7,844,973 £954,204 £8,799,177 And the NPV is: Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -£18,200,000 -£950,000 -£19,150,000 -£19,150,000 1 £9,551,200 £9,551,200 £8,378,246 2 £9,347,360 £9,347,360 £7,192,490 3 £9,184,288 £9,184,288 £6,199,133 4 £9,053,830 £9,053,830 £5,360,594 5 £8,949,464 £8,949,464 £4,648,071 6 £8,865,971 £8,865,971 £4,039,217 7 £3,816,817 £8,799,177 £950,000 £13,565,994 £5,421,477 So, the sensitivity of the NPV to changes in the price of the new club is: NPV/P = (£22,089,229 - £13,598,385)/(£750 – 700) NPV/P = £169,817 For every pound increase (decrease) in the price of the clubs, the NPV increases (decreases) by £169,817 To calculate the sensitivity of the NPV to changes in the quantity sold of the new club, we simply need to change the quantity sold. We will choose 60,000 units, but the choice is irrelevant as the sensitivity will be the same no matter what quantity we choose. We will calculate the sales and variable costs first. Since we will lose sales of the expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total sales for the new project will be: Sales New clubs £700  60,000 = £42,000,000 Exp. clubs £1,100  (– 13,000) = –14,300,000 Cheap clubs £400  10,000 = 4,000,000 £31,700,000 For the variable costs, we must include the units gained or lost from the existing clubs. Note that the variable costs of the expensive clubs are an inflow. If we are not producing the pairs any more, we will save these variable costs, which is an inflow. So: Var. costs New clubs £320  60,000 = £19,200,000 Exp. clubs £600  (–13,000) = –7,800,000 Cheap clubs £180  10,000 = 1,800,000 £13,200,000 The pro forma income statement will be: Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income £31,700,000 £13,200,000.00 £7,500,000 28% 1 £31,700,000 £13,200,000 £7,500,000 £3,640,000 £7,360,000 £2,060,800 £5,299,200 2 £31,700,000 £13,200,000 £7,500,000 £2,912,000 £8,088,000 £2,264,640 £5,823,360 3 £31,700,000 £13,200,000 £7,500,000 £2,329,600 £8,670,400 £2,427,712 £6,242,688 4 £31,700,000 £13,200,000 £7,500,000 £1,863,680 £9,136,320 £2,558,170 £6,578,150 5 £31,700,000 £13,200,000 £7,500,000 £1,490,944 £9,509,056 £2,662,536 £6,846,520 6 £31,700,000 £13,200,000 £7,500,000 £1,192,755 £9,807,245 £2,746,029 £7,061,216 7 £31,700,000 £13,200,000 £7,500,000 £954,204 £10,045,796 £2,812,823 £7,232,973 Using the bottom up OCF calculation, we get: Year Net Income Depreciation Operating Cash Flow 1 £5,299,200 £3,640,000 £8,939,200 2 £5,823,360 £2,912,000 £8,735,360 3 £6,242,688 £2,329,600 £8,572,288 4 £6,578,150 £1,863,680 £8,441,830 5 £6,846,520 £1,490,944 £8,337,464 6 £7,061,216 £1,192,755 £8,253,971 7 £7,232,973 £954,204 £8,187,177 The NPV at this quantity is: Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -£18,200,000 -£950,000 -£19,150,000 -£19,150,000 1 £8,939,200 £8,939,200 £7,841,404 2 £8,735,360 £8,735,360 £6,721,576 3 £8,572,288 £8,572,288 £5,786,050 4 £8,441,830 £8,441,830 £4,998,241 5 £8,337,464 £8,337,464 £4,330,218 6 £8,253,971 £8,253,971 £3,760,398 7 £3,816,817 £8,187,177 £950,000 £12,953,994 £5,176,899 NPV = £19,464,786 So, the sensitivity of the NPV to changes in the quantity sold is: NPV/P = (£19,464,786 - £13,598,385)/(£750 – 700) NPV/P = £1,173.28 For an increase (decrease) of one set of clubs sold per year, the NPV increases (decreases) by £1,173.28. 17. a. The base-case NPV is: NPV = –€1,800,000 + €420,000(PVIFA16%,10) NPV = €229,955.54 b. We would abandon the project if the cash flow from selling the equipment is greater than the present value of the future cash flows. We need to find the sale quantity where the two are equal, so: €1,400,000 = (€60)Q(PVIFA16%,9) Q = €1,400,000/[€60(4.6065)] Q = 5,065 Abandon the project if Q < 5,065 units, because the NPV of abandoning the project is greater than the NPV of the future cash flows. c. The €1,400,000 is the market value of the project. If you continue with the project in one year, you forego the €1,400,000 that could have been used for something else. d. If the project is a success, present value of the future cash flows will be: PV future CFs = €60(9,000)(PVIFA16%,9) PV future CFs = €2,487,533.69 If the quantity sold is 4,000, we would abandon the project, and the cash flow would be €1,400,000. Since the project has an equal likelihood of success or failure in one year, the expected value of the project in one year is the average of the success and failure cash flows, plus the cash flow in one year, so: Expected value of project at year 1 = [(€2,487,533.69 + €1,400,000)/2] + €420,000 Expected value of project at year 1 = €2,363,766.85 The NPV is the present value of the expected value in one year plus the cost of the equipment, so: NPV = –€1,800,000 + (€2,363,766.85)/1.16 NPV = €237,730.04 If we couldn’t