QUESTION
Question1
Petty Pasties Limited expects to earn $0.350 per share this year, up from $0.305 last year. Petty Pasties has announced that 55% of earnings will be retained for reinvestment and the balance will be distributed as a dividend to shareholders. Petty Pasties expects to earn an after tax return of 15% on any funds that it retains. Shareholders in the company require a 10% return on their investment. What is the fair value of the share price of the firm?
Question 2
The accountants of Belligerent Limited are analysing the viability of a proposed new division. They estimate that this project will have a life of four years before the market is swamped by the lifting of a patent they hold over the product that will be manufactured by the division. The accounting revenues of the division for each year are as follows:
| Year |
1 |
2 |
3 |
4 |
| Revenue |
$1.5m |
$2.0m |
$2.5m |
$3.0m |
All sales are made on three months credit and there are no bad debts. The costs of production, which are assumed paid on the last day of the year, are as follows:
| Year |
1 |
2 |
3 |
4 |
| Revenue |
$0.75m |
$1.0m |
$1.25m |
$1.5m |
At the start of the project an investment of $1 million will be required in equipment, which will be depreciated straight-line to a zero book value over the life of the project. It is anticipated that the equipment may be sold for scrap value of $100,000 at the end of year four. A cash float of $500,000 will be required at the start of the project to support temporary imbalances in cash flows, and inventory is expected to increase by $300,000 at the start of the project. These are both recoverable at the end of the life of the project. A $1 million invoice has been received for a scientific study on the technology associated with the proposed project and while it will be paid at commencement of the project, the accountants expect to expense this in equal amounts over the four year life of the project. Head office costs to be apportioned to the project amount to $500,000 per year although there is no evidence that head office costs are affected by the project.
The required rate of return on the project is 10% after-tax. The tax rate is 30% and there is no deferral of tax payments. Inflation is expected to be zero and the company is generating profits from other businesses.
Required
Calculate the net present value of the proposed project. Should the project be accepted? Why?
Question 3
Frosty Fridges has recently completed a $400,000 market evaluation study and product prototype. Based on this information, Frosty has estimated that 10,000 of its new cold rooms could be sold annually over the next 8 years at a price of $9,615 each. Subcontractors would assemble and install the cold rooms at a cost per installation of $7,550. Fixed costs to be incurred in making the new product would be $12 million per year, plus $1 million per year of allocated overhead.
Start-up costs include $40 million to build the production facilities on an existing parcel of land valued at $2.5 million. The production facilities would be completely financed by bank debt (interest only for 8 years) at the rate of 8.75%. The loan would be repaid in full by Frosty at the end of the project. The production facilities would be depreciated straight-line over the life of the project, after which the facilities (including the land) would be sold for $8.4 million. The value of the land is not expected to change.
Frosty would also incur fully-deductible expenses of $1.4 million at the commencement of the project (year zero). Frosty is a profitable company and pays tax at the rate of 30% on all profits and capital gains.
Taxes are paid in the year in which they are incurred. Frosty uses a 10% discount rate on all new projects.
(a) Should Frosty produce the cold rooms? Why?
(b) Calculate the minimum sales price for each cold room if the bank debt could be obtained at 7.5% p.a. interest only for the term of the loan.
(c) Ignoring (b) above, calculate the minimum sales price for each cold room if depreciation was calculated using the reducing-balance method for tax purposes at a rate of 35% p.a.?
Question 4
Maurice Madagascar, the CEO of Werde Incorporated, is considering an investment of $420,000 in a machine that has a 7-year life and no salvage value. The machine is depreciated by a straight-line method with a zero salvage value over the seven years. The appropriate discount rate for cash flows of the project is 18%, and the corporate tax rate for the company is 30%. Following are details for the project under various scenarios, which are expected to occur with equal probability.
|
Pessimistic |
Base Case |
Optimistic |
|
| Unit sales per annum |
23,000 |
25,000 |
27,000 |
| Price per unit |
$38 |
$40 |
$42 |
| Variable costs per unit |
$21 |
$20 |
$19 |
| Fixed costs per annum |
$320,000 |
$300,000 |
$280,000 |
(a) What is your conclusion about the project?
(b) Suppose that the CFO of Werde is more conservative and believes that the pessimistic scenario has a 50% probability of occurrence, while the optimistic scenario only has a 10% probability of occurrence. Discuss the viability of the project under these conditions.
Question 5
Buttle Limited is considering buying CRM software so that it can more effectively deal with its wholesale customers. The software package costs $750,000 today and will be depreciated to a zero book value using the straight-line method over its five-year economic life. The marketing department predicts that sales will be $600,000 per year for the next three years, after which Buttle will exit this sector of the market. Cost of goods sold and operating expenses (pre depreciation) are predicted to be 25% of sales. After three years the software can be sold for $40,000. Buttle also needs to add working capital of $30,000 to support the project, which is fully recoverable. The company tax rate for Buttle is 30% and the required rate of return is 18% (after-tax).
(a) What is the NPV of the new software, assuming zero inflation?
(b) Suppose instead inflationary expectations are 4% per year, and that this is included in thediscount rate but not the forecasts. What is the NPV of the project under these assumptions?
Question 6
Malley Markets must decide when to replace a major item of equipment, which requires increasing amounts of maintenance each year. The resale value of the equipment falls every year. The following table presents this data.
|
Year |
Maintenance costs |
Resale value |
|
Today |
$0 |
$90,000 |
|
1 |
$20,000 |
$85,000 |
|
2 |
$27,500 |
$77,500 |
|
3 |
$32,500 |
$70,000 |
|
4 |
$45,000 |
$60,000 |
|
5 |
$50,000 |
$50,000 |
Malley can purchase new equipment for $300,000. The new equipment will have an economic life of six years, and as a result of new technology, will require maintenance of only $2,000 at the end of each year. Malley expects to be able to sell the equipment for $120,000 at the end of six years. Assume Malley will pay no taxes, and the appropriate discount rate is 10%.
When should the company replace its current equipment?
