Question Tag: Payback Period

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a) Pagsana Company plans to introduce a new product line for production of its local drink in Walewale. The company, therefore, decided to acquire either a semi-automated plant or an automated plant. The relevant data for the two proposed plants are as follows:

Required:
i) Select the appropriate plant on the basis of:

  • Payback Period (4 marks)
  • Net Present Value

(7 marks)

ii) Explain TWO (2) advantages of discounted cashflow method of investment appraisal. (4 marks)

a)i) Pay Back Period is defined as the period, usually expressed in years, which it takes
the cash flows from a capital investment project to equal the cash flows generate

(3 marks)

Decision:
Semi-automated plant is considered more suitable because of PBP of 4 years as against
5 years for an automated plant.
(1 marks)
Using Discounted Cash Flow, the NPV of the Plants


(3 marks)
Decision
It is advisable to select automated plant that gives a higher NPV though the capital
requirement of the plants differs. (1 mark)

ii)Advantages of Discounted Cash Flow

  • It uses the time value of money.
  • It uses the cost of capital.
  • Uses cash flow instead of accounting profit.
  • Considers the entire life of the project.

(Any 2 points @ 2 marks each = 4 marks)

The following mutually exclusive investment opportunities are being proposed to Kwame, who wants reliable cash receipts on an annual basis:

Proposal A:

Purchase of a commercial vehicle at the cost of GH¢90,000 that will generate weekly sales of GH¢800. The owner will incur the following annual expenses on the vehicle:

Expenses GH¢
Insurance 1,200
Tyres 10,400
Roadworthy 1,400
Routine maintenance 9,000

Note: Assume 52 weeks in a year.

Proposal B:

The repair of an unoccupied two-bedroom flat at the cost of GH¢90,000. The flat was bought by Kwame for GH¢650,000 three years ago. The monthly rental will be GH¢1,450 subject to 8% rent tax. The owner will also pay property tax of GH¢1,200 per year.

Required:
i) Advise Kwame which of the proposals is acceptable using the payback period method of investment appraisal. (8 marks)
ii) Explain TWO (2) factors that can affect the reliability of the cash flow of the transport business. (2 marks)
iii) State TWO (2) qualitative factors that may influence the decision to opt for proposal B. (2 marks)
iv) Explain TWO (2) reasons the NPV may be a better appraisal technique than the payback period. (3 marks)

i) Payback Period Calculation for Proposal A (Transport):

Receipts GH¢
Weekly sales (GH¢800 × 52 weeks) 41,600
Less: Direct expenses (22,000)
Net cash inflow 19,600

Payback Period for Proposal A = GH¢90,000 ÷ GH¢19,600 = 4.59 years

ii) Payback Period Calculation for Proposal B (Rental):

Receipts GH¢
Monthly rent (GH¢1,450 × 12 months) 17,400
Less: Rent tax (8%) (1,392)
Net rental income 16,008
Less: Property tax (1,200)
Net cash inflow 14,808

Payback Period for Proposal B = GH¢90,000 ÷ GH¢14,808 = 6.08 years

Advice: Based on the payback period method, Proposal A (Transport) is preferable with a payback period of 4.59 years compared to 6.08 years for Proposal B (Rental).

(Marks are evenly spread using ticks = 8 marks)

ii) Factors Affecting Reliability of Cash Flow in Transport Business:

  1. Fluctuations in Passenger Demand: Changes in customer demand due to external factors like competition, weather, or economic downturns can affect revenue.
  2. Maintenance and Fuel Costs: Any increase in direct operational costs, such as fuel prices or unexpected repairs, can reduce net cash inflows and affect the accuracy of the cash flow projections.

(2 marks)

iii) Qualitative Factors Influencing the Decision to Opt for Proposal B:

  1. Appreciation of Property Value: The property may increase in value over time, providing long-term capital gains beyond rental income.
  2. Risk Exposure: The rental business may have a lower risk profile compared to the transport business, which is exposed to higher operational risks like accidents or breakdowns.