abandon the project, the present value of the future cash flows when the quantity is 4,000 will be: PV future CFs = €60(4,000)(PVIFA16%,9) PV future CFs = €1,105,570.53 The gain from the option to abandon is the abandonment value minus the present value of the cash flows if we cannot abandon the project, so: Gain from option to abandon = €1,400,000 – 1,105,570.53 Gain from option to abandon = €294,429.47 We need to find the value of the option to abandon times the likelihood of abandonment. So, the value of the option to abandon today is: Option value = (.50)(€294,429.47)/1.16 Option value = €126,909.25 18. If the project is a success, present value of the future cash flows will be: PV future CFs = €60(18,000)(PVIFA16%,9) PV future CFs = €4,975,067.39 If the sales are only 4,000 units, we know we will abandon the project, with a value of €1,400,000. Since the project has an equal likelihood of success or failure in one year, the expected value of the project in one year is the average of the success and failure cash flows, plus the cash flow in one year, so: Expected value of project at year 1 = [(€4,975,067.39 + €1,400,000)/2] + €420,000 Expected value of project at year 1 = €3,607,533.69 The NPV is the present value of the expected value in one year plus the cost of the equipment, so: NPV = –€1,800,000 + €3,607,533.69/1.16 NPV = €1,309,942.84 The gain from the option to expand is the present value of the cash flows from the additional units sold, so: Gain from option to expand = €60(9,000)(PVIFA16%,9) Gain from option to expand = €2,487,533.69 We need to find the value of the option to expand times the likelihood of expansion. We also need to find the value of the option to expand today, so: Option value = (.50)(€2,487,533.69)/1.16 Option value = €1,072,212.80 19. The payoff from taking the lump sum is $5,000, so we need to compare this to the expected payoff from taking one percent of the profit. The decision tree for the movie project is: Big audience 30% $10,000,00 0 Movie is good 10% Make movie Script is good Movie is bad Read script 70% Small audience Script is bad No profit 90% Don't make movie No profit The value of one percent of the profits as follows. There is a 30 percent probability the movie is good, and the audience is big, so the expected value of this outcome is: Value = $10,000,000 × .30 Value = $3,000,000 The value that the movie is good, and has a big audience, assuming the script is good is: Value = $3,000,000 × .10 Value = $300,000 This is the expected value for the studio, but the screenwriter will only receive one percent of this amount, so the payment to the screenwriter will be: Payment to screenwriter = $300,000 × .01 Payment to screenwriter = $3,000 The screenwriter should take the upfront offer of $5,000. 20. We must first determine the depreciation schedule of the investment asset. (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 €600,000 €120,000 €120,000 €480,000 2 €480,000 €96,000 €216,000 €384,000 3 €384,000 €76,800 €292,800 €307,200 4 €307,200 €61,440 €354,240 €245,760 5 €245,760 €49,152 €403,392 €196,608 Given that the accounting profit will be different each year, the only way to calculate the break-even sale price is to use Solver in a spreadsheet. The solution is given below: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 20,000 €64.03 €15 €900,000 €0 1 20,000 €1,280,678 €300,000 €900,000 €120,000 -€39,322 -€11,796 -€27,525 2 20,000 €1,280,678 €300,000 €900,000 €96,000 -€15,322 -€4,596 -€10,725 3 20,000 €1,280,678 €300,000 €900,000 €76,800 €3,878 €1,164 €2,715 4 20,000 €1,280,678 €300,000 €900,000 €61,440 €19,238 €5,772 €13,467 5 20,000 €1,280,678 €300,000 €900,000 €49,152 €31,526 €9,458 €22,068 The break-even sale price is €64.03. 21. The base cash flow worksheet for the investment is given below. The calculation method can be goal seek or solver. The break-even number of barrels that gives an NPV of £0 is 304,550 barrels. 0 1 2 3 4 5 Investment -12,000,000 Revenues 25,582,227 25,582,227 25,582,227 25,582,227 25,582,227 Costs -21,744,893 -21,744,893 -21,744,893 -21,744,893 -21,744,893 Net Cash Flow -12,000,000 3,837,334 3,837,334 3,837,334 3,837,334 3,837,334 PV(CF) -12,000,000 3,251,978 2,755,914 2,335,520 1,979,254 1,677,334 22. a. The NPV of the project is sum of the present value of the cash flows generated by the project. The cash flows from this project are an annuity, so the NPV is: NPV = –AED200,000,000 + AED60,000,000(PVIFA14%,6) NPV = AED33,320,051 b. The company should abandon the project if the PV of the revised cash flows for the next nine years is less than the project’s after-tax salvage value. Since the option to abandon the project occurs in year 1, discount the revised cash flows to year 1 as well. To