SOLUTION
| Amounts in $ | ||||||||||||
| Ques 1 | To calculate value of share- | |||||||||||
| It is given, | ||||||||||||
| Earnings | 0.305 | |||||||||||
| Expected earnings | 0.35 | |||||||||||
| Since we are not using Gordon’s model so past earnings would not be used for trend. | ||||||||||||
| Retention ratio | 55% or 0.55 | |||||||||||
| Required rate of return | 10%or 0.10 | |||||||||||
| Return on retained earnings | 15% or 0.15 | |||||||||||
| Equity ts tax free only, so no treatment for tax. | ||||||||||||
| Now, | Return on equity =Retention ratio x return on retained earnings | |||||||||||
| = | 0.0825 | |||||||||||
| Dividend for next year = Expected earnings x dividend pay out ratio | ||||||||||||
| = | 0.1575 | |||||||||||
| And, | Value of share = Expected dividend /(Required rate of return – ROE) | |||||||||||
| = | 9 | |||||||||||
| Here, since required rate of return is greater than return on equity, single stage dividend discount model has been used. | ||||||||||||
| Value of share is $9. | ||||||||||||
| All Amounts in $ | ||||||||||||
| Ques 2 | Initial investment | (1,000,000) | ||||||||||
| cash float required | (500,000) | |||||||||||
| inventory | (300,000) | |||||||||||
| Total initial cash outflows | -1800000 | |||||||||||
| Annual cash flows | Year | 1 | 2 | 3 | 4 | |||||||
| Revenue | 1,500,000 | 2,000,000 | 2,500,000 | 3,000,000 | ||||||||
| Cost of production | (750,000) | (1,000,000) | (1,250,000) | (1,500,000) | ||||||||
| Depreciation | (250,000) | (250,000) | (250,000) | (250,000) | ||||||||
| Earnings before tax | 500,000 | 750,000 | 1,000,000 | 1,250,000 | ||||||||
| Tax @ 30% | (150,000) | (225,000) | (300,000) | (375,000) | ||||||||
| Profits after tax | 350,000 | 525,000 | 700,000 | 875,000 | ||||||||
| Add back depreciation | 250,000 | 250,000 | 250,000 | 250,000 | ||||||||
| Cash inflows | 600,000 | 775,000 | 950,000 | 1,125,000 | ||||||||
| PVF @10% | 0.90909 | 0.82645 | 0.75131 | 0.68301 | ||||||||
| PV of cash flows | 545,455 | 640,496 | 713,749 | 768,390 | 2,668,090 | |||||||
| PV of total annual cash flows | ||||||||||||
| Terminal cash flows | ||||||||||||
| Scrap value of machine | 100,000 | |||||||||||
| Book value at the end of 4 years | – | |||||||||||
| Gain on sale | 100,000 | |||||||||||
| Tax on capital gain | (30,000) | |||||||||||
| Net cash flow from scrap | 70,000 | |||||||||||
| Cash float released at the end of 4 years | 500,000 | |||||||||||
| Inventory released at the end of 4 years | 300,000 | |||||||||||
| Total terminal cash flows | 870,000 | |||||||||||
| PV of terminal cash flows | 594,222 | |||||||||||
| NPV | = | Initial cash flows+PV of annual cash flows+PV of terminal cash flows | ||||||||||
| = | 1,462,311 | |||||||||||
| Since the project is yielding a positive NPV, it is profitable to accept the project. | ||||||||||||
| Assumptions | ||||||||||||
| 1 | It has been assumed that the expense of $1million on scientific research of the technology related to the project is a sunk cost. | |||||||||||
| It has been already incurred irrespective of whether the project is accepted or not. | ||||||||||||
| 2 | Head office overheads are also not being affected by the project hence $500000 is not being considered. | |||||||||||
| Ques 3 | Initial cash flows | |||||||||||
| All amounts in $ | ||||||||||||
| Deductible expense at the start | (1,400,000) | |||||||||||
| Tax benefit @30% | 420,000 | |||||||||||
| Total cash flows | (980,000) | |||||||||||
| Annual Cash Flows | ||||||||||||
| Revenue | 96,150,000 | |||||||||||
| (No. of units soldxSale price) | ||||||||||||
| Cost of installation(@$7550 each) | (75,500,000) | |||||||||||
| Fixed cost of production p.a. | (12,000,000) | |||||||||||
| Interest on bank debt | (3,500,000) | |||||||||||
| Depreciation on production facilities | (5,000,000) | |||||||||||
| Profit before tax | 150,000 | |||||||||||
| Tax @ 30% | (45,000) | |||||||||||
| Profit after tax | 105,000 | |||||||||||
| Add back depreciation | 5000000 | |||||||||||
| Net annual Cash flow | 5,105,000 | |||||||||||
| Year | Annual cash flow | PVF@10% | PV of cash flows | |||||||||
| 1 | 5,105,000 | 0.90909 | 4,640,909 | |||||||||
| 2 | 5,105,000 | 0.82645 | 4,219,008 | |||||||||
| 3 | 5,105,000 | 0.75131 | 3,835,462 | |||||||||
| 4 | 5,105,000 | 0.68301 | 3,486,784 | |||||||||
| 5 | 5,105,000 | 0.62092 | 3,169,803 | |||||||||
| 6 | 5,105,000 | 0.56447 | 2,881,639 | |||||||||
| 7 | 5,105,000 | 0.51316 | 2,619,672 | |||||||||
| 8 | 5,105,000 | 0.46651 | 2,381,520 | |||||||||
| PV of total annual cash flows | 27,234,798 | |||||||||||
| Terminal cash flows | ||||||||||||
| Scrap value of machine | 5,900,000 | |||||||||||
| Book value of machine | – | |||||||||||
| Capital gain | 5,900,000 | |||||||||||
| Tax on capital gain@ 30% | (1,770,000) | |||||||||||
| Net cash flow from sale of machine | 4,130,000 | |||||||||||
| Repayment of loan in full | (40,000,000) | |||||||||||
| Total terminal cash flows | (35,870,000) | |||||||||||
| PV of terminal cash flows | (16,733,620) | |||||||||||
| NPV | = | Initial cash flows+Annual cash flows+Terminal cash flows | ||||||||||
| = | 9,521,179 | |||||||||||
| a) | Frosty should produce the cold rooms because the project is giving a positive NPV of $9,521,179. | |||||||||||