(2 marks)

iv) Why NPV May Be Preferred Over Payback Period:

  1. Time Value of Money: NPV takes into account the time value of money, discounting future cash flows, whereas the payback period simply considers the time required to recover the initial investment.
  2. Comprehensive Evaluation: NPV considers all cash flows over the project’s life, ensuring that projects with longer-term profitability are not rejected solely because of a longer payback period.

a) Johnson & Co is a medium sized company that is engaged in delivery services. As a result
of the recent increase in the demand for services, the Managing Director (MD) is planning
for the future business performance. The MD plans to acquire a delivery van at the cost of
GH¢85,000. The expected net cash flow per year are as follows:

The Sales Manager has indicated to the MD that he will recoup his investment in less than four years and for that reason, it’s a good investment.

The Management Accountant has however drawn his attention to the fact that the manager has not factored time value of money and the cost of capital in his analysis. He could not however suggest the cost of capital since financial institutions are charging different interest rates.

Required:

i) Calculate the cost of capital when used would result in a break-even, when the useful life of the van is five years with residual value of GH¢8,500. (11 marks)

ii) Using TWO (2) points each, compare and contrast the payback method of investment appraisal and the discounted cash flow method.

(4 marks)

 

ii) Contrasting payback and discounted cash flow:

  • The payback period is the number of years necessary to recover funds invested in a project. When calculating the payback period, we don’t take time value of money into account. Discounted cash flow takes into account time value of money.
  • For a conventional project, payback period is always lower than discounted payback period. It’s because the calculation of the discounted payback period takes into account the present value of future cash inflows. So, based on this criterion, it’s going to take longer before the original investment is recovered.

Comparing payback and discounted cash flow

  • Both payback period and discounted payback period ignore cash flows occurring after recovering the original investment.
  • The payback period and the discounted payback period are measures that allow us to assess in how many years the original investment will pay back.
  • We prefer investment A to investment B if (discounted) payback period for investment A is lower than (discounted) payback period for investment B.

 

a) Bee Ltd manufactures high-quality mobile phones for its local market. Due to less competition, Bee Ltd sales have grown significantly over the past few years and are expected to grow. Bee Ltd is planning to launch a new model, ‘Ohenewa’.

The company has already spent GH¢1 million on Research and Development and will require a further investment of GH¢5.5 million in production equipment. This cost excludes the GH¢1.1 million installation fee. The project has a life span of five years. In the end, the equipment will have a residual value of GH¢0.6 million. Sales and production of Ohenewa over its lifecycle are expected to be:

Year Units
1 6,500
2 7,500
3 8,000
4 7,800
5 7,000

The selling price in Year 1 and Year 2 will be GH¢750 per unit. However, the selling price will be reduced to GH¢600 per unit in Year 3 and will remain at this level for the remainder of the project. The variable cost as a percentage of sales is 55% over the entire product lifecycle. The fixed overhead, including depreciation cost expected to be incurred directly due to increasing the production capacity, is GH¢2 million per annum.

Other information:

  • A cost of capital of 12% per annum is used to evaluate projects of this type.
  • Bee Ltd has a history of accepting similar projects which pay back within three years.
  • Ignore inflation and taxation.

Required:
i) Calculate the Payback Period for the Ohenewa project. (10 marks)
ii) Evaluate the acceptability of the project based on the calculation in i) above. (2 marks)

i) Payback Period Calculation:

Year Net Cash Flow (GH¢) Cumulative Cash Flow (GH¢)
0 (6,600,000) (6,600,000)
1 1,393,750 (5,206,250)
2 1,731,250 (3,475,000)
3 1,360,000 (2,115,000)
4 1,306,000 (809,000)
5 1,690,000 881,000

Payback Period = 4 years + 809,0001,690,000×12\frac{809,000}{1,690,000} \times 12 months = 4 years 5 months
(10 marks)

ii) Evaluation:
The project should be rejected as the payback period of 4 years 5 months is more than the company’s acceptable payback period of three years. (2 marks)

Workings:

  • Annual Depreciation:

Depreciation=6,600,000−600,0005=GH¢1,200,000\text{Depreciation} = \frac{6,600,000 – 600,000}{5} = GH¢1,200,000

  • Net Cash Flows:
    • Year 1: (6,500×GH¢750)×0.45−GH¢800,000=GH¢1,393,750(6,500 \times GH¢750) \times 0.45 – GH¢800,000 = GH¢1,393,750
    • Year 2: (7,500×GH¢750)×0.45−GH¢800,000=GH¢1,731,250(7,500 \times GH¢750) \times 0.45 – GH¢800,000 = GH¢1,731,250
    • Year 3: (8,000×GH¢600)×0.45−GH¢800,000=GH¢1,360,000(8,000 \times GH¢600) \times 0.45 – GH¢800,000 = GH¢1,360,000
    • Year 4: (7,800×GH¢600)×0.45−GH¢800,000=GH¢1,306,000(7,800 \times GH¢600) \times 0.45 – GH¢800,000 = GH¢1,306,000
    • Year 5: (7,000×GH¢600)×0.45+600,000−GH¢800,000=GH¢1,690,000(7,000 \times GH¢600) \times 0.45 + 600,000 – GH¢800,000 = GH¢1,690,000

It is said that of all the capital investment evaluation approaches, the Payback (PB) and Accounting Rate of Return (ARR) methods are widely used in practice. But these methods are not without limitations.

Required:

i) State TWO justifications of Payback Period and ONE justification of ARR for their popularity in practice as investment appraisal techniques.
(3 marks)

ii) Outline TWO limitations each for Payback Period and ARR as investment appraisal techniques.
(4 marks)

 

i) Justifications for the popularity of Payback Period:

  1. Liquidity Constraints: The Payback Period is considered useful when firms face liquidity constraints and require a fast return on their investments.
  2. Simple Screening Device: It serves as a simple first-level screening device that identifies projects that should be subjected to more rigorous investigations.

Justification for the popularity of ARR:

  1. Managerial Performance Measure: ARR is a widely used financial measure of managerial performance, so managers are likely to be interested in how any new investment contributes to the business unit’s overall accounting rate of return.

ii) Limitations of Payback Period:

  1. Ignores Time Value of Money: The Payback Period method ignores the time value of money, making it less accurate for long-term investments.
  2. Ignores Cash Flows After Payback: It also ignores any cash flows that are earned after the payback period, potentially missing out on the overall profitability of the investment.

Limitations of ARR:

  1. Ignores Time Value of Money: Similar to the Payback Period, ARR fails to take into consideration the time value of money.
  2. Relies on Percentage Return: ARR relies on a percentage return rather than an absolute value, which may not accurately reflect the true profitability of an investment.

Sabir Company is considering whether to invest in a project whose details are as follows.
The project will involve the purchase of equipment costing GH¢2,000,000. The equipment will be used to produce a range of products for which the following estimates have been made.

Incremental fixed costs are GH¢1,200,000 per annum. The sales prices allow for expected price increases over the period. However, cost estimates are based on current costs and do not allow for expected inflation in costs. Inflation is expected to be 3% per year for variable costs and 4% per year for fixed costs. The incremental fixed costs are all cash expenditure items. Tax on profits is at the rate of 30%, and tax is payable in the same year in which the liability arises.

Sabir Company uses a four-year project appraisal period, but it is expected that the equipment will continue to be operational and in use for several years after the end of the first four-year period.

The company’s cost of capital for investment appraisal purposes is 10%. Capital projects are expected to pay back within two years on a non-discounted basis and within three years on a discounted basis. Tax allowable depreciation will be available on the equipment at the rate of 25% per year on a reducing balance basis. Any balancing allowance or balancing charge is not attributed to a project unless the asset is actually disposed of at the end of the project period.