determine the level of expected cash flows below which the company should abandon the project, calculate the equivalent annual cash flows the project must earn to equal the after-tax salvage value. We will solve for C2, the revised cash flow beginning in year 2. So, the revised annual cash flow below which it makes sense to abandon the project is: After-tax salvage value = C2(PVIFA14%,5) AED50,000,000 = C2(PVIFA14%,5) C2 = AED50,000,000 / PVIFA14%,5 C2 = AED14,564.177 23. a. The NPV of the project is the sum of the present value of the cash flows generated by the project. The annual cash flow for the project is the number of units sold times the cash flow per unit, which is: Annual cash flow = 10(£300,000) Annual cash flow = £3,000,000 The cash flows from this project are an annuity, so the NPV is: NPV = –£10,000,000 + £3,000,000(PVIFA25%,5) NPV = –£1,932,160.00 b. The company will abandon the project if unit sales are not revised upward. If the unit sales are revised upward, the after-tax cash flows for the project over the last four years will be: New annual cash flow = 20(£300,000) New annual cash flow = £6,000,000 The NPV of the project will be the initial cost, plus the expected cash flow in year one based on 10 unit sales projection, plus the expected value of abandonment, plus the expected value of expansion. We need to remember that the abandonment value occurs in year 1, and the present value of the expansion cash flows are in year one, so each of these must be discounted back to today. So, the project NPV under the abandonment or expansion scenario is: NPV = –£10,000,000 + £3,000,000 / 1.25 + .50(£5,000,000) / 1.25 + [.50(£6,000,000)(PVIFA25%,4)] / 1.25 NPV = £67,840.00 24. Irrespective of the scenario, the initial investment is €1,500,000. Thus, the depreciation schedule is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 €1,500,000 €300,000 €300,000 €1,200,000 2 €1,200,000 €240,000 €540,000 €960,000 3 €960,000 €192,000 €732,000 €768,000 4 €768,000 €153,600 €885,600 €614,400 5 €614,400 €614,400 €1,500,000 €0 Under the pessimistic scenario, the annual sales is 24,200 units (= market size * market share). The NPV is as follows: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 24,200 €115.00 €72 €850,000 40% 1 24,200 €2,783,000 €1,742,400 €850,000 €300,000 -€109,400 -€43,760 -€65,640 2 24,200 €2,783,000 €1,742,400 €850,000 €240,000 -€49,400 -€19,760 -€29,640 3 24,200 €2,783,000 €1,742,400 €850,000 €192,000 -€1,400 -€560 -€840 4 24,200 €2,783,000 €1,742,400 €850,000 €153,600 €37,000 €14,800 €22,200 5 24,200 €2,783,000 €1,742,400 €850,000 €614,400 -€423,800 -€169,520 -€254,280 Year Net Income Depreciation Operating Cash Flow 1 -£65,640 £300,000 £234,360 2 -£29,640 £240,000 £210,360 3 -£840 £192,000 £191,160 4 £22,200 £153,600 £175,800 5 -£254,280 £614,400 £360,120 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£1,500,000 -£1,500,000 -£1,500,000 1 £234,360 £234,360 £207,398 2 £210,360 £210,360 £164,743 3 £191,160 £191,160 £132,483 4 £175,800 £175,800 £107,821 5 £360,120 £360,120 £195,459 NPV = -£692,095 Expected Scenario: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 30,000 €120.00 €70 €800,000 40% 1 30,000 €3,600,000 €2,100,000 €800,000 €300,000 €400,000 €160,000 €240,000 2 30,000 €3,600,000 €2,100,000 €800,000 €240,000 €460,000 €184,000 €276,000 3 30,000 €3,600,000 €2,100,000 €800,000 €192,000 €508,000 €203,200 €304,800 4 30,000 €3,600,000 €2,100,000 €800,000 €153,600 €546,400 €218,560 €327,840 5 30,000 €3,600,000 €2,100,000 €800,000 €614,400 €85,600 €34,240 €51,360 Year Net Income Depreciation Operating Cash Flow 1 £240,000 £300,000 £540,000 2 £276,000 £240,000 £516,000 3 £304,800 £192,000 £496,800 4 £327,840 £153,600 £481,440 5 £51,360 £614,400 £665,760 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£1,500,000 -£1,500,000 -£1,500,000 1 £540,000 £540,000 £477,876 2 £516,000 £516,000 £404,104 3 £496,800 £496,800 £344,307 4 £481,440 £481,440 £295,276 5 £665,760 £665,760 £361,348 NPV = £382,911 Optimistic Scenario: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 35,100 €125.00 €68 €750,000 40% 1 35,100 €4,387,500 €2,386,800 €750,000 €300,000 €950,700 €380,280 €570,420 2 35,100 €4,387,500 €2,386,800 €750,000 €240,000 €1,010,700 €404,280 €606,420 3 35,100 €4,387,500 €2,386,800 €750,000 €192,000 €1,058,700 €423,480 €635,220 4 35,100 €4,387,500 €2,386,800 €750,000 €153,600 €1,097,100 €438,840 €658,260 5 35,100 €4,387,500 €2,386,800 €750,000 €614,400 €636,300 €254,520 €381,780 Year Net Income Depreciation Operating Cash Flow 1 £570,420 £300,000 £870,420 2 £606,420 £240,000 £846,420 3 £635,220 £192,000 £827,220 4 £658,260 £153,600 £811,860 5 £381,780 £614,400 £996,180 Year Investment OCF Net Cash Flow PV Cash Flows 0 -£1,500,000 -£1,500,000 -£1,500,000 1 £870,420 £870,420 £770,283 2 £846,420 £846,420 £662,871 3 £827,220 £827,220 £573,305 4 £811,860 £811,860 £497,929 5 £996,180 £996,180 £540,687 NPV = £1,545,075 The NPV under the pessimistic scenario is negative, but the company should probably accept the project. 