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PFM 4-2

Question 01 (Joy Co)
Question 02 (Shades Co)
Question 03 (Costa Co)
Question 04 (BRT Co)
Question 05 (Builder Co)
Question 06 (Easter Co)
Question 07 (Trecor Co)
Question 01 (Pinks Co)
Question 02 (Copper Co)
Question 03 (VYXYN Co)
Question 04 (Hebac Co)
Question 05 (Pelta Co)
Question 06 (Melanie Co)
Question 07 (Hraxin Co)
Question 08 (Degnis Co)
Question 09 (Project E)
Question 10 (AGD Co)
Question 01 (Joy Co)

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1 / 5

The following scenario relates to questions 144–148.

 Joy Co

The following information relates to an investment project which is being evaluated by the directors of Joy Co, a listed company. The initial investment, payable at the start of the first year of operation, is $3.9 million.

Year 1 2 3 4
Net operating cash flow ($000) 1,200 1,500 1,600 1,580
Scrap value ($000)       100

The directors believe that this investment project will increase shareholder wealth if it achieves a return on capital employed greater than 15%. As a matter of policy, the directors require all investment projects to be evaluated using both the payback and return on capital employed methods. Shareholders have recently criticised the directors for using these investment appraisal methods, claiming that Joy Co ought to be using the academically-preferred net present value method.

The directors have a remuneration package which includes a financial reward for achieving an annual return on capital employed greater than 15%. The remuneration package does not include a share option scheme.

149. What is the payback period of the investment project?

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150. Based on the average investment method, what is the percentage return on capital employed of the investment project, to one decimal place?

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151. Which TWO of the following statements about investment appraisal methods are correct?

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152. Which of the following statements about Joy Co is/are correct?

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153. Which of the following statements about Joy Co directors’ remuneration package is/are correct?

  1. Directors’ remuneration should be determined by senior executive directors.
  2. Introducing a share option scheme would help bring directors’ objectives in line with shareholders’ objectives.
  3. Linking financial rewards to a target return on capital employed will encourage short-term profitability and discourage capital investment.

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Question 02 (Shades Co)

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The following scenario relates to questions 149–153.

Shades Co.

Shades Co. is considering a project with the following cash flows.

Year Initial investment Variable costs Cash inflows Net cash flows

$’000 $’000 $’000 $’000

0 (11,000) (11,000)

1 (3,200) 10,300 7,100

2 (3,200) 10,300 7,100

Cash flows arise from selling 1,030,000 units at $10 per unit. The company has a cost of capital of 9%.

The net present value (NPV) of the project is $1,490.

154. What is the discounted payback of the project?

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155. What is the internal rate of return (IRR) of the project (using discount rates of 15% and 20%)?

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156. Which TWO of the following statements are true of the IRR and the NPV methods of appraisal?

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157. What is the sensitivity of the project to changes in sales volume (to one decimal place)?

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158. Which of the following statements is/are true?

A. Using random numbers to generate possible values of project variables, a simulation model can generate a standard deviation of expected project outcomes.

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B. The problem with risk and uncertainty in investment appraisal is that neither can be quantified or measured.

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C. The sensitivity of NPV to a change in sales volume can be calculated as NPV divided by the present value of future sales income.

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D. The certainty equivalent approach converts risky cash flows into riskless equivalent amounts which are discounted by a capital asset pricing model (CAPM) derived project-specific cost of capital.

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Question 03 (Costa Co)

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The following scenario relates to questions 149–153.

 Costa Co

Costa Co needs to replace a major piece of office equipment that is in constant use and for which there is expected to continue to be use for the foreseeable future. Two types of machine are available with different capital costs, useful lives, scrap values and annual running costs.

Machine 1 will initially cost $480,000, have a life of four years, scrap value of $60,000 and annual running costs of $72,000.

Machine 2 will initially cost $540,000, have a life of three years, scrap value of $120,000 and annual running costs of $47,000.

Costa Co’s cost of capital is 10%. Assume all cash flows, except the initial capital cost, occur at the end of the relevant year and assume that taxation and inflation can be ignored.

159. What is the equivalent annual cost of machine 2 (to the nearest $000)?

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160. Drag and drop the relevant statements to indicate whether they are true or false.

(1) The equivalent annual cost calculation assumes the same type of machine is going to be used into the foreseeable future.

(2) The equivalent annual cost calculation assumes the capabilities of Machine 1 and Machine 2 are identical.

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161. It is now felt that the final scrap value of the machines depends on two factors: whether or not a new supplier enters the market (which would reduce the likely scrap value) and the strength of the dollar against other currencies (since sales of used machines will be made abroad and invoiced in the foreign currency). Adverse effects will each reduce the scrap value by 10% of the figure used in the investment appraisal. The relevant probabilities are as follows.