| b) | If the rate of interest on bank loan is 7.5% p.a. then interest on bank loan would be 3000000 p.a. | |||||||||||
| Now, | Cost of production before depreciation and tax= | Installation cost+fixed cost+interest | ||||||||||
| = | 84,500,000 | |||||||||||
| Let the unit selling price be $ Y | ||||||||||||
| Annual profit before depreciation and tax | = | 10,000xY-84,500,000 | ||||||||||
| Profit after depreciation before tax | = | 10,000Y-84,500,000-5,000,000 | ||||||||||
| = | 10,000Y-89,500,000 | |||||||||||
| Tax | = | 30%(10,000Y-89,500,000) | ||||||||||
| = | 3,000Y-26,850,000 | |||||||||||
| Annual cash flow from operation | = | 10,000Y-84,500,000-3,000Y+26,850,000 | ||||||||||
| = | 7000Y-57,650,000 | |||||||||||
| For obtaining 10% return on the project, NPV should be zero. Hence, | ||||||||||||
| (7000Y-57,650,000)xPVAF@10% for 8years+Initial cash flows+terminal cash flows = 0 | ||||||||||||
| Therefore | (7000Y-57650000)*5.33493-980000-16733620 | = | 0 | |||||||||
| 37344.51Y-307558714.5-17713620 | = | 0 | ||||||||||
| This gives us, | 37344.51Y | = | 325272334.5 | |||||||||
| Y | = | 8710.044247 | ||||||||||
| Minimum selling price for obtaining 10% rate of return when interes rate on debt is 7.5% should be $8710 | ||||||||||||
| 63700000 | ||||||||||||
| c) | If depreciation is provided @ 35% p.a. on reducing balance method then annual cost of production will change as follows | |||||||||||
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||||
| Depreciation on production facilities | (14,000,000) | (9,100,000) | (5,915,000) | (3,844,750) | (2,499,088) | (1,624,407) | (1,055,864) | (686,312) | ||||
| Tax benefit on depreciation | 4,200,000 | 2,730,000 | 1,774,500 | 1,153,425 | 749,726 | 487,322 | 316,759 | 205,894 | ||||
| PVF@10% | 0.90909 | 0.82645 | 0.75131 | 0.68301 | 0.62092 | 0.56447 | 0.51316 | 0.46651 | ||||
| PV of tax benefit | 3,818,182 | 2,256,198 | 1,333,208 | 787,805 | 465,521 | 275,081 | 162,548 | 96,051 | 9,194,593 | |||
| PV of total tax benefit from depreciation | ||||||||||||
| Let selling price be Y | ||||||||||||
| Revenue | 10000Y | |||||||||||
| Cost of installation(@$7550 each) | (75,500,000) | |||||||||||
| Fixed cost of production p.a. | (12,000,000) | |||||||||||
| Interest on bank debt | (3,500,000) | |||||||||||
| Profit before depreciation | 10000Y-91000000 | |||||||||||
| Tax @30% | 3000Y-27300000 | |||||||||||
| Profit after tax | 7000Y-63700000 | |||||||||||
| PVAF@10% for 8 years | 5.33493 | |||||||||||
| PV of profit after tax | 37344.51Y-339835041 | |||||||||||
| Add PV of total tax benefit from depreciation | 9194593.187 | |||||||||||
| PV of total annual cash flows | 37344.51Y-330640447.8 | |||||||||||
| Terminal cash flows | ||||||||||||
| Scrap value | 5,900,000 | |||||||||||
| written down value | 1,274,579 | |||||||||||
| gain on sale | 4,625,421 | |||||||||||
| tax on capital gain | 1,387,626 | |||||||||||
| Cash flow on sale of machine | 4,512,374 | |||||||||||
| Repayment of loan in full | (40,000,000) | |||||||||||
| Total terminal cash flows | (35,487,626) | |||||||||||
| PV of total terminal cash flows | (16,555,240) | |||||||||||
| For obtaining 10% return on the project, NPV should be zero. Hence, | ||||||||||||
| Initial cash flows+PV of total annual cash flows+PV of total terminal cash flows=0 | ||||||||||||
| 980000+37344.51Y-330640447.8-16555240 | = | 0 | ||||||||||
| 37344.51Y-346215688 | = | 0 | ||||||||||
| Y | = | 9270.859 | ||||||||||
| Minimum Selling price of cold unit should be $9271 for attaining a rate of return of 10% when depreciation is provided at 35% on reduced value basis. | ||||||||||||
| Assumptions-It has been assumed that tax benefit of initial deductible expense has been realised in the same year. | ||||||||||||
| Cost of vacant land used for setting up production has not been considered assuming no cash outflows occurred because of it. | ||||||||||||
| Consequently its resale value has also not been taken in terminal cash inflows. | ||||||||||||
| Ques 4 | Initial investments | |||||||||||
| Cost of machine | -420000 | |||||||||||
| Pessimistic scenario | ||||||||||||
| Annual cash flows | ||||||||||||
| Revenue= Units soldxselling price | ||||||||||||
| Profit after tax=(1-tax rate)(Revenue-variable cost-fixed cost p.a.-depreciation) | ||||||||||||
| = | 70%[(23,000×38)-(23,000×21)-320,000-60,000] | |||||||||||
| = | 7700 | |||||||||||
| Cash flows= | profit after tax+depreciation | |||||||||||
| = | 67700 | |||||||||||
| PV of total annual cash flows for 7 years=Annual cash flowsxPVAF@18% for 7 years | ||||||||||||
| PV of total annual cash flows for 7 years | = | 67700×3.811527 | = | 258040.3779 | ||||||||
| NPV in pessimistic case | = | Initial cash flows+PVof total annual cash flows+PV of terminal cash flows | ||||||||||
| = | (161,960) | |||||||||||
| Base scenario | ||||||||||||
| Annual cash flows | ||||||||||||
| Revenue= Units soldxselling price | ||||||||||||
| Profit after tax=(1-tax rate)(Revenue-variable cost-fixed cost p.a.-depreciation) | ||||||||||||
| = | 70%[(25,000×40)-(25,000×20)-320,000-60,000] | |||||||||||
| = | 84000 | |||||||||||
| Cash flows= | profit after tax+depreciation | |||||||||||
| = | 144000 | |||||||||||
| PV of total annual cash flows for 7 years=Annual cash flowsxPVAF@18% for 7 years | ||||||||||||