25. This question is designed to get students to think about how they would carry out a capital budgeting analysis in practice. As such, they should be encourage to explore the different issues themselves. There is no one correct solution here and students to should come up with different approaches to the capital budgeting process. 26. With reducing balances, we must calculate the depreciation schedule. (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b)) 1 €1,500,000 €300,000 €300,000 €1,200,000 2 €1,200,000 €240,000 €540,000 €960,000 3 €960,000 €192,000 €732,000 €768,000 4 €768,000 €153,600 €885,600 €614,400 5 €614,400 -€185,600 €700,000 €800,000 The Cash Flow Analysis now follows. Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 40,000 €230.00 €210 €600,000 32% 1 40,000 €9,200,000 €8,400,000 €600,000 €300,000 -€100,000 -€32,000 -€68,000 2 40,000 €9,200,000 €8,400,000 €600,000 €240,000 -€40,000 -€12,800 -€27,200 3 40,000 €9,200,000 €8,400,000 €600,000 €192,000 €8,000 €2,560 €5,440 4 40,000 €9,200,000 €8,400,000 €600,000 €153,600 €46,400 €14,848 €31,552 5 40,000 €9,200,000 €8,400,000 €600,000 -€185,600 €385,600 €123,392 €262,208 Year Net Income Depreciation Operating Cash Flow 1 -€68,000 €300,000 €232,000 2 -€27,200 €240,000 €212,800 3 €5,440 €192,000 €197,440 4 €31,552 €153,600 €185,152 5 €262,208 -€185,600 €76,608 The Total Operating Cash Flow is £904,000. The annual Operating Cash Flows are given in the table above. The NPV is given below: Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€1,500,000 -€450,000 -€1,950,000 -€1,950,000 1 €232,000 €232,000 €205,310 2 €212,800 €212,800 €166,654 3 €197,440 €197,440 €136,836 4 €185,152 €185,152 €113,557 5 €800,000 €76,608 €450,000 €1,326,608 €720,030 NPV = -€607,614 b. In the best-case, the OCF is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 €1,275,000 €255,000 €255,000 €1,020,000 2 €1,020,000 €204,000 €459,000 €816,000 3 €816,000 €163,200 €622,200 €652,800 4 €652,800 €130,560 €752,760 €522,240 5 €522,240 -€397,760 €355,000 €920,000 Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 40,000 €253.00 €210 €600,000 32% 1 40,000 €10,120,000 €8,400,000 €600,000 €255,000 €865,000 €276,800 €588,200 2 40,000 €10,120,000 €8,400,000 €600,000 €204,000 €916,000 €293,120 €622,880 3 40,000 €10,120,000 €8,400,000 €600,000 €163,200 €956,800 €306,176 €650,624 4 40,000 €10,120,000 €8,400,000 €600,000 €130,560 €989,440 €316,621 €672,819 5 40,000 €10,120,000 €8,400,000 €600,000 -€397,760 €1,517,760 €485,683 €1,032,077 Year Net Income Depreciation Operating Cash Flow 1 €588,200 €255,000 €843,200 2 €622,880 €204,000 €826,880 3 €650,624 €163,200 €813,824 4 €672,819 €130,560 €803,379 5 €1,032,077 -€397,760 €634,317 Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€1,275,000 -€427,500 -€1,702,500 -€1,702,500 1 €843,200 €843,200 €746,195 2 €826,880 €826,880 €647,568 3 €813,824 €813,824 €564,021 4 €803,379 €803,379 €492,728 5 €920,000 €634,317 €427,500 €1,981,817 €1,075,651 NPV = €1,823,662. The worst-case OCF is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 €1,725,000 €345,000 €345,000 €1,380,000 2 €1,380,000 €276,000 €621,000 €1,104,000 3 €1,104,000 €220,800 €841,800 €883,200 4 €883,200 €176,640 €1,018,440 €706,560 5 €706,560 €26,560 €1,045,000 €680,000 Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 40,000 €207.00 €210 €600,000 32% 1 40,000 €8,280,000 €8,400,000 €600,000 €345,000 - €1,065,000 - €340,800 -€724,200 2 40,000 €8,280,000 €8,400,000 €600,000 €276,000 -€996,000 - €318,720 -€677,280 3 40,000 €8,280,000 €8,400,000 €600,000 €220,800 -€940,800 - €301,056 -€639,744 4 40,000 €8,280,000 €8,400,000 €600,000 €176,640 -€896,640 - €286,925 -€609,715 5 40,000 €8,280,000 €8,400,000 €600,000 €26,560 -€746,560 - €238,899 -€507,661 Year Net Income Depreciation Operating Cash Flow 1 -€724,200 €345,000 -€379,200 2 -€677,280 €276,000 -€401,280 3 -€639,744 €220,800 -€418,944 4 -€609,715 €176,640 -€433,075 5 -€507,661 €26,560 -€481,101 Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€1,725,000 -€472,500 -€2,197,500 -€2,197,500 1 -€379,200 -€379,200 -€335,575 2 -€401,280 -€401,280 -€314,261 3 -€418,944 -€418,944 -€290,349 4 -€433,075 -€433,075 -€265,613 5 €680,000 -€481,101 €472,500 €671,399 €364,409 NPV = -€3,038,890 27. To calculate the sensitivity to changes in quantity sold, we will choose a quantity of 41,000. The OCF at this level of sale is: Sales Revenues Variable Costs Fixed Costs Depreciation 20% EBT Tax Net Income 41,000 €230.00 €210 €600,000 32% 1 