Required:

a) Calculate the net present value (NPV) of the project.
(11 marks)

b) To the nearest month, calculate the non-discounted payback period and the discounted payback period.
(4 marks)

c) Explain the meaning of market volatility in financial markets.
(3 marks)

d) Explain the difference between a bull and bear market.
(2 marks)

a) Workings
Year Written down value


Total Present Value of Net Cash Flows: GH¢2,786,000
Year 0 Capital Outlay: GH¢2,000,000
Project Four-Year NPV: GH¢786,000

b) Payback and Discounted Payback

Year Cash Flow (GH¢’000) Cumulative Cash Flow (GH¢’000) Discounted Cash Flow (GH¢’000) Cumulative Discounted Cash Flow (GH¢’000)
0 (2,000) (2,000) (2,000) (2,000)
1 279 (1,721) 254 (1,746)
2 974 (826) 805 (1,007)
3 1,546 720 1,161 154
4 828 1,548 566 720

Non-discounted Payback Period: 2 years + [(826/1,546) × 12] = 2 years 6 months
(2 marks)

Discounted Payback Period: 2 years + [(1,007/1,161) × 12] = 2 years 10 months
(2 marks)

c) Market Volatility Explanation:

Market volatility in financial markets is a measure of the extent to which the price of a financial security (such as a share’s market price), or a market as a whole, or an interest rate, or a currency, or a commodity changes over time. High volatility means rapid and large changes in a price or rate over a short period of time. Low volatility means smaller and less frequent price changes.

Volatility refers to price movements in both directions, up and down. If prices move over time always in the same direction (either up or down, but not both), this does not mean high volatility. Volatility implies uncertainty about the way that prices will move next, and by how much. High volatility creates high financial risk. Investors will want higher returns to invest in financial instruments where price volatility is high.
(3 marks)

d) Bull and Bear Markets Explanation:

In a bull market, prices on the whole move upwards continually over time. For example, in a bull stock market, share prices on the whole continue to rise over time.

In a bear market, prices on the whole move downwards continually over time. For example, in a bear stock market, share prices on the whole continue to fall over time.
(2 marks)

 

a) Payback method refers to the period of time it takes for the cash flows to cover the initial cost of investment or recoup the initial cost of investment. The period is usually calculated in years.

Required:
Identify TWO advantages and TWO disadvantages of using the payback method in investment appraisal.
(4 marks)

b) DÉCOR Ltd is analyzing the purchase of a new machine to produce product Z. The machine is expected to cost GH¢2,000,000. Production and sales of product Z are forecast as follows:

Year 1 2 3 4
Production & Sales (units/year) 70,000 106,000 150,000 72,000

The current selling price is GH¢30 per unit and is expected to increase by 5% a year. The current variable cost is GH¢18 per unit and is expected to increase by 6% per year. Fixed costs will remain the same, but an increase in working capital is required. Analysis of historical data of the levels of working capital of product Z indicates that, at the start of each year, investment in working capital will need to be 10% of sales revenue of that year.

The company pays tax at 25% per year in the year in which taxable profit occurs. The tax liability is reduced by the capital allowance on the machinery, and DÉCOR Ltd can claim on a straight-line basis over the four-year life of the proposed investment (capital allowance rate of 25% per annum). The new machine will have zero scrap value at the end of the four years. The cost of capital is 15% per year.

Required:
Calculate the Net Present Value (NPV) of the proposed investment and advise whether the proposed investment should be undertaken.
(11 marks)

c) An American company sells goods to a Ghanaian buyer for US$280,000 when the exchange rate is $1 = GH¢4.20. The Ghanaian buyer is allowed three months’ credit, and when the American company eventually receives the US dollars three months later and exchanges them for dollars, the exchange rate has moved to $1 = GH¢4.60.

Required:
i) What was the foreign exchange loss to the Ghanaian buyer?
(3 marks)

ii) Explain currency risk in relation to the above.
(2 marks)

iii) Explain transaction risk in relation to the above.
(2 marks)

iv) What will be the effect of the above on the company’s trading profits?
(3 marks)

a) Advantages and Disadvantages of Payback Method

Advantages:

  1. Simplicity: The payback method is easy to calculate and understand, making it accessible to managers without extensive financial expertise.
  2. Liquidity Focus: It provides a quick estimate of the liquidity risk by showing how quickly an investment can recover its initial cost.