New supplier       Probability       Strong $        Probability

Yes                    0.4                 Yes                  0.3

No                    0.6                  No                   0.7

What is now the expected value of the scrap proceeds from machine 2?

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162. To overcome the difficulties of incorporating probabilities into the investment appraisal calculations, Costa Co could perform a simulation exercise to help reach a decision. Indicate which of the following statements, relating to simulation, is/are

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163. Which of the following statements about Costa Co’s replacement decision are true?

1) The decision between machine 1 and machine 2 could be found by calculating total NPV of each machine over a 12 year period.

2) The replacement analysis model assumes that Costa Co replaces like with like each time it needs to replace an existing asset.

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Question 04 (BRT Co)

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BRT Co (6/11, amended)

The following scenario relates to questions 159–163.

BRT Co has developed a new confectionery line that can be sold for $5.00 per box and that is expected to have continuing popularity for many years. The finance director has proposed that investment in the new product should be evaluated over a four-year time-horizon, even though sales would continue after the fourth year, on the grounds that cash flows after four years are too uncertain to be included.

The variable cost (in current price terms) will depend on sales volume, as follows.

Sales volume (boxes) Less than 1 million 1–1.9 million 2–2.9 million 3–3.9 million

Variable cost ($ per box) 2.80 3.00 3.00 3.05

Forecast sales volumes are as follows.

Year 1 2 3 4

Demand (boxes) 0.7 million 1.6 million 2.1 million 3.0 million

Tax

Tax-allowable depreciation on a 25% reducing balance basis could be claimed on the cost of equipment. Profit tax of 30% per year will be payable one year in arrears. A balancing allowance would be claimed in the fourth year of operation.

Inflation

The average general level of inflation is expected to be 3% per year for the selling price and variable costs. BRT Co uses a nominal after-tax cost of capital of 12% to appraise new investment projects.

A trainee accountant at BRT Co has started a spreadsheet to calculate the net present value (NPV) of a proposed new project.

164. What is the sales figure for Year 2 (cell D3 in the spreadsheet), to the nearest $’000? $

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164. What are the variable costs for Year 3 (cell E4 in the spreadsheet), to the nearest $’000? $

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166. What are the tax benefits generated by the tax-allowable depreciation on the equipment in Year 4 (cell F8), to the nearest $’000? $

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167. Which of the following statements about the project appraisal are true/false?

A. The trainee accountant has used the wrong percentage for the cost of capital.

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B. Ignoring sales after four years underestimates the value of the project.

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C. The working capital figure in Year 4 is wrong.

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168. The trainee accountant at BRT Co has calculated the internal rate of return (IRR) for the project. Are the following statements true or false?

1 When cash flow patterns are conventional, the NPV and IRR methods will give the same    accept or reject decision.

The project is financially viable under IRR if it exceeds the cost of capital.

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Question 05 (Builder Co)

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Builder Co

The following scenario relates to questions 169-173.

Builder Co is appraising four different projects but is experiencing capital rationing in Year 0. No capital rationing is expected in future periods but none of the four projects that Builder Co is considering can be postponed, so a decision must be made now. Builder Co’s cost of capital is 12%.

The following information is available.

Project Outlay in Year 0 $ PV $ NPV $
Amster 100,000 111,400 11,400
Wind 56,000 62,580 6,580
Ultra 60,000 68,760 8,760
Tubor 90,000 102,400 12,400

169. Arrange the projects in order of their preference to Builder using the profitability index, with the most attractive first.

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170. Which of the following statements about Builder Co’s decision to use PI is true?

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171. Several years later, there is no capital rationing and Builder Co decides to replace an existing machine. Builder Co has the choice of either a Super machine (lasting four years) or a Great machine (lasting three years).

The following present value table includes the figures for a Super machine.

  0 1 2 3 4
Maintenance costs   (20,000) (29,000) (32,000) (35,000)
Investment and scrap (250,000)       25,000
Net cash flow (250,000) (20,000) (29,000) (32,000) (10,000)
Discount at 12% 1.000 0.893 0.797 0.712 0.636
Present values (250,000)  (17,860)  (23,113) (22,784) (6,360)

Tax and tax-allowable depreciation should be ignored.

What is the equivalent annual cost (EAC) of the Super machine (to the nearest whole number)?

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172. Which of the following statements concerning Builder Co’s use of the EAC are true?

1 The use of equivalent annual cost is appropriate in periods of high inflation.

2 The EAC method assumes that the machine can be replaced by exactly the same machine in perpetuity.

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173. The following potential cash flows are predicted for maintenance costs for the Great machine:

Year             Cash flow        Probability $

2                 19,000                0.55

2                 26,000                0.45

3                 21,000                0.3

3                 25,000                0.25

3                 31,000                0.45

What is the expected present value of the maintenance costs for Year 2 (to the nearest whole number)?