41,000 €9,430,000 €8,610,000 €600,000 €300,000 -€80,000 -€25,600 -€54,400 2 41,000 €9,430,000 €8,610,000 €600,000 €240,000 -€20,000 -€6,400 -€13,600 3 41,000 €9,430,000 €8,610,000 €600,000 €192,000 €28,000 €8,960 €19,040 4 41,000 €9,430,000 €8,610,000 €600,000 €153,600 €66,400 €21,248 €45,152 5 41,000 €9,430,000 €8,610,000 €600,000 -€185,600 €405,600 €129,792 €275,808 Year Net Income Depreciation Operating Cash Flow 1 -€54,400 €300,000 €245,600 2 -€13,600 €240,000 €226,400 3 €19,040 €192,000 €211,040 4 €45,152 €153,600 €198,752 5 €275,808 -€185,600 €90,208 Total operating cash flow is €972,000 The sensitivity of changes in the OCF to quantity sold is: OCF/Q = (€972,000 – 904,000)/(41,000 – 40,000) OCF/Q = +€68 The NPV at this level of sales is: Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€1,500,000 -€450,000 -€1,950,000 -€1,950,000 1 €245,600 €245,600 €217,345 2 €226,400 €226,400 €177,304 3 €211,040 €211,040 €146,261 4 €198,752 €198,752 €121,898 5 €800,000 €90,208 €450,000 €1,340,208 €727,411 NPV = -€559,780 And the sensitivity of NPV to changes in the quantity sold is: NPV/Q = (–€559,780 – (–607,614))/(41,000 – 40,000) NPV/Q = +€47.83 You wouldn’t want the quantity to fall below the point where the NPV is zero. We know the NPV changes €43.61 for every unit sale, so we can divide the NPV for 40,000 units by the sensitivity to get a change in quantity. Doing so, we get: –€607,614 = €47.83(Q) Q = –12,703 For a zero NPV, we need to increase sales by 12,703 units, so the minimum quantity is: QMin = 40,000 + 12,703 QMin = 52,703 units 28. a. We first have to determine the depreciation schedule. (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 € 10,000,000 € 2,000,000 € 2,000,000 € 8,000,000 2 € 8,000,000 € 1,600,000 € 3,600,000 € 6,400,000 3 € 6,400,000 € 1,280,000 € 4,880,000 € 5,120,000 4 € 5,120,000 € 5,120,000 € 10,000,000 € - Now calculate the operating cash flow: Revenues Operating Costs Depreciation 20% EBT Tax Net Income € 8,000,000 € 2,000,000 34% 1 € 8,000,000 € 2,000,000 € 2,000,000 € 4,000,000 € 1,360,000 € 2,640,000 2 € 8,000,000 € 2,000,000 € 1,600,000 € 4,400,000 € 1,496,000 € 2,904,000 3 € 8,000,000 € 2,000,000 € 1,280,000 € 4,720,000 € 1,604,800 € 3,115,200 4 € 8,000,000 € 2,000,000 € - € 5,120,000 € 880,000 € 299,200 Year Net Income Depreciation Operating Cash Flow 1 € 2,640,000 € 2,000,000 € 4,640,000 2 € 2,904,000 € 1,600,000 € 4,504,000 3 € 3,115,200 € 1,280,000 € 4,395,200 4 € 580,800 € 5,120,000 € 5,700,800 Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€ 10,000,000 -€ 3,000,000 -€ 13,000,000 -€ 13,000,000 1 € 4,640,000 € 4,640,000 € 3,965,812 2 € 4,504,000 € 4,504,000 € 3,290,233 3 € 4,395,200 € 4,395,200 € 2,744,233 4 € - € 5,700,800 € 3,000,000 € 8,700,800 € 4,643,182 NPV = £1,643,461 Three Year Project (Abandon in Year 3) (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 € 10,000,000 € 2,000,000 € 2,000,000 € 8,000,000 2 € 8,000,000 € 1,600,000 € 3,600,000 € 6,400,000 3 € 6,400,000 € 3,400,000 € 7,000,000 € 3,000,000 Revenues Operating Costs Fixed Costs Depreciation 20% EBT Tax Net Income £8,000,000 £2,000,000 34% £8,000,000 1 £8,000,000 £2,000,000 £2,000,000 £4,000,000 £1,360,000 £2,640,000 £8,000,000 2 £8,000,000 £2,000,000 £1,600,000 £4,400,000 £1,496,000 £2,904,000 £8,000,000 3 £8,000,000 £2,000,000 £3,400,000 £2,600,000 £884,000 £1,716,000 £8,000,000 Year Net Income Depreciation Operating Cash Flow 1 € 2,640,000 € 2,000,000 € 4,640,000 2 € 2,904,000 € 1,600,000 € 4,504,000 3 € 1,716,000 € 3,400,000 € 5,116,000 Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€ 10,000,000 -€ 3,000,000 -€ 13,000,000 -€ 13,000,000 1 € 4,640,000 € 4,640,000 € 3,965,812 2 € 4,504,000 € 4,504,000 € 3,290,233 3 € 3,000,000 € 5,116,000 € 3,000,000 € 11,116,000 € 6,940,503 NPV = €1,196,548. Two Year Project (Abandon in Year 2) (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 € 10,000,000 € 2,000,000 € 2,000,000 € 8,000,000 2 € 8,000,000 € 2,000,000 € 4,000,000 € 6,000,000 Revenues Operating Costs Fixed Costs Depreciation 20% EBT Tax Net Income € 8,000,000 € 2,000,000 € 0 € 8,000,000 1 € 8,000,000 € 2,000,000 € 2,000,000 € 4,000,000 € 1,360,000 € 2,640,000 € 8,000,000 2 € 8,000,000 € 2,000,000 € 2,000,000 € 4,000,000 € 1,360,000 € 2,640,000 € 8,000,000 Year Net Income Depreciation Operating Cash Flow 1 € 2,640,000 € 2,000,000 € 4,640,000 2 € 2,640,000 € 2,000,000 € 4,640,000 Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€ 10,000,000 -€ 2,000,000 -€ 12,000,000 -€ 12,000,000 1 € 4,640,000 € 4,640,000 € 3,965,812 2 € 6,000,000 € 4,640,000 € 2,000,000 € 12,640,000 € 9,233,691 NPV = £1,199,503 One Year Project (Abandon in Year 1) (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 € 10,000,000 € 3,500,000 € 3,500,000 € 6,500,000 Revenues