| PV of total annual cash flows for 7 years | = | 144000×3.811527 | = | 548,860 | ||||||||
| NPV in base case | = | Initial cash flows+PVof total annual cash flows+PV of terminal cash flows | ||||||||||
| = | 128,860 | |||||||||||
| Optimistic Scenario | ||||||||||||
| Annual cash flows | ||||||||||||
| Revenue= Units soldxselling price | ||||||||||||
| Profit after tax=(1-tax rate)(Revenue-variable cost-fixed cost p.a.-depreciation) | ||||||||||||
| = | 70%[(27,000×42)-(27,000×19)-320,000-60,000] | |||||||||||
| = | 168700 | |||||||||||
| Cash flows= | profit after tax+depreciation | |||||||||||
| = | 228700 | |||||||||||
| PV of total annual cash flows for 7 years=Annual cash flowsxPVAF@18% for 7 years | ||||||||||||
| PV of total annual cash flows for 7 years | = | 228700×3.811527 | = | 871,696 | ||||||||
| NPV in optimistic scene | = | Initial cash flows+PVof total annual cash flows+PV of terminal cash flows | ||||||||||
| = | 451,696 | |||||||||||
| a) | The project will give a negative NPV of $(161,960) in the pessimistic scenario and positive NPV of $128,860 and $451,696 in the base and optimistic case respectively. | |||||||||||
| b) | Supposing that the CEO is more conservative and has expected the probability of pessimist scene as 50% and optimistic case as 10%. | |||||||||||
| We calculate the expected NPV to assess the viability of the project. | ||||||||||||
| Statement showing expected NPV | ||||||||||||
| Pessimistic case | Base case | Optimistic case | ||||||||||
| NPVxProbability | (161960)x0.50 | 128860×0.40 | 451696×0.10 | |||||||||
| (80,980) | 51,544 | 45,170 | ||||||||||
| Expected NPV=-80980+51544+45169.6 = 15733.6 | ||||||||||||
| Since the project is showing positive expected NPV as per the probability expectation of CEO, the project is feasable and profitable to take up. | ||||||||||||
| Ques 5 | Initial cash flow | All amounts in $ | ||||||||||
| Cost of CRM software | (750,000) | |||||||||||
| working capital requirement | (30,000) | |||||||||||
| Total initial cash flow | (780,000) | |||||||||||
| Annual cash flows | ||||||||||||
| Sales | 600,000 | |||||||||||
| COGS and operating expenses @ 25% of sales | (150,000) | |||||||||||
| Depreciation(750,000/5 years) | (150,000) | |||||||||||
| Profit before tax | 300,000 | |||||||||||
| tax @30% | (90,000) | |||||||||||
| Profit after tax | 210,000 | |||||||||||
| Add back depreciation | 150,000 | |||||||||||
| Annual Cash flows | 360,000 | |||||||||||
| PV of total annual cash flows for 3 years @ 18% = Annual cash flowsxPVAF@18% for 3 years | ||||||||||||
| which is= | 360,000 x 2.17427 | |||||||||||
| PV of total annual cash flows | 782,737 | |||||||||||
| Terminal cash flows at the end of three years | ||||||||||||
| Scrap value of software | 40,000 | |||||||||||
| written down value of software | 300,000 | |||||||||||
| loss on sale of software | (260,000) | |||||||||||
| release of working capital | 30,000 | |||||||||||
| cash flows at the end | 70,000 | |||||||||||
| PV of terminal cash flows | 42,604 | |||||||||||
| NPV of project | = | Initial cash flows+PV of annual cash flows+PV of terminal cash flows | ||||||||||
| = | (780000)+782737+42604 | |||||||||||
| = | 45,341 | |||||||||||
| a) | NPV of the new project assuming zero inflation is $45,341. Hence the project seems to be viable. | |||||||||||
| b) | In order to take inflation into account we have to calculate a nominal discount rate, where, | |||||||||||
| Nominal discount rate = (1+real rate)(1+inflation rate) | ||||||||||||
| = | (1+0.18)(1+0.04) | |||||||||||
| = | 1.2272 | |||||||||||
| hence this rate is 0.227 or 22.7% | ||||||||||||
| PV of annual cash flows for 3 years @22.7%=Annual cash flowsxPVAF@22.7%for 3 years. | ||||||||||||
| which is= | 360,000×2.02055 | |||||||||||
| = | 727398 | |||||||||||
| PV of terminal cash flows @ 22.7% = cash flows at the endxPVF@22.7% for 3rd year | ||||||||||||
| = | 70,000×0.541335 | |||||||||||
| = | 37,893 | |||||||||||
| NPV of the project at nominal rate of return of 22.7% =(-780,000)+(727,398)+(37,893) | ||||||||||||
| = | (14,709) | |||||||||||
| since the project is giving negative NPV on inflation adjusted rate of return, it is not feasible to undertake in inflationary expectations of 4% per year. | ||||||||||||
| Ques 6 | Let us analyse all the possibilities available to Malley Markets. i.e replacing the equipment today , or in year 1 or 2 ans so on | |||||||||||
| a) | If equipment is replaced today i.e.year 0 | |||||||||||
| Initial cash flows | ||||||||||||
| Sale of old equipment | 90,000 | |||||||||||
| Purchase of new equipment | (300,000) | |||||||||||
| cash flows in year 0 | (210,000) | |||||||||||
| Annual maintenance of new machine | (2,000) | |||||||||||
| PV of annual maintenance @10% for 6 years= annual maintenancexPVAF @10% for 6 years | ||||||||||||
| = | 2000×4.35526 | |||||||||||
| = | (8,711) | |||||||||||
| PV of terminal cash flow=120,000xPVF @10% for 6th year | ||||||||||||
| = | 67,737 | |||||||||||
| NPV | = | (150,974) | ||||||||||
| b) | If equipment is replaced in Year 1 | |||||||||||
| Initial cash flows would be = resale value-maintenance cost-purchsare of new equipment | ||||||||||||
| = | (235,000) | |||||||||||
| PV of initial cash flow= initial cash flowxPVF @10% for 1 year | ||||||||||||