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Question 06 (Easter Co)

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Easter Co

The following scenario relates to questions 174-178.

Easter Co is about to hold its annual strategic planning meeting and a number of capital investment projects will be discussed. A summary of the projects’ cash flows is shown below.

Project NPV $000 Investment $000
A 4,900 3,200
B 7,400 9,300
C 5,900 7,300
D 7,500 5,200
E 9,000 5,600

The investment will need to be made at the start of the coming year; no projects can be delayed and none are divisible. The funds available for these projects are limited to $10,000,000.

174. Indicate, whether the following statements about capital rationing are true or false.

A. Both hard and soft capital rationing are the result of external factors

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B. Soft rationing is the result of external factors, hard rationing is the result of internal policies

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C. Hard rationing is the result of external factors, soft rationing is the result of internal policies

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D. Both hard and soft capital rationing are the result of internal policies

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175. From the list below, select which TWO projects should be accepted, based on the circumstances described?

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176. What projects would be accepted if it was found that projects A and E were mutually exclusive?

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177. What projects, and fractions of projects, would be accepted if a partner could be found to invest in a proportion of one of the projects making them effectively infinitely divisible (ignoring the mutually exclusive limitation)?

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178. A sixth project, Project F, is causing considerable confusion, particularly among those members of the board of Easter Co whose sole means of appraising projects is to find an internal rate of return (IRR) using the spreadsheet function on their computers. The summarised cash flows of Project F are as follows.

Time 0      Invest     $4.00m

Time 1    Receive    $8.80m

Time 2     Spend      $4.83m

The spreadsheet function requires you to enter the cash flows of a project and also enter a guess for the IRR. The directors are struggling to guess the IRR for this sixth project.

What is the likely cause of the confusion over project F?

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Question 07 (Trecor Co)

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1 / 7

Trecor Co (Specimen exam 2007, amended)

The following scenario relates to questions 179–184.

Trecor Co plans to buy a machine costing $250,000 which will last for 4 years and then be sold for $5,000. Net cash flows before tax are expected to be as follows.

  T1 T2 T3 T4
Net cash flow $ 122,000 143,000 187,000 78,000

Depreciation is charged on a straight-line basis over the life of an asset.

176. Calculate the before-tax return on capital employed (accounting rate of return) based on the average investment (to the nearest whole percentage). %

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180. Are the following statements on return on capital employed (ROCE) true or false?

A. ROCE can be used to compare two mutually exclusive projects.

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B. If ROCE is less than the target ROCE then the purchase of the machine can be recommended.

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181. Trecor Co can claim tax-allowable depreciation on a 25% reducing balance basis. It pays tax at an annual rate of 30% one year in arrears. What amount of tax relief would be received by Trecor in time 4 of a net present value (NPV) calculation? $

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182. What is the payback period for the machine (to the nearest whole month)?

A. Years

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B. Months

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183. Which TWO of the following statements about the internal rate of return (IRR) are TRUE?

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Question 01 (Pinks Co)

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184. Pinks Co (Mar/Jun 2019)

Pinks Co is a large company listed on a major stock exchange. In recent years, the board of Pinks Co has been criticised for weak corporate governance and two of the company’s non-executive directors have just resigned. A recent story in the financial media has criticised the performance of Pinks Co and claims that the company is failing to satisfy the objectives of its key stakeholders.

Pinks Co is appraising an investment project which it hopes will boost its performance. The project will cost $20 million, payable in full at the start of the first year of operation. The project life is expected to be four years. Forecast sales volumes, selling price, variable cost and fixed costs are as follows:

Year 1 2 3 4
Sales (units/year) 300,000 410,000 525,000 220,000
Selling price ($/unit) 125 130 140 120
Variable cost ($/unit) 71 71 71 71
Fixed costs ($’000/year) 3,000 3,100 3,200 3,000

Selling price and cost information are in current price terms, before applying selling price inflation of 5% per year, variable cost inflation of 3.5% per year and fixed cost inflation of 6% per year.

Pinks Co pays corporation tax of 26%, with the tax liability being settled in the year in which it arises. The company can claim tax-allowable depreciation on the full initial investment of $20 million on a 25% reducing balance basis. The investment project is expected to have zero residual value at the end of four years.

Pinks Co has a nominal after-tax cost of capital of 12% and a real after-tax cost of capital of 8%. The general rate of inflation is expected to be 3.7% per year for the foreseeable future.