Operating Costs Fixed Costs Depreciation 20% EBT Tax Net Income £8,000,000 £2,000,000 34% 1 € 8,000,000 € 2,000,000 € 3,500,000 € 2,500,000 € 850,000 € 1,650,000 € 5,150,000 Year Net Income Depreciation Operating Cash Flow 1 € 1,650,000 € 3,500,000 € 5,150,000 Year Investment OCF NWC Net Cash Flow PV Cash Flows 0 -€ 10,000,000 -€ 2,000,000 -€ 12,000,000 -€ 12,000,000 1 € 6,500,000 € 5,150,000 € 2,000,000 € 13,650,000 € 11,666,667 NPV = -€333,333 It is optimal to abandon the project in year 4 since the project has the maximum NPV at this time. 29. a. The NPV of the project is sum of the present value of the cash flows generated by the project. The cash flows from this project are an annuity, so the NPV is: NPV = –$9,000,000 + $1,750,000(PVIFA12%,10) NPV = $887,890.30 b. The company will abandon the project if value of abandoning the project is greater than the value of the future cash flows. The present value of the future cash flows if the company revises it sales downward will be: PV of downward revision = $520,000(PVIFA12%,9) PV of downward revision = $2,770,689 Since this is more than the value of abandoning the project, the company should not abandon in one year. 30. You will need to Solver in a spreadsheet to solve this problem. First, determine the cash flow from selling the old harvester. When calculating the salvage value, remember that tax liabilities or credits are generated on the difference between the resale value and the book value of the asset. Using the original purchase price of the old harvester to determine annual depreciation, the depreciation schedule for the old harvester is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 €45,000 €9,000 €9,000 €36,000 2 €36,000 €7,200 €16,200 €28,800 3 €28,800 €5,760 €21,960 €23,040 4 €23,040 €4,608 €26,568 €18,432 5 €18,432 -€1,568 €25,000 €20,000 Since the resale value of the old harvester is greater than the book value, there will be a tax liability of €1,568. After-tax salvage value = Market value + tC(Book value – Market value) After-tax salvage value = €20,000 + .34(-€1,568) After-tax salvage value = €19,467 Next, we need to calculate the incremental depreciation. We need to calculate depreciation tax shield generated by the new harvester less the forgone depreciation tax shield from the old harvester. Let P be the break-even purchase price of the new harvester. To put the spreadsheet together, assume for now that P = €45,000. This will be the input figure in the Solver algorithm. So, we find: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 €45,000 €9,000 €9,000 €36,000 2 €36,000 €7,200 €16,200 €28,800 3 €28,800 €5,760 €21,960 €23,040 4 €23,040 €4,608 €26,568 €18,432 5 €18,432 €3,686 €30,254 €14,746 6 €14,746 €2,949 €33,204 €11,796 7 €11,796 €2,359 €35,563 €9,437 8 €9,437 €1,887 €37,450 €7,550 9 €7,550 €1,510 €38,960 €6,040 10 €6,040 €1,208 €40,168 €4,832 And the depreciation tax shield on the old harvester is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) -4 €45,000 €9,000 €9,000 €36,000 -3 €36,000 €7,200 €16,200 €28,800 -2 €28,800 €5,760 €21,960 €23,040 -1 €23,040 €4,608 €26,568 €18,432 0 €18,432 €3,686 €30,254 €14,746 1 €14,746 €2,949 €33,204 €11,796 2 €11,796 €2,359 €35,563 €9,437 3 €9,437 €1,887 €37,450 €7,550 4 €7,550 €1,510 €38,960 €6,040 5 €6,040 €1,208 €40,168 €4,832 6 €4,832 €966 €41,135 €3,865 7 €3,865 €773 €41,908 €3,092 8 €3,092 €618 €42,526 €2,474 9 €2,474 €495 €43,021 €1,979 10 €1,979 €396 €43,417 €1,583 So, the incremental depreciation tax, which is the depreciation tax shield from the new harvester, minus the depreciation tax shield from the old harvester, is: Year Depreciation New Depreciation Old Incremental Depreciation 1 €9,000 €2,949 €6,051 2 €7,200 €2,359 €4,841 3 €5,760 €1,887 €3,873 4 €4,608 €1,510 €3,098 5 €3,686 €1,208 €2,478 6 €2,949 €966 €1,983 7 €2,359 €773 €1,586 8 €1,887 €618 €1,269 9 €1,510 €495 €1,015 10 €1,208 €396 €812 We can now carry out the cash flow analysis. Operating Costs Incremental Depreciation EBT Tax Net Income Operating Cash Flow €10,000 34% 1 €10,000 €6,051 €3,949 €1,343 €2,606 €8,657 2 €10,000 €4,841 €5,159 €1,754 €3,405 €8,246 3 €10,000 €3,873 €6,127 €2,083 €4,044 €7,917 4 €10,000 €3,098 €6,902 €2,347 €4,555 €7,653 5 €10,000 €2,478 €7,522 €2,557 €4,964 €7,443 6 €10,000 €1,983 €8,017 €2,726 €5,291 €7,274 7 €10,000 €1,586 €8,414 €2,861 €5,553 €7,139 8 €10,000 €1,269 €8,731 €2,969 €5,762 €7,031 9 €10,000 €1,015 €8,985 €3,055 €5,930 €6,945 10 €10,000 €812 €9,188 €3,124 €6,064 €6,876 Investment OCF Net Cash Flow PV Cash Flows 0 -€25,533 -€25,533 -€25,533 1 €8,657 €8,657 €7,528 2 €8,246 €8,246 €6,235 3 €7,917 €7,917 €5,205 4 €7,653 €7,653 €4,376 5 €7,443 €7,443 €3,700 6 €7,274 €7,274 €3,145 7 €7,139 €7,139 €2,684 8 €7,031 €7,031 €2,299 9 €6,945 €6,945 €1,974 