| = | (213,636) | |||||||||||
| PV of annual maintenance of new machine@10% for next 6 years | ||||||||||||
| = | (7,919) | |||||||||||
| PV of terminal cash flow=120000xPVF @10% for 7th year | ||||||||||||
| = | 61578.96 | |||||||||||
| NPV | = | (159,976) | ||||||||||
| c) | If equipment is sold in Year 2 | |||||||||||
| PV of cash flow in year 1 | -18181.8 | |||||||||||
| cash flows in year 2 | = | -250000 | ||||||||||
| PV of initial cash flow=initial cash flowxPVF @10% for 2nd year | ||||||||||||
| = | -206610 | |||||||||||
| PV of annual maintenance of new machine @10% for next 6 years | ||||||||||||
| = | (7,199) | |||||||||||
| PV of terminal cash flow=120000x PVF @10% for 8thyear | ||||||||||||
| = | 55980 | |||||||||||
| NPV | = | (176,011) | ||||||||||
| d) | If equipment is sold in year 3 | |||||||||||
| PV of cash flow in year 1 | -18181.8 | |||||||||||
| PV of cash flow in year 2 | -22727.1 | |||||||||||
| PV of cash flow in year 3 | -197171.9925 | |||||||||||
| PV of annaul maintenance of new machine @ 10% for next 6 years | ||||||||||||
| = | (6,544) | |||||||||||
| PV of terminal cash flow=120000x PVF @ 10% for 9th year | ||||||||||||
| = | 50891.64 | |||||||||||
| NPV | = | (193,734) | ||||||||||
| e) | If equipment is sold in year 4 | |||||||||||
| PV of cash flow in year 1 | (18,182) | |||||||||||
| PV of cash flow in year 2 | (22,727) | |||||||||||
| Pv of cash flow in year 3 | (24,418) | |||||||||||
| PV of cash flow in year 4 | (194,658) | |||||||||||
| PV of annual maintenance of new machine @10% for next 6 years | ||||||||||||
| = | (5,949) | |||||||||||
| PV of terminal cash flow = 120000xPVF @10% for 10th year | ||||||||||||
| = | 46265.16 | |||||||||||
| NPV | = | (219,669) | ||||||||||
| f) | If equipment is sold in yaer 5 | |||||||||||
| PV of cash flow in year 1 | (18,182) | |||||||||||
| PV of cash flow in year 2 | (22,727) | |||||||||||
| Pv of cash flow in year 3 | (24,418) | |||||||||||
| PV of cash flow in year 4 | (30,735) | |||||||||||
| PV of cash flow in year 5 | (186,276) | |||||||||||
| PV of annual maintenance of new equipment @ 10% for next 6 years | ||||||||||||
| = | (5,409) | |||||||||||
| PV of terminal cash flow=120000xPVF @10% for 11th year | ||||||||||||
| = | 4205.9256 | |||||||||||
| NPV | = | (283,541) | ||||||||||
| Comparing all the above possibilities, we conclude that machine should be replaced in year o means today only as the NPV is highest today. | ||||||||||||
| Assumptions | Calculations have been made assuming that Malley will run the new machine for full 6 years after replacement. | |||||||||||
GI21
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| Amounts in $ | ||||||||||||
| Ques 1 | To calculate value of share- | |||||||||||
| It is given, | ||||||||||||
| Earnings | 0.305 | |||||||||||
| Expected earnings | 0.35 | |||||||||||
| Since we are not using Gordon’s model so past earnings would not be used for trend. | ||||||||||||
| Retention ratio | 55% or 0.55 | |||||||||||
| Required rate of return | 10%or 0.10 | |||||||||||
| Return on retained earnings | 15% or 0.15 | |||||||||||
| Equity ts tax free only, so no treatment for tax. | ||||||||||||
| Now, | Return on equity =Retention ratio x return on retained earnings | |||||||||||
| = | 0.0825 | |||||||||||
| Dividend for next year = Expected earnings x dividend pay out ratio | ||||||||||||
| = | 0.1575 | |||||||||||
| And, | Value of share = Expected dividend /(Required rate of return – ROE) | |||||||||||
| = | 9 | |||||||||||
| Here, since required rate of return is greater than return on equity, single stage dividend discount model has been used. | ||||||||||||
| Value of share is $9. | ||||||||||||
| All Amounts in $ | ||||||||||||
| Ques 2 | Initial investment | (1,000,000) | ||||||||||
| cash float required | (500,000) | |||||||||||
| inventory | (300,000) | |||||||||||
| Total initial cash outflows | -1800000 | |||||||||||
| Annual cash flows | Year | 1 | 2 | 3 | 4 | |||||||
| Revenue | 1,500,000 | 2,000,000 | 2,500,000 | 3,000,000 | ||||||||
| Cost of production | (750,000) | (1,000,000) | (1,250,000) | (1,500,000) | ||||||||
| Depreciation | (250,000) | (250,000) | (250,000) | (250,000) | ||||||||
| Earnings before tax | 500,000 | 750,000 | 1,000,000 | 1,250,000 | ||||||||
| Tax @ 30% | (150,000) | (225,000) | (300,000) | (375,000) | ||||||||
| Profits after tax | 350,000 | 525,000 | 700,000 | 875,000 | ||||||||
| Add back depreciation | 250,000 | 250,000 | 250,000 | 250,000 | ||||||||
| Cash inflows | 600,000 | 775,000 | 950,000 | 1,125,000 | ||||||||
| PVF @10% | 0.90909 | 0.82645 | 0.75131 | 0.68301 | ||||||||
| PV of cash flows | 545,455 | 640,496 | 713,749 | 768,390 | 2,668,090 | |||||||
| PV of total annual cash flows | ||||||||||||
| Terminal cash flows | ||||||||||||
| Scrap value of machine | 100,000 | |||||||||||
| Book value at the end of 4 years | – | |||||||||||
| Gain on sale | 100,000 | |||||||||||
| Tax on capital gain | (30,000) | |||||||||||
| Net cash flow from scrap | 70,000 | |||||||||||
| Cash float released at the end of 4 years | 500,000 | |||||||||||
| Inventory released at the end of 4 years | 300,000 | |||||||||||
| Total terminal cash flows | 870,000 | |||||||||||
| PV of terminal cash flows | 594,222 | |||||||||||