Required

A. (i) Calculate the nominal net present value of Pinks Co’s investment project.

Nominal terms appraisal of the investment project

Year 1 2 3 4
  $000 $000 $000 $000
Sales revenue 39,375 58,765 85,087 32,089
Variable cost (22,047) (31,185) (41,328) (17,923)
Contribution 17,328 27,580 43,759 14,166
Fixed costs (3,180) (3,483) (3,811) (3,787)
Cash flows before tax 14,148 24,097 39,948 10,379
Tax at 26% (3,679) (6,265) (10,387) (2,699)
TAD benefits 1,300 975 731 2,194
Cash flows after tax 11,769 18,807 30,292 9,874
 Discount at 12% 0.893 0.797 0.712 0.636
Present values 10,510 14,989 21,568 6,280

$000

Sum of PVs of future cash flows             53,347

Initial investment                                    (20,000)

NPV                                                         33,347

Workings

Year 1 2 3 4
Selling price ($/unit) 125 130 140 120
Inflated by 5%/year 131.25 143.33 162.07 145.86
Sales volume (units/year) 300,000 410,000 525,000 220,000
Sales revenue ($000/year) 39,375 58,765 85,087 32,089

 

Variable cost ($/unit) 71 71 71 71
Inflated by 3.5%/year 73.49 76.06 78.72 81.47
Sales volume(units/year) 300,000 410,000 525,000 220,000
Variable cost ($000/year) 22,047 31,185 41,328 17,923

 

Fixed costs ($000/year) 3,000 3,100 3,200 3,000
Inflated by 6%/year 3,180 3,483 3,811 3,787

 

TAD ($000) 5,000 3,750 2,813 8,437
TAD benefits ($000) 1 1,300 975 731 2,194

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(ii) Calculate the real net present value of Pinks Co’s investment project and comment on your findings.

Time 1

$000

2

$000

3

$000

4

$000

Nominal cash flows after tax 11,769 18,807 30,292 9,874
deflated at 3.7% pa (W1) 0.964 0.930 0.897 0.865
Real cash flows after tax 11,345 17,491 27,172 8,541
Discount at real rate 8% 0.926 0.857 0.794 0.735
Present value 10,505 14,990 21,575 6,278

 

$000

Sum of the PV of cash inflows      53,348

Investment outlay                         (20,000)

NPV                                               33,348

Comment

The two approaches give the same outcome (there is a small rounding difference). The first approach has higher cash flows due to inflation, and a higher cost of capital due to inflation. The second approach strips the general rate of inflation out of both the cash flows and the cost of capital and therefor has no impact on the NPV.

Workings

The deflation factors are calculated as (1 + 0.0.37)–n, where n is the time period.

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B. Discuss FOUR ways to encourage managers to achieve stakeholder objectives.

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Question 02 (Copper Co)

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185. Copper Co (Mar/Jun 18)

Copper Co is concerned about the risk associated with a proposed investment and is looking for ways to incorporate risk into its investment appraisal process. The company has heard that probability analysis may be useful in this respect and so the following information relating to the proposed investment has been prepared:

Year 1 Year 2
Cash flow ($) Probability Cash flow ($) Probability
1,000,000 0.1 2,000,000 0.3
2,000,000 0.5 3,000,000 0.6
3,000,000 0.4 5,000,000 0.1

However, the company is not sure how to interpret the results of an investment appraisal based on probability analysis.

The proposed investment will cost $3.5m, payable in full at the start of the first year of operation. Copper Co uses a discount rate of 12% in investment appraisal.

Required

(a) Using a joint probability table:

(i) Calculate the mean (expected) NPV of the proposed investment.

Expected NPV (ENPV) calculation

Year PV of Y1 (see workings)

$’000

Prob PV of Y2 (see workings) $’000 Prob Total PV

$’000

Joint prob PV x JP

$’000

NPV

$’000

PV scenario 1 893 0.1 1,594 0.3 2,487 0.03 74.6 (1,013)
      2,391 0.6 3,284 0.06 197.0 (216 )
      3,985 0.1 4,878 0.01 48.8 1,378
PV scenario 2 1,786 0.5 1,594 0.3 3,380 0.15 507.0 (120)
      2,391 0.6 4,177 0.30 1,253 1,677
      3,985 0.1 5,771 0.05 288.6 2,271
PV scenario 3 2,679 0.4 1,594 0.3 4,273 0.12 512.8 773
      2,391 0.6 5,070 0.24 1,216.8 1,570
      3,985 0.1 6,664 0.04 266.6 3,164
              Sum of PV    4,365
              Investment (3,500)
              ENPV =          865

Workings

Discounting at 12%; discount factor time 1 = 0.893, time 2 = 0.797

Time 1 PV 2 PV
Low cash flow 1 1,000 893 2,000 1,594
Medium cash flow 2 2,000 1,786 3,000 2,391
High cash flow 3 3,000 2,679 5,000 3,985

Joint probabilities are calculated by multiplying the probabilities in year 1 and year 2 eg the first joint probability shown of 0.03 is calculated as 0.1 (year 1) x 0.3 (year 2).