Disadvantages:

  1. Ignores Time Value of Money: The method does not account for the time value of money, meaning future cash flows are treated as equally valuable as immediate ones.
  2. Ignores Cash Flows After Payback: It only considers the period until the initial investment is recovered and disregards any cash flows that occur after the payback period.

b) NPV Calculation for DÉCOR Ltd’s Proposed Investment

Revenue Calculations:

Year 1 2 3 4
Units Sold 70,000 106,000 150,000 72,000
Selling Price (GH¢) 30 31.5 33.08 34.73
Sales Revenue (GH¢) 2,100,000 3,339,000 4,962,000 2,500,560

Variable Costs Calculations:

Year 1 2 3 4
Units Sold 70,000 106,000 150,000 72,000
Variable Cost (GH¢) 18 19.08 20.22 21.44
Total Variable Costs (GH¢) 1,260,000 2,022,480 3,033,000 1,543,680

Net Cash Flow Calculations:

Year 0 1 2 3 4
Sales Revenue (GH¢) 2,100,000 3,339,000 4,962,000 2,500,560
Variable Costs (GH¢) (1,260,000) (2,022,480) (3,033,000) (1,543,680)
Fixed Costs (GH¢)
Contribution (GH¢) 840,000 1,316,520 1,929,000 956,880
Capital Allowance (GH¢) (2,000,000) 500,000 500,000 500,000 500,000
Taxable Profit (GH¢) 340,000 816,520 1,429,000 456,880
Tax @ 25% (GH¢) (85,000) (204,130) (357,250) (114,220)
Net Profit After Tax (GH¢) 255,000 612,390 1,071,750 342,660
Add: Capital Allowance (GH¢) 500,000 500,000 500,000 500,000
Net Cash Flows (GH¢) (2,000,000) 755,000 1,112,390 1,571,750 842,660
Working Capital Requirement (GH¢) (210,000) (123,900) (162,300) 246,144 250,056
Net Cash Flow After WC (GH¢) (2,210,000) 631,100 950,090 1,817,894 1,092,716
Discount Factor @ 15% 1.000 0.8696 0.7561 0.6575 0.5718
Present Value (GH¢) (2,210,000) 548,805 718,363 1,195,265 624,815

Net Present Value (NPV): GH¢877,248
Decision: The project should be undertaken since the NPV is positive, indicating an addition to shareholder value.

c) Currency Risk Analysis

i) Foreign Exchange Loss to the Ghanaian Buyer: The original expectation was to pay:

US$280,000×GH¢4.2=GH¢1,176,000

However, the payment after the exchange rate change was:

US$280,000×GH¢4.6=GH¢1,288,000

Foreign Exchange Loss = GH¢112,000

ii) Currency Risk Explanation: Currency risk arises from exposure to the consequences of a rise or fall in an exchange rate. Here, the Ghanaian buyer was exposed to the risk of a fall in the value of the cedi, leading to a higher payment in cedi terms.

iii) Transaction Risk Explanation: Transaction risk occurs when a financial transaction is settled at a future date, exposing the company to potential exchange rate fluctuations. Here, the risk lasted from when the goods were sold on credit until the time of payment.

iv) Effect on Company’s Trading Profits: Trading profits can be significantly affected by currency movements. In this case, the foreign exchange loss of GH¢112,000 reduces the company’s profit, highlighting the impact of exchange rate volatility on financial performance.

In investment appraisal, many methods are available for use by finance and project professionals. One of these methods is the Payback period, but stakeholders have often raised questions on the usefulness of this method due to a number of limitations inherent in the use of the method.