| NPV | = | Initial cash flows+PV of annual cash flows+PV of terminal cash flows | ||||||||||
| = | 1,462,311 | |||||||||||
| Since the project is yielding a positive NPV, it is profitable to accept the project. | ||||||||||||
| Assumptions | ||||||||||||
| 1 | It has been assumed that the expense of $1million on scientific research of the technology related to the project is a sunk cost. | |||||||||||
| It has been already incurred irrespective of whether the project is accepted or not. | ||||||||||||
| 2 | Head office overheads are also not being affected by the project hence $500000 is not being considered. | |||||||||||
| Ques 3 | Initial cash flows | |||||||||||
| All amounts in $ | ||||||||||||
| Deductible expense at the start | (1,400,000) | |||||||||||
| Tax benefit @30% | 420,000 | |||||||||||
| Total cash flows | (980,000) | |||||||||||
| Annual Cash Flows | ||||||||||||
| Revenue | 96,150,000 | |||||||||||
| (No. of units soldxSale price) | ||||||||||||
| Cost of installation(@$7550 each) | (75,500,000) | |||||||||||
| Fixed cost of production p.a. | (12,000,000) | |||||||||||
| Interest on bank debt | (3,500,000) | |||||||||||
| Depreciation on production facilities | (5,000,000) | |||||||||||
| Profit before tax | 150,000 | |||||||||||
| Tax @ 30% | (45,000) | |||||||||||
| Profit after tax | 105,000 | |||||||||||
| Add back depreciation | 5000000 | |||||||||||
| Net annual Cash flow | 5,105,000 | |||||||||||
| Year | Annual cash flow | PVF@10% | PV of cash flows | |||||||||
| 1 | 5,105,000 | 0.90909 | 4,640,909 | |||||||||
| 2 | 5,105,000 | 0.82645 | 4,219,008 | |||||||||
| 3 | 5,105,000 | 0.75131 | 3,835,462 | |||||||||
| 4 | 5,105,000 | 0.68301 | 3,486,784 | |||||||||
| 5 | 5,105,000 | 0.62092 | 3,169,803 | |||||||||
| 6 | 5,105,000 | 0.56447 | 2,881,639 | |||||||||
| 7 | 5,105,000 | 0.51316 | 2,619,672 | |||||||||
| 8 | 5,105,000 | 0.46651 | 2,381,520 | |||||||||
| PV of total annual cash flows | 27,234,798 | |||||||||||
| Terminal cash flows | ||||||||||||
| Scrap value of machine | 5,900,000 | |||||||||||
| Book value of machine | – | |||||||||||
| Capital gain | 5,900,000 | |||||||||||
| Tax on capital gain@ 30% | (1,770,000) | |||||||||||
| Net cash flow from sale of machine | 4,130,000 | |||||||||||
| Repayment of loan in full | (40,000,000) | |||||||||||
| Total terminal cash flows | (35,870,000) | |||||||||||
| PV of terminal cash flows | (16,733,620) | |||||||||||
| NPV | = | Initial cash flows+Annual cash flows+Terminal cash flows | ||||||||||
| = | 9,521,179 | |||||||||||
| a) | Frosty should produce the cold rooms because the project is giving a positive NPV of $9,521,179. | |||||||||||
| b) | If the rate of interest on bank loan is 7.5% p.a. then interest on bank loan would be 3000000 p.a. | |||||||||||
| Now, | Cost of production before depreciation and tax= | Installation cost+fixed cost+interest | ||||||||||
| = | 84,500,000 | |||||||||||
| Let the unit selling price be $ Y | ||||||||||||
| Annual profit before depreciation and tax | = | 10,000xY-84,500,000 | ||||||||||
| Profit after depreciation before tax | = | 10,000Y-84,500,000-5,000,000 | ||||||||||
| = | 10,000Y-89,500,000 | |||||||||||
| Tax | = | 30%(10,000Y-89,500,000) | ||||||||||
| = | 3,000Y-26,850,000 | |||||||||||
| Annual cash flow from operation | = | 10,000Y-84,500,000-3,000Y+26,850,000 | ||||||||||
| = | 7000Y-57,650,000 | |||||||||||
| For obtaining 10% return on the project, NPV should be zero. Hence, | ||||||||||||
| (7000Y-57,650,000)xPVAF@10% for 8years+Initial cash flows+terminal cash flows = 0 | ||||||||||||
| Therefore | (7000Y-57650000)*5.33493-980000-16733620 | = | 0 | |||||||||
| 37344.51Y-307558714.5-17713620 | = | 0 | ||||||||||
| This gives us, | 37344.51Y | = | 325272334.5 | |||||||||
| Y | = | 8710.044247 | ||||||||||
| Minimum selling price for obtaining 10% rate of return when interes rate on debt is 7.5% should be $8710 | ||||||||||||
| 63700000 | ||||||||||||
| c) | If depreciation is provided @ 35% p.a. on reducing balance method then annual cost of production will change as follows | |||||||||||
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||||
| Depreciation on production facilities | (14,000,000) | (9,100,000) | (5,915,000) | (3,844,750) | (2,499,088) | (1,624,407) | (1,055,864) | (686,312) | ||||
| Tax benefit on depreciation | 4,200,000 | 2,730,000 | 1,774,500 | 1,153,425 | 749,726 | 487,322 | 316,759 | 205,894 | ||||
| PVF@10% | 0.90909 | 0.82645 | 0.75131 | 0.68301 | 0.62092 | 0.56447 | 0.51316 | 0.46651 | ||||
| PV of tax benefit | 3,818,182 | 2,256,198 | 1,333,208 | 787,805 | 465,521 | 275,081 | 162,548 | 96,051 | 9,194,593 | |||
| PV of total tax benefit from depreciation | ||||||||||||
| Let selling price be Y | ||||||||||||
| Revenue | 10000Y | |||||||||||
| Cost of installation(@$7550 each) | (75,500,000) | |||||||||||
| Fixed cost of production p.a. | (12,000,000) | |||||||||||
| Interest on bank debt | (3,500,000) | |||||||||||
| Profit before depreciation | 10000Y-91000000 | |||||||||||
| Tax @30% | 3000Y-27300000 | |||||||||||
| Profit after tax | 7000Y-63700000 | |||||||||||
| PVAF@10% for 8 years | 5.33493 | |||||||||||
| PV of profit after tax | 37344.51Y-339835041 | |||||||||||
| Add PV of total tax benefit from depreciation | 9194593.187 | |||||||||||