2 / 5

(ii) Calculate the probability of the investment having a negative NPV.

3 / 5

(iii) Calculate the NPV of the most likely outcome.

4 / 5

(iv) Comment on the financial acceptability of the proposed investment.

5 / 5

B. Discuss TWO of the following methods of adjusting for risk and uncertainty in investment appraisal:

(i) Simulation

(ii) Adjusted payback

(iii) Risk-adjusted discount rates

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Question 03 (VYXYN Co)

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186. VYXYN Co (Mar/Jun 17)

Vyxyn Co is evaluating a planned investment in a new product costing $20m, payable at the start of the first year of operation. The product will be produced for four years, at the end of which production will cease. The investment project will have a terminal value of zero. Financial information relating to the investment project is as follows:

Year 1 2 3 4
Sales volume (units/year) 440,000 550,000 720,000 400,000
 Selling price ($/unit) 26.50 28.50 30.00 26.00
Fixed cost ($/year) 1,100,000 1,121,000 1,155,000 1,200,000

These selling prices have not yet been adjusted for selling price inflation, which is expected to be 3.5% per year. The annual fixed costs are given above in nominal terms.

Variable cost per unit depends on whether competition is maintained between key suppliers of components. The purchasing department has made the following forecast:

Competition Strong Moderate Weak
Probability 45% 35% 20%
Variable cost ($/unit) 10.80 12.00 14.70

The variable costs in this forecast are before taking account of variable cost inflation of 4.0% per year.

Vyxyn Co can claim tax-allowable depreciation on a 25% per year reducing balance basis on the full investment cost of $20m and pays corporation tax of 28% one year in arrears.

It is planned to finance the investment project with an issue of 8% loan notes, redeemable in ten years’ time. Vyxyn Co has a nominal after-tax weighted average cost of capital of 10%, a real after-tax weighted average cost of capital of 7% and a cost of equity of 11%.

Required:

(a) Discuss the difference between risk and uncertainty in relation to investment appraisal.

2 / 3

B. Calculate the expected net present value of the investment project and comment on its financial acceptability and on the risk relating to variable cost.

NPV calculation

Year 1 2 3 4 5
  $000 $000 $000 $000 $000
Sales income 12,069 16,791 23,947 11,936  
Variable cost (5,491) (7,139) (9,720) (5,616)  
Contribution 6,578 9,652 14,227 6,320  
Fixed cost (1,100) (1,121) (1,155) (1,200)  
Taxable cash flow 5,478 8,531 13,072 5,120  
Taxation at 28%   (1,534) (2,389) (3,660) (1,434)
TAD tax benefits   1,400 1,050 788 2,362
After-tax cash flow 5,478 8,397 11,733 2,248 928
Discount at 10% 0.909 0.826 0.751 0.683 0.621
Present values 4,980 6,936 8,812 1,535 576

$000

PV of future cash flows        22,839

Initial investment                 (20,000)

ENPV                                     2,839

Comment

The probability that variable cost per unit will be $12.00 per unit or less is 80% and so the probability of a positive NPV is therefore at least 80%. However, the effect on the NPV of the variable cost increasing to $14.70 per unit must be investigated, as this may result in a negative NPV. The expected NPV is positive and so the investment project is likely to be acceptable on financial grounds.

Workings

Sales revenue

Year 1 2 3 4
Selling price ($/unit) 26.50 28.50 30.00 26.00
Inflated at 3.5% per year 27.43 30.53 33.26 29.84
Sales volume (000 units/year) 440 550 720 400
Sales income ($000/year) 12,069 16,791 23,947 11,936

Variable cost

Mean variable cost = ($10.80 × 0.45) + ($12.00 × 0.35) + ($14.70 × 0.20) = $12.00 per unit

Year 1 2 3 4
Variable cost ($/unit) 12.00 12.00 12.00 12.00
Inflated at 4% per year 12.48 12.98 13.50 14.04
Sales volume (000 units/year) 440 550 720 400
Variable cost ($000/year) 5,491 7,139 9,720 5,616

 

Year 1 2 3 4 1 2 3 4
TAD ($000) 5,000 3,750 2,813 8,437
Tax benefits at 28% ($000) 1,400 1,050 788 2,362*

* ($20m × 0.28) – 1,400 – 1,050 – 788 = $2,362,000

3 / 3

C. Critically discuss how risk can be considered in the investment appraisal process.

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Question 04 (Hebac Co)

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187. Hebac Co (Sep 16)

Hebac Co is preparing to launch a new product in a new market which is outside its current business operations. The company has undertaken market research and test marketing at a cost of $500,000, as a result of which it expects the new product to be successful. Hebac Co plans to charge a lower selling price initially and then increase the selling price on the assumption that the new product will establish itself in the new market. Forecast sales volumes, selling prices and variable costs are as follows:

Year 1 2 3 4
Sales volume (units/year) 200,000 800,000 900,000 400,000
Selling price ($/unit) 15 18 22 22
Variable costs ($/unit) 9 9 9 9

Selling price and variable cost are given here in current price terms before taking account of forecast selling price inflation of 4% per year and variable cost inflation of 5% per year.