Required:
Explain FOUR (4) limitations of using the Payback period method in investment appraisals. (5 marks)

The limitations of using the Payback period method in investment appraisals include:

  1. Ignores the time value of money: The Payback period method does not consider the time value of money, which means it treats all cash flows as if they occur at the same time. This can lead to misleading conclusions about the value of future cash flows.
  2. Does not measure profitability: The method focuses only on how quickly an investment can recoup its initial cost, without considering the overall profitability of the project. Projects that generate higher returns in the long run may be overlooked if they have a longer payback period.
  3. Arbitrary choice of period: The decision on what constitutes an acceptable payback period is often arbitrary and may not align with the strategic objectives of the company or the economic realities of the project.
  4. Ignores cash flows after the payback period: The method does not take into account any cash flows that occur after the payback period. As a result, it may favor projects with quick returns but lower total returns, ignoring projects that could be more profitable in the long term.

(Marks allocation: 4 points @ 1.25 marks each = 5 marks)

a) Toolo Ghana Ltd was recently formed as a special purpose vehicle (SPV) to provide a secondary market for investors involved in the domestic debt exchange programme who want to sell off their holdings for immediate cash.

The SPV was embarking on this special initiative as a one-off project; The company in year zero will acquire a total of GH¢500 million worth of bonds from investors and pay for all at the same time for cash.

Based on the projections, the expected cash inflows from the bonds are as follows:

  • Year 1 = GH¢100 million
  • Year 2 = Year 1 cash flows + 20% increase
  • Year 3 = Year 2 cash flows + 15% increase
  • Year 4 = Year 3 cash flows + 25% increase
  • Year 5 = Year 4 cash flows + 20% increase

A special investment in systems and software, computers and other fixed assets is GH¢6 million in year zero and tax deductible depreciation is on a straight-line basis with a scrap value of GH¢1 million. Salaries and wages and other administrative expenses will be GH¢1 million in year 1 and grow at 15% per annum on the previous year’s figure. Rent is also determined at GH¢0.5 million in year 1 and growing by GH¢100,000 each year.

The internal cost of capital is 22% whilst corporate tax rate is 25%.

Required:

i) Calculate the Net Present Value (NPV) of this project and advise whether Toolo Ltd should embark on the project.
(12 marks)

ii) Explain TWO (2) reasons why NPV is preferred to payback period.
(3 marks)

b) Soso Ghana Ltd is considering investing in project Sankofa which has been appraised to have an expected return of 25% per annum. The project’s beta is 1.9 and the risk-free interest rate is 14% per annum, which is 9% below the average return on equity stocks on the market.

Required:

Calculate the required return on project Sankofa and advise Soso Ghana Ltd whether it should invest in the project.
(5 marks)

 

 

NPV = (506,000)+291,760 = (214239.9)

Decision: NPV is negative and the initiative should not be accepted.

 

 

ii) Reasons why NPV is preferred to payback period

  • Considers time value of money
  • considers only cash flows and not profit
  • Considers cash flows after payback period
  •  Shows magnitude increase in shareholder value

b) Computation of RRR
Expected return = 25%
Return (r ) = rf + B(Rm – rf)

Rf = 14%
B=1.9
Rm = 14% +9% = 23%
r = 14% + 1.9 (23% -14%)
= 31.1%

Decision: Since the required return of 31.1% is higher than the expected return of
25% for project Sankofa, the project should be avoided.

ASANTA Ghana Ltd is considering investing in the following projects which are considered mutually exclusive:

PROJECT GO PROJECT COME
Annual cash inflows GH¢1,000,000 GH¢2,000,000
Cost of Machine GH¢2,500,000 GH¢6,000,000
Scrap value of Machine GH¢250,000 GH¢1,000,000
Expected life of the Project 5 years 5 years

ASANTA Ghana Ltd uses the straight line method of depreciation. However, tax-allowable depreciation is 30% on a straight-line basis. The cost of capital for the company is 20% per annum.

Required:

  1. Calculate the Accounting Rate of Return (ARR) for each project. (4 marks)
  2. Calculate the Net Present Value (NPV) for each project. (4 marks)
  3. Compute the Internal Rate of Return (IRR) for each project. (4 marks)
  4. Compute the Payback period for each project. (3 marks)

(Note: In each of the above, advise the Company on which of the projects to implement or undertake.)