| PV of total annual cash flows | 37344.51Y-330640447.8 | |||||||||||
| Terminal cash flows | ||||||||||||
| Scrap value | 5,900,000 | |||||||||||
| written down value | 1,274,579 | |||||||||||
| gain on sale | 4,625,421 | |||||||||||
| tax on capital gain | 1,387,626 | |||||||||||
| Cash flow on sale of machine | 4,512,374 | |||||||||||
| Repayment of loan in full | (40,000,000) | |||||||||||
| Total terminal cash flows | (35,487,626) | |||||||||||
| PV of total terminal cash flows | (16,555,240) | |||||||||||
| For obtaining 10% return on the project, NPV should be zero. Hence, | ||||||||||||
| Initial cash flows+PV of total annual cash flows+PV of total terminal cash flows=0 | ||||||||||||
| 980000+37344.51Y-330640447.8-16555240 | = | 0 | ||||||||||
| 37344.51Y-346215688 | = | 0 | ||||||||||
| Y | = | 9270.859 | ||||||||||
| Minimum Selling price of cold unit should be $9271 for attaining a rate of return of 10% when depreciation is provided at 35% on reduced value basis. | ||||||||||||
| Assumptions-It has been assumed that tax benefit of initial deductible expense has been realised in the same year. | ||||||||||||
| Cost of vacant land used for setting up production has not been considered assuming no cash outflows occurred because of it. | ||||||||||||
| Consequently its resale value has also not been taken in terminal cash inflows. | ||||||||||||
| Ques 4 | Initial investments | |||||||||||
| Cost of machine | -420000 | |||||||||||
| Pessimistic scenario | ||||||||||||
| Annual cash flows | ||||||||||||
| Revenue= Units soldxselling price | ||||||||||||
| Profit after tax=(1-tax rate)(Revenue-variable cost-fixed cost p.a.-depreciation) | ||||||||||||
| = | 70%[(23,000×38)-(23,000×21)-320,000-60,000] | |||||||||||
| = | 7700 | |||||||||||
| Cash flows= | profit after tax+depreciation | |||||||||||
| = | 67700 | |||||||||||
| PV of total annual cash flows for 7 years=Annual cash flowsxPVAF@18% for 7 years | ||||||||||||
| PV of total annual cash flows for 7 years | = | 67700×3.811527 | = | 258040.3779 | ||||||||
| NPV in pessimistic case | = | Initial cash flows+PVof total annual cash flows+PV of terminal cash flows | ||||||||||
| = | (161,960) | |||||||||||
| Base scenario | ||||||||||||
| Annual cash flows | ||||||||||||
| Revenue= Units soldxselling price | ||||||||||||
| Profit after tax=(1-tax rate)(Revenue-variable cost-fixed cost p.a.-depreciation) | ||||||||||||
| = | 70%[(25,000×40)-(25,000×20)-320,000-60,000] | |||||||||||
| = | 84000 | |||||||||||
| Cash flows= | profit after tax+depreciation | |||||||||||
| = | 144000 | |||||||||||
| PV of total annual cash flows for 7 years=Annual cash flowsxPVAF@18% for 7 years | ||||||||||||
| PV of total annual cash flows for 7 years | = | 144000×3.811527 | = | 548,860 | ||||||||
| NPV in base case | = | Initial cash flows+PVof total annual cash flows+PV of terminal cash flows | ||||||||||
| = | 128,860 | |||||||||||
| Optimistic Scenario | ||||||||||||
| Annual cash flows | ||||||||||||
| Revenue= Units soldxselling price | ||||||||||||
| Profit after tax=(1-tax rate)(Revenue-variable cost-fixed cost p.a.-depreciation) | ||||||||||||
| = | 70%[(27,000×42)-(27,000×19)-320,000-60,000] | |||||||||||
| = | 168700 | |||||||||||
| Cash flows= | profit after tax+depreciation | |||||||||||
| = | 228700 | |||||||||||
| PV of total annual cash flows for 7 years=Annual cash flowsxPVAF@18% for 7 years | ||||||||||||
| PV of total annual cash flows for 7 years | = | 228700×3.811527 | = | 871,696 | ||||||||
| NPV in optimistic scene | = | Initial cash flows+PVof total annual cash flows+PV of terminal cash flows | ||||||||||
| = | 451,696 | |||||||||||
| a) | The project will give a negative NPV of $(161,960) in the pessimistic scenario and positive NPV of $128,860 and $451,696 in the base and optimistic case respectively. | |||||||||||
| b) | Supposing that the CEO is more conservative and has expected the probability of pessimist scene as 50% and optimistic case as 10%. | |||||||||||
| We calculate the expected NPV to assess the viability of the project. | ||||||||||||
| Statement showing expected NPV | ||||||||||||
| Pessimistic case | Base case | Optimistic case | ||||||||||
| NPVxProbability | (161960)x0.50 | 128860×0.40 | 451696×0.10 | |||||||||
| (80,980) | 51,544 | 45,170 | ||||||||||
| Expected NPV=-80980+51544+45169.6 = 15733.6 | ||||||||||||
| Since the project is showing positive expected NPV as per the probability expectation of CEO, the project is feasable and profitable to take up. | ||||||||||||
| Ques 5 | Initial cash flow | All amounts in $ | ||||||||||
| Cost of CRM software | (750,000) | |||||||||||
| working capital requirement | (30,000) | |||||||||||
| Total initial cash flow | (780,000) | |||||||||||
| Annual cash flows | ||||||||||||
| Sales | 600,000 | |||||||||||
| COGS and operating expenses @ 25% of sales | (150,000) | |||||||||||
| Depreciation(750,000/5 years) | (150,000) | |||||||||||
| Profit before tax | 300,000 | |||||||||||
| tax @30% | (90,000) | |||||||||||
| Profit after tax | 210,000 | |||||||||||
| Add back depreciation | 150,000 | |||||||||||
| Annual Cash flows | 360,000 | |||||||||||
| PV of total annual cash flows for 3 years @ 18% = Annual cash flowsxPVAF@18% for 3 years | ||||||||||||
| which is= | 360,000 x 2.17427 | |||||||||||