Incremental fixed costs of $500,000 per year in current price terms would arise as a result of producing the new product. Fixed cost inflation of 8% per year is expected.

The initial investment cost of production equipment for the new product will be $2.5 million, payable at the start of the first year of operation. Production will cease at the end of four years because the new product is expected to have become obsolete due to new technology. The production equipment would have a scrap value at the end of four years of $125,000 in future value terms.

Investment in working capital of $1.5 million will be required at the start of the first year of operation. Working capital inflation of 6% per year is expected and working capital will be recovered in full at the end of four years.

Hebac Co pays corporation tax of 20% per year, with the tax liability being settled in the year in which it arises. The company can claim tax-allowable depreciation on a 25% reducing balance basis on the initial investment cost, adjusted in the final year of operation for a balancing allowance or charge. Hebac Co currently has a nominal after-tax weighted average cost of capital (WACC) of 12% and a real after-tax WACC of 8.5%. The company uses its current WACC as the discount rate for all investment projects.

Required:

(a) Calculate the net present value of the investment project in nominal terms and comment on its financial acceptability.

Year 1 2 3 4
  $000 $000 $000 $000
Sales revenue 3,120 15,576 22,275 10,296
Variable cost (1,890) (7,936) (9,378) (4,376)
Contribution 1,230 7,640 12,897 5,920
Fixed cost (540) (583) (630) (680)
Taxable cash flow 690 7,057 12,267 5,240
Taxation (138) (1,411) (2,453) (1,048)
TAD tax benefits 125 94 70 186
After-tax cash flow 677 5,740 9,884 4,378
Scrap value       125
Working capital (90) (95) (102) 1,787
Net cash flows 587 5,645 9,782 6,290
Discount at 12% 0.893 0.797 0.712 0.636
Present values 524 4,499 6,965 4,000

$000

PV of future cash flows        15,988

Initial investment                    4,000 (2.5m + 1.5m)

NPV                                      11,988

The NPV is strongly positive and so the project is financially acceptable.

Workings

Sales revenue

Year 1 2 3 4
Selling price ($/unit) 15 18 22 22
Inflated at 4% per year 15.60 19.47 24.75 25.74
Sales volume (000 units/year) 200 800 900 400
Sales revenue ($000/year) 3,120 15,576 22,275 10,296

Variable cost

Year 1 2 3 4
Variable cost ($/unit) 9 9 9 9
Inflated at 5% per year 9.45 9.92 10.42 10.94
Sales volume (000 units/year) 200 800 900 400
Variable cost ($000/year) 1,890 7,936 9,378 4,376

Tax benefits of tax-allowable depreciation

Year 1 2 3 4
  $000 $000 $000 $000
Tax-allowable depreciation 625 469 352 929
Tax benefit 125 94 70 186*

*((2,500 – 125) × 0.2) –-125 – 94 – 70 = $186,000

Working capital

Year 0 1 2 3 4
   $000 $000 $000 $000 $000
Working capital 1,500        
Inflated at 6% 1,590 1,685 1,787    
Incremental   90 95 102 1,787

2 / 2

B. Discuss how the capital asset pricing model can assist Hebac Co in making a better investment decision with respect to its new product launch.

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Question 05 (Pelta Co)

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188. Pelta Co (Sep/Dec 17) ]

The directors of Pelta Co are considering a planned investment project costing $25m, payable at the start of the first year of operation. The following information relates to the investment project:

  Year 1 Year 2 Year 3 Year 4
Sales volume (units/year) 520,000 624,000 717,000 788,000
Selling price ($/unit) 30.00 30.00 30.00 30.00
Variable costs ($/unit) 10.00 10.20 10.61 10.93
Fixed costs ($/year) 700,000 735,000 779,000 841,000

This information needs adjusting to take account of selling price inflation of 4% per year and variable cost inflation of 3% per year. The fixed costs, which are incremental and related to the investment project, are in nominal terms. The year 4 sales volume is expected to continue for the foreseeable future.

Pelta Co pays corporation tax of 30% one year in arrears. The company can claim tax-allowable depreciation on a 25% reducing balance basis.