10 €4,832 €6,876 €11,708 €2,894 Notice that we used the value of the new machine + the after tax salvage value of the old machine as the initial investment (-€45,000+€19,467). NPV = €14,507 If the spreadsheet is set up properly, you should now use Solver to find the breakeven purchase price. The value that Solver arrives at is €63,496. The full spreadsheet is given below: Depreciation Schedule: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(b) 1 €63,496 €12,699 €12,699 €50,797 2 €50,797 €10,159 €22,859 €40,638 3 €40,638 €8,128 €30,986 €32,510 4 €32,510 €6,502 €37,488 €26,008 5 €26,008 €5,202 €42,690 €20,806 6 €20,806 €4,161 €46,851 €16,645 7 €16,645 €3,329 €50,180 €13,316 8 €13,316 €2,663 €52,843 €10,653 9 €10,653 €2,131 €54,974 €8,522 10 €8,522 €1,704 €56,678 €6,818 Incremental Depreciation: Year Depreciation New Depreciation Old Incremental Depreciation 1 €12,699 €2,949 €9,750 2 €10,159 €2,359 €7,800 3 €8,128 €1,887 €6,240 4 €6,502 €1,510 €4,992 5 €5,202 €1,208 €3,994 6 €4,161 €966 €3,195 7 €3,329 €773 €2,556 8 €2,663 €618 €2,045 9 €2,131 €495 €1,636 10 €1,704 €396 €1,309 Operating Cash Flow: Operating Costs Incremental Depreciation EBT Tax Net Income Operating Cash Flow €10,000 34% 1 €10,000 €9,750 €250 €85 €165 €9,915 2 €10,000 €7,800 €2,200 €748 €1,452 €9,252 3 €10,000 €6,240 €3,760 €1,278 €2,482 €8,722 4 €10,000 €4,992 €5,008 €1,703 €3,305 €8,297 5 €10,000 €3,994 €6,006 €2,042 €3,964 €7,958 6 €10,000 €3,195 €6,805 €2,314 €4,491 €7,686 7 €10,000 €2,556 €7,444 €2,531 €4,913 €7,469 8 €10,000 €2,045 €7,955 €2,705 €5,250 €7,295 9 €10,000 €1,636 €8,364 €2,844 €5,520 €7,156 10 €10,000 €1,309 €8,691 €2,955 €5,736 €7,045 Cash Flow Analysis: Investment OCF Net Cash Flow PV Cash Flows 0 -€44,029 -€44,029 -€44,029 1 €9,915 €9,915 €8,622 2 €9,252 €9,252 €6,996 3 €8,722 €8,722 €5,735 4 €8,297 €8,297 €4,744 5 €7,958 €7,958 €3,956 6 €7,686 €7,686 €3,323 7 €7,469 €7,469 €2,808 8 €7,295 €7,295 €2,385 9 €7,156 €7,156 €2,034 10 €6,818 €7,045 €13,863 €3,427 31. Since Unmondo does not pay taxes, depreciation is not relevant. This makes the analysis somewhat simpler. We can go straight to calculating operational cash flows. Pessimistic Scenario Sales Cost Savings PV Cost Savings 400,000 € 2 1 400,000 €800,000 €714,286 2 400,000 €800,000 €637,755 3 400,000 €800,000 €569,424 4 400,000 €800,000 €508,414 5 400,000 €800,000 €453,941 6 400,000 €800,000 €405,305 7 400,000 €800,000 €361,879 NPV = -€9,000,000+€3,651,005 = -€5,348,995. Expected Scenario Sales Cost Savings PV Cost Savings 500,000 € 4 1 500,000 €2,000,000 €1,785,714 2 500,000 €2,000,000 €1,594,388 3 500,000 €2,000,000 €1,423,560 4 500,000 €2,000,000 €1,271,036 5 500,000 €2,000,000 €1,134,854 6 500,000 €2,000,000 €1,013,262 7 500,000 €2,000,000 €904,698 8 500,000 €2,000,000 €807,766 9 500,000 €2,000,000 €721,220 10 500,000 €2,000,000 €643,946 NPV = -€9,000,000+€11,300,446 = €2,300,446. Optimistic Scenario Sales Cost Savings PV Cost Savings 600,000 € 5 1 600,000 €3,000,000 €2,678,571 2 600,000 €3,000,000 €2,391,582 3 600,000 €3,000,000 €2,135,341 4 600,000 €3,000,000 €1,906,554 5 600,000 €3,000,000 €1,702,281 6 600,000 €3,000,000 €1,519,893 7 600,000 €3,000,000 €1,357,048 8 600,000 €3,000,000 €1,211,650 9 600,000 €3,000,000 €1,081,830 10 600,000 €3,000,000 €965,920 11 600,000 €3,000,000 €862,428 12 600,000 €3,000,000 €770,025 13 600,000 €3,000,000 €687,523 NPV = -€9,000,000+€19,270,645 = €10,270,645. b. Given that the cost of market research is low compared to the net present value of all three scenarios, you should undertake it before starting the project. 32. The gold price can go up or down. At t=1, the price is 50% likely to be $2,100 and 50% likely to be $1,900. In year two, t=2, the price is likely to be $2,200, $2,000, or $1,800. In year three, the price will be $2,300, $2,100, $1,900, or $1,700. t=0 t=1 t=2 t=3 $2,300 $2,200 $2,100 $2,100 $2,000 $2,000 $1,900 $1,900 $1,800 $1,700 The net cash flow per ounce at each node is t=0 t=1 t=2 t=3 =($2,300-920) = $1,380 = ($2,200 – 920) = $1,280 =($2,100-920) = $1,180 =($2,100-920) = $1,180 =($2,000 – 920) =$1,080 = ($2,000 – 920) = $1,080 =($1,900-920) = $980 = ($1,900 – 920) = $980 =($1,800-920) = $880 = ($1,700 – 920) = $780 Start from t = 3 and work back. t=0 t=1 t=2 =1000*$1,280 + [1000*($1,380*0.5 + $1,180*0.5)]/1.14 $1,180 =$5,614,035 $1,080 =1000*$1,080+[1000*($1,180*0.5+$980*0.5)]/1.14 =$4,736,842 $980 =1000*$880+[1000*($980*0.5+$780*0.5)]/1.14 =$3,859,649 t=0 t=1 =1000*$1,180+[$5,614,035*0.5+$4,736,842*0.5]/1.14 = $19,194,521 $1,080 =1000*$980+[$4,736,842*0.5 + $3,859,649*0.5]/1.14 = $16,116,651 t=0 =1000*$1,080+[$19,194,521*0.5 + $16,116,651*0.5]/1.14 =$62,896,793 If you open the mine now, the NPV will be NPVt=0 = -$800,000 + $62,896,793 = $62,096,793 Since the mine has a positive NPV now, you should start the project immediately. 