| PV of total annual cash flows | 782,737 | |||||||||||
| Terminal cash flows at the end of three years | ||||||||||||
| Scrap value of software | 40,000 | |||||||||||
| written down value of software | 300,000 | |||||||||||
| loss on sale of software | (260,000) | |||||||||||
| release of working capital | 30,000 | |||||||||||
| cash flows at the end | 70,000 | |||||||||||
| PV of terminal cash flows | 42,604 | |||||||||||
| NPV of project | = | Initial cash flows+PV of annual cash flows+PV of terminal cash flows | ||||||||||
| = | (780000)+782737+42604 | |||||||||||
| = | 45,341 | |||||||||||
| a) | NPV of the new project assuming zero inflation is $45,341. Hence the project seems to be viable. | |||||||||||
| b) | In order to take inflation into account we have to calculate a nominal discount rate, where, | |||||||||||
| Nominal discount rate = (1+real rate)(1+inflation rate) | ||||||||||||
| = | (1+0.18)(1+0.04) | |||||||||||
| = | 1.2272 | |||||||||||
| hence this rate is 0.227 or 22.7% | ||||||||||||
| PV of annual cash flows for 3 years @22.7%=Annual cash flowsxPVAF@22.7%for 3 years. | ||||||||||||
| which is= | 360,000×2.02055 | |||||||||||
| = | 727398 | |||||||||||
| PV of terminal cash flows @ 22.7% = cash flows at the endxPVF@22.7% for 3rd year | ||||||||||||
| = | 70,000×0.541335 | |||||||||||
| = | 37,893 | |||||||||||
| NPV of the project at nominal rate of return of 22.7% =(-780,000)+(727,398)+(37,893) | ||||||||||||
| = | (14,709) | |||||||||||
| since the project is giving negative NPV on inflation adjusted rate of return, it is not feasible to undertake in inflationary expectations of 4% per year. | ||||||||||||
| Ques 6 | Let us analyse all the possibilities available to Malley Markets. i.e replacing the equipment today , or in year 1 or 2 ans so on | |||||||||||
| a) | If equipment is replaced today i.e.year 0 | |||||||||||
| Initial cash flows | ||||||||||||
| Sale of old equipment | 90,000 | |||||||||||
| Purchase of new equipment | (300,000) | |||||||||||
| cash flows in year 0 | (210,000) | |||||||||||
| Annual maintenance of new machine | (2,000) | |||||||||||
| PV of annual maintenance @10% for 6 years= annual maintenancexPVAF @10% for 6 years | ||||||||||||
| = | 2000×4.35526 | |||||||||||
| = | (8,711) | |||||||||||
| PV of terminal cash flow=120,000xPVF @10% for 6th year | ||||||||||||
| = | 67,737 | |||||||||||
| NPV | = | (150,974) | ||||||||||
| b) | If equipment is replaced in Year 1 | |||||||||||
| Initial cash flows would be = resale value-maintenance cost-purchsare of new equipment | ||||||||||||
| = | (235,000) | |||||||||||
| PV of initial cash flow= initial cash flowxPVF @10% for 1 year | ||||||||||||
| = | (213,636) | |||||||||||
| PV of annual maintenance of new machine@10% for next 6 years | ||||||||||||
| = | (7,919) | |||||||||||
| PV of terminal cash flow=120000xPVF @10% for 7th year | ||||||||||||
| = | 61578.96 | |||||||||||
| NPV | = | (159,976) | ||||||||||
| c) | If equipment is sold in Year 2 | |||||||||||
| PV of cash flow in year 1 | -18181.8 | |||||||||||
| cash flows in year 2 | = | -250000 | ||||||||||
| PV of initial cash flow=initial cash flowxPVF @10% for 2nd year | ||||||||||||
| = | -206610 | |||||||||||
| PV of annual maintenance of new machine @10% for next 6 years | ||||||||||||
| = | (7,199) | |||||||||||
| PV of terminal cash flow=120000x PVF @10% for 8thyear | ||||||||||||
| = | 55980 | |||||||||||
| NPV | = | (176,011) | ||||||||||
| d) | If equipment is sold in year 3 | |||||||||||
| PV of cash flow in year 1 | -18181.8 | |||||||||||
| PV of cash flow in year 2 | -22727.1 | |||||||||||
| PV of cash flow in year 3 | -197171.9925 | |||||||||||
| PV of annaul maintenance of new machine @ 10% for next 6 years | ||||||||||||
| = | (6,544) | |||||||||||
| PV of terminal cash flow=120000x PVF @ 10% for 9th year | ||||||||||||
| = | 50891.64 | |||||||||||
| NPV | = | (193,734) | ||||||||||
| e) | If equipment is sold in year 4 | |||||||||||
| PV of cash flow in year 1 | (18,182) | |||||||||||
| PV of cash flow in year 2 | (22,727) | |||||||||||
| Pv of cash flow in year 3 | (24,418) | |||||||||||
| PV of cash flow in year 4 | (194,658) | |||||||||||
| PV of annual maintenance of new machine @10% for next 6 years | ||||||||||||
| = | (5,949) | |||||||||||
| PV of terminal cash flow = 120000xPVF @10% for 10th year | ||||||||||||
| = | 46265.16 | |||||||||||
| NPV | = | (219,669) | ||||||||||
| f) | If equipment is sold in yaer 5 | |||||||||||
| PV of cash flow in year 1 | (18,182) | |||||||||||
| PV of cash flow in year 2 | (22,727) | |||||||||||
| Pv of cash flow in year 3 | (24,418) | |||||||||||
| PV of cash flow in year 4 | (30,735) | |||||||||||
| PV of cash flow in year 5 | (186,276) | |||||||||||
| PV of annual maintenance of new equipment @ 10% for next 6 years | ||||||||||||
| = | (5,409) | |||||||||||
| PV of terminal cash flow=120000xPVF @10% for 11th year | ||||||||||||
| = | 4205.9256 | |||||||||||
| NPV | = | (283,541) | ||||||||||
| Comparing all the above possibilities, we conclude that machine should be replaced in year o means today only as the NPV is highest today. | ||||||||||||
| Assumptions | Calculations have been made assuming that Malley will run the new machine for full 6 years after replacement. | |||||||||||