The views of the directors of Pella Co are that all investment projects must be evaluated over four years of operations, with an assumed terminal value at the end of the fourth year of 5% of the initial investment cost. Both net present value and discounted payback must be used, with a maximum discounted payback period of two years. The real after-tax cost of capital of Pelta Co is 7% and its nominal after-tax cost of capital is 12%.

Required

(a) (i) Calculate the net present value of the planned investment project.

Year 1 2 3 4 5
  $’000 $’000 $’000 $’000 $’000
Sales income 16,224 20,248 24,196 27,655  
Variable costs (5,356) (6,752) (8,313) (9,694)  
Contribution 10,868 13,495 15,883 17,962  
Fixed costs (700) (735) (779) (841)  
Cash flows before tax 10,168 12,760 15,104 17,121  
Corporation tax   (3,050) (3,828) (4,531) (5,136)
TAD tax benefits   1,875 1,406 1,055 2,789
After-tax cash flow 10,168 11,585 12,682 13,644 (2,347)
Terminal value       1,250  
Project cash flow 10,168 11,585 12,682 14,894 (2,347)
Discount at 12% 0.893 0.797 0.712 0.636 0.567
Present values 9,080 9,233 9,030 9,473 (1,331)

PV of future cash flows ($000)    35,485

Initial investment ($000)            (25,000)

NPV                                             10,485

Workings

Year 1 2 3 4
Sales volume (units/year) 520,000 624,000 717,000 788,000
Selling price ($/unit) 30.00 30.00 30.00 30.00
Inflated by 4% per year 31.20 32.45 33.75 35.10
Income ($000/year) 16,224 20,248 24,196 27,655

 

Year 1 2 3 4
Sales volume (units/year) 520,000 624,000 717,000 788,000
Variable cost ($/unit) 10.00 10.20 10.61 10.93
Inflated by 3% per year 10.30 10.82 11.59 12.30
Total ($000/year) 5,356 6,752 8,313 9,694

 

Year 1 2 3 4
Fixed costs ($000 per year) 700 735 779 841

 

Year 1 2 3 4
TAD ($000 per year) 6,250 4,688 3,516 9,297
TAD benefits ($000/year ) 1,875 1,406 1,055 2,789

2 / 4

(ii) Calculate the discounted payback period of the planned investment project.

Year 1 2 3 4 5
  $000 $000 $000 $000 $000
Present values 9,080 9,233 9,030 9,473 (1,331)
Cumulative net present value (15,920)  (6,687) 2,343 11,815 10,485

Discounted payback (years)

Discounted payback occurs approximately 74% (6,687/9,030) through the third year ie the discounted payback period is about 2.7 years.

3 / 4

(b) Discuss the financial acceptability of the investment project.

4 / 4

C. Critically discuss the views of the directors on Pelta Co’s investment appraisal.

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Question 06 (Melanie Co)

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189. Melanie Co (Sept/Dec 18)

Melanie Co is considering the acquisition of a new machine with an operating life of three years. The new machine could be leased for three payments of $55,000, payable annually in advance.

Alternatively, the machine could be purchased for $160,000 using a bank loan at a cost of 8% per year. If the machine is purchased, Melanie Co will incur maintenance costs of $8,000 per year, payable at the end of each year of operation. The machine would have a residual value of $40,000 at the end of its three-year life.

Melanie Co’s production manager estimates that if maintenance routines were upgraded, the new machine could be operated for a period of four years with maintenance costs increasing to $12,000 per year, payable at the end of each year of operation. If operated for four years, the machine’s residual value would fall to $11,000. Taxation should be ignored.

Required

A. (i) Assuming that the new machine is operated for a three-year period, evaluate whether Melanie Co should use leasing or borrowing as a source of finance.

Time 0 1 2 3
  $ $ $ $
Lease        
Lease payment (55,000) (55,000) (55,000)  
PV factor at 8% 1.000 0.926 0.857  
Present value (55,000) (50,930) (47,135)  
Present value cost (153,065)      

 

Borrow and buy        
Initial cost (160,000)      
Residual value       40,000
Maintenance   (8,000) (8,000) (8,000)
Total (160,000) (8,000) (8,000) 32,000
PV factor at 8% 1.000 0.926 0.857 0.794
Present value (160,000) (7,408) (6,856) 25,408
Present value cost (148,856)      

As borrow and buy offers the cheapest present value cost the machine should be financed by borrowing.

2 / 3

(ii) Using a discount rate of 10%, calculate the equivalent annual cost of purchasing and operating the machine for both three years and four years, and recommend which replacement interval should be adopted.