33. We will deal with the good scenario first. The depreciation schedule of the investment asset is: (a) (b) (c) (d) Year Starting Value Depreciation 20% Accumulated Depreciation Residual Value 20% (a)-(c) 1 £6,000,000 £1,200,000 £1,200,000 £4,800,000 2 £4,800,000 £960,000 £2,160,000 £3,840,000 3 £3,840,000 £768,000 £2,928,000 £3,072,000 4 £3,072,000 £614,400 £3,542,400 £2,457,600 5 £2,457,600 £491,520 £4,033,920 £1,966,080 6 £1,966,080 £393,216 £4,427,136 £1,572,864 7 £1,572,864 £314,573 £4,741,709 £1,258,291 8 £1,258,291 £251,658 £4,993,367 £1,006,633 9 £1,006,633 £201,327 £5,194,694 £805,306 10 £805,306 £805,306 £6,000,000 £0 The Net Income in this scenario is given below: Year Sales Revenues Variable Costs EBT Tax Net Income 50000 £60 £30 28% 1 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 2 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 3 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 4 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 5 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 6 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 7 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 8 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 9 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 10 50000 £3,000,000 £1,500,000 £1,500,000 £420,000 £1,080,000 The NPV is then: Year Investment Operating Cash Flows Net Cash Flows PV Cash Flows 0 -£6,000,000 -£6,000,000 -6000000 1 £1,080,000 £1,080,000 964285.7143 2 £1,080,000 £1,080,000 860969.3878 3 £1,080,000 £1,080,000 768722.6676 4 £1,080,000 £1,080,000 686359.5247 5 £1,080,000 £1,080,000 612821.0042 6 £1,080,000 £1,080,000 547161.6109 7 £1,080,000 £1,080,000 488537.1526 8 £1,080,000 £1,080,000 436193.8862 9 £1,080,000 £1,080,000 389458.827 10 £0 £1,080,000 £1,080,000 347731.0955 NPV = £102,240.87 Scenario Bad: Operating Cash Flows are: Year Sales Revenues Variable Costs EBT Tax Net Income 30000 £55 £30 28% 1 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 2 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 3 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 4 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 5 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 6 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 7 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 8 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 9 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 10 30000 £1,650,000 £900,000 £750,000 £210,000 £540,000 NPV is: Year Investment Operating Cash Flows Net Cash Flows PV Cash Flows 0 -£6,000,000 -£6,000,000 -6000000 1 £540,000 £540,000 482142.8571 2 £540,000 £540,000 430484.6939 3 £540,000 £540,000 384361.3338 4 £540,000 £540,000 343179.7623 5 £540,000 £540,000 306410.5021 6 £540,000 £540,000 273580.8054 7 £540,000 £540,000 244268.5763 8 £540,000 £540,000 218096.9431 9 £540,000 £540,000 194729.4135 10 £0 £540,000 £540,000 173865.5478 NPV = -£2,948,879 If each scenario is equally likely, the expected net present value is NPV = (£102,240 + -£2,948,879)/0.5 = -£1,423,319. b. If the bad scenario occurs the present value of the remaining cash flows are PV = £540,000*PVIFA(10%,9) = £3,109,872.86 If Grace and Danger can sell off the equipment for £5.4 million, it would be preferable to do so. c. If the good scenario occurs, Grace and Danger can increase production by another 25,000 units. The value of this option to expand is determined by finding the NPV of the expanded run and then discounting it back to time 0. Remember that the decision is only made when the company finds out that the product has been a success, which is in year one. This means that the expansion takes place from year 2. Operating cash flow is: Year Sales Revenues Variable Costs EBT Tax Net Income 25000 £60 £35 28% 2 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 3 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 4 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 5 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 6 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 7 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 8 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 9 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 10 25000 £1,500,000 £875,000 £625,000 £175,000 £450,000 The Value of this option to expand at time 1 is: PV1= £450000*PVIFA(10%,9) = £2,591,561. Discounted back to time zero, the PV is £2,355,964. Given that there is only a 50% chance of the good scenario occurring, the value of the option to expand is 0.5 * £2,355,964 = £1,177,982. Solution Manual for Corporate Finance David Hillier, Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Bradford Jordan 9780077139148