3-year replacement cycle

  Year 0 Year 1 Year 2 Year 3 Year 4
  $ $ $ $ $
Initial cost (160,000)        
Residual value       40,000  
Maintenance   (8,000) (8,000) (8,000)  
Total (160,000) (8,000) (8,000) 32,000  
PV factor at 10% 1.000 0.909 0.826 0.751  
Present value (160,000) (7,272) (6,608) 24,032  
Present value cost (149,848)        

EAC 3-year cycle = PV cost/Annuity factor 3 years at 10%

EAC = –$149,848/2.487 (60,253)

4-year replacement cycle

Initial cost (160,000)        
Residual value         11,000
Maintenance   (12,000) (12,000) (12,000) (12,000)
Total (160,000) (12,000) (12,000) (12,000) (1,000)
PV factor at 10% 1.000 0.909 0.826 0.751 0.683
Present value (160,000) (10,908 ) (9,912) (9,012) (683)
Present value cost (190,515)        

EAC 4-year cycle = PV cost/Annuity factor 4 years at 10%

EAC = –$190,515/3.170 = (60,099)

Recommendation

The machine should be replaced every four years as the equivalent annual cost is lower.

3 / 3

B. Critically discuss FOUR reasons why NPV is regarded as superior to IRR as an investment appraisal technique.

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Question 07 (Hraxin Co)

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190. Hraxin Co (June 15 – Amended)

 Hraxin Co is appraising an investment project which has an expected life of four years and which will not be repeated. The initial investment, payable at the start of the first year of operation, is $5 million. Scrap value of $500,000 is expected to arise at the end of four years.

There is some uncertainty about what price can be charged for the units produced by the investment project, as this is expected to depend on the future state of the economy. The following forecast of selling prices and their probabilities has been prepared:

Future economic state Weak Medium Strong
Probability of future economic state 35% 50% 15%
Selling price in current price terms $25 per unit $30 per unit $35 per unit

These selling prices are expected to be subject to annual inflation of 4% per year, regardless of which economic state prevails in the future.

Forecast sales and production volumes, and total nominal variable costs, have already been forecast, as follows:

 Year 1 2 3 4
Sales and production (units) 150,000 250,000 400,000 300,000
 Nominal variable cost ($000 ) 2,385 4,200 7,080 5,730

Incremental overheads of $400,000 per year in current price terms will arise as a result of undertaking the investment project. A large proportion of these overheads relate to energy costs which are expected to increase sharply in the future because of energy supply shortages, so overhead inflation of 10% per year is expected.

The initial investment will attract tax-allowable depreciation on a straight-line basis over the four-year project life. The rate of corporation tax is 30% and tax liabilities are paid in the year in which they arise. Hraxin Co has traditionally used a nominal after-tax discount rate of 11% per year for investment appraisal.

Required:

A. Calculate the expected net present value of the investment project and comment on its financial acceptability.

Calculation of expected net present value

  1 2 3 4
  $000 $000 $000 $000
Revenue 4,524 7,843 13,048 10,179
Variable cost (2,385) (4,200) (7,080) (5,730)
Contribution 2,139 3,643 5,968 4,449
Overhead (440) (484) (532) (586)
Cash flow before tax 1,699 3,159 5,436 3,863
Tax (510) (948) (1,631) (1,159)
Depreciation benefits 338 338 338 338
Cash flow after tax 1,527 2,549 4,143 3,042
Scrap value       500
Project cash flow 1,527 2,549 4,143 3,542
Discount at 11% 0.901 0.812 0.731 0.659
Present values 1,376 2,070 3,029 2,334

$000

PV of future cash flows                       8,809

Initial investment                               (5,000)

Expected net present value (ENPV)   3,809

The investment project has a positive ENPV of $3,809,000. This is a mean or average NPV which will result from the project being repeated many times. However, as the project is not being repeated, the NPVs associated with each future economic state must be calculated as it is one of these NPVs which is expected to occur. The decision by management on the financial acceptability of the project will be based on these NPVs and the risk associated with each one.

Workings

Mean or average selling price = (25 × 0.35) + (30 × 0.5) + (35 × 0.15) = $29 per unit

Year 1 2 3 4
Inflated selling price ($ per unit) 30.16 31.37 32.62 33.93
Sales volume (units/year) 150,000 250,000 400,000 300,000
Sales revenue ($000/year) 4,524 7,843 13,048 10,179

 

Year 1 2 3 4
Inflated overhead ($000/year) 440 484 532 586

Total tax-allowable depreciation = 5,000,000 – 500,000 = $4,500,000

Annual tax-allowable depreciation = 4,500,000/4 = $1,125,000 per year

Annual cash flow from tax-allowable depreciation = 1,125,000 × 0.3 = $337,500 per year.

2 / 3

B. Critically discuss if sensitivity analysis will assist Hraxin Co in assessing the risk of the investment project.

3 / 3

C. Describe the process that would be undertaken to decide whether to lease or buy an asset for a long term investment.