Question Tag: NPV Calculation

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  • 10 Marks

MA – May 2017 – L2 – Q1a – Introduction to capital budgeting,

Calculate the break-even rate for a taxi service investment considering a 5% annual cash flow increase over five years.

Kwame, after his National Service and with no hope of securing a job in the formal sector, has decided to run a taxi service. The following forecast has been made for the operation of a service between Abisim and Sunyani:

  1. Revenue totaling GH¢300 a week for 52 weeks in a year. This is net of fuel and other variable costs.
  2. Tyres: four pieces for a year at GH¢120 per unit.
  3. Maintenance and servicing: GH¢120 per month.
  4. Salaries: GH¢3,000 per year.
  5. Insurance: GH¢350 per year.

The net cash flow will increase at 5% per annum for the next five years due to inflation. The cost of the vehicle is estimated at GH¢28,000. The project appears quite profitable based on the NPV criteria using the Government policy rate of 26%. However, the banks are offering rates far higher than the policy rate.

Required:

You are to calculate the break-even rate for the project.

(10 marks)

The guiding rate is the internal rate of return (IRR). Any borrowing rate greater than that will render the venture unprofitable.

Calculation of cash flow:

Item Amount (GH¢)
Receipt (300×52) 15,600.00
Less:
Tyres 480.00
Maintenance (120×12) 1,440.00
Salaries 3,000.00
Insurance 350.00
Net Cash Flow 10,330.00

Calculation of NPV at different rates:

Year Cash Flow (GH¢) DF (26%) DCF (GH¢) DF (30%) DCF (GH¢)
0 (28,000.00) 1.00 (28,000) 1.00 (28,000)
1 10,330 0.794 8,202.02 0.769 7,943.77
2 10,846.5 0.630 6,833.30 0.592 6,421.13
3 11,388.83 0.500 5,694.41 0.455 5,181.92
4 11,958.27 0.397 4,747.43 0.350 4,185.40
5 12,556.18 0.315 3,955.20 0.269 3,377.61
NPV 1,432.36 (890.17)

IRR Calculation:

IRR = 26% + (1432.36 ÷ 2322.53) × 4
IRR = 26% + 2.47% = 28.47%

  • 20 Marks

FM – DEC 2023 – L2 – Q4 – Capital rationing | Introduction to Investment Appraisal | Sources of finance: debt

Explanation of capital rationing concepts, NPV and profitability index calculations, and factors influencing debt finance decisions.

a) In periods of difficult global financial environment, raising of capital is a challenge necessitating the need for prudent and best use of scarce capital for projects.

Required:
i) Explain the term capital rationing. (2 marks)
ii) Distinguish between soft capital rationing and hard capital rationing giving an example each. (3 marks)

b) Akonta Ghana Ltd has excess funds of GH¢200 million and is looking for attractive investment opportunities that will yield a return of 15% per annum or better to deploy the funds. An extract from a Feasibility report submitted by a team of investment and project experts is as follows:

Project Initial Investment Required (GH¢) Constant Annual Cash Inflow (GH¢) Project Life (Years)
A 80,000,000 36,000,000 4
B 40,000,000 23,000,000 3
C 78,000,000 30,000,000 5
D 40,000,000 20,000,000 4
E 40,000,000 22,000,000 3

The cash flows per project are constant for the life span of each project and each project is divisible for the purpose of capital allocation.

Required:
i) Calculate the Net Present Values (NPVs) of each project. (7 marks)
ii) Rank the projects using Profitability Index and allocate the GH¢200 million among the projects. (3 marks)

c) There are many sources of debt finance available to a company which has viable and profitable investment opportunities to utilise the funds. It is, however, very important for the Finance Manager to do a thorough work before deciding the type and source of debt finance to tap into.

Required:
Explain THREE (3) factors a Finance Manager should consider when deciding the type of debt finance to raise. (5 marks)

a)
i) Capital Rationing

Capital rationing refers to the allocation of scarce or restricted capital among acceptable projects based on the most profitable and efficient use of the capital. For example, if a company has a total available capital of GH¢1 million to invest among competing profitable projects whose total capital investment required exceeds GH¢1 million, the company will have to allocate or ration the capital in order of best values or profitability. (2 marks)

ii) Soft and Hard Capital Rationing

  • Soft Capital Rationing is the situation where the constraint on raising and using capital is internally driven by policies and decisions. For example, a company with past poor return on investment compared to initial projections may implement internal tightening of capital allocations and raising of returns expectation on projects.
  • Hard Capital Rationing occurs when a company faces constraints in raising capital due to external factors such as market conditions or investor reluctance. An example would be a company unable to raise additional funds through equity due to unfavorable stock market conditions.

(1.5 marks each = 3 marks)

b)
i) Net Present Value (NPV) Calculations

Project Initial Investment Outlay (GH¢) Constant Annual Cash flows (GH¢) Annuity Discount Factor @ 15% Present Value (GH¢) Net Present Value (GH¢)
A 80,000,000 36,000,000 2.855 102,780,000 22,780,000
B 40,000,000 23,000,000 2.283 52,509,000 12,509,000
C 78,000,000 30,000,000 3.352 100,560,000 22,560,000
D 40,000,000 20,000,000 2.855 57,100,000 17,100,000
E 40,000,000 22,000,000 2.283 50,226,000 10,226,000

(7 marks)

ii) Profitability Index Ranking and Allocation

Project Initial Investment Outlay (GH¢) Present Value (GH¢) Profitability Index (PI) Rank Amount Allocated (GH¢)
D 40,000,000 57,100,000 1.43 1 40,000,000
B 40,000,000 52,509,000 1.31 2 40,000,000
C 78,000,000 100,560,000 1.29 3 78,000,000
A 80,000,000 102,780,000 1.28 4 42,000,000
E 40,000,000 50,226,000 1.26 5 0

Total Allocated: GH¢200,000,000

(3 marks)

c) Factors to Consider When Deciding the Type of Debt Finance

  • Cost: This includes the interest rate, issuance costs, and any other fees associated with the debt. The cost of debt finance can significantly affect the viability and profitability of the projects being financed. The tax implications and the basis of interest rates (fixed vs. variable) are also critical considerations.
  • Purpose and Maturity: The purpose of the finance will determine the maturity of the debt. Long-term investments like capital expenditure should be financed with long-term debt, while working capital requirements should be financed with short-term debt instruments like overdrafts.
  • Gearing Level/Financial Risk: The company’s existing level of debt relative to equity (gearing) and the associated financial risk must be evaluated. High gearing may limit the company’s ability to raise additional debt and may expose the company to higher financial risk.
  • Flexibility: The terms and conditions and covenants that go with the facility
    should be reviewed and ensure that they friendly and will not squeeze the
    company unfavourably. Ability to restructure and renegotiate during difficult
    times should be considered
  • Control: Will the new source lead to dilution of control of existing shareholder
    and will they be happy? Will any debt put a lot of restrictions on shareholder and
    dividend payment and will they be happy? All should be considered and
    analysed. Will the debt providers exercise a; lot of control and interference in the
    management?
  • Security/Collateral: Providing collateral or security for the debt is also crucial and
    should be carefully considered. The bigger and longer the debt tenor the more the
    requirement to provide security or Collateral.

(5 marks)

  • 20 Marks

FM – AUG 2022 – L2 – Q4 – Capital structure

Evaluates the decision between leasing and buying, calculates NPV, and explains the benefits of listing on the stock market.

a) Lease or Buy decision could be a tough call to make, especially considering that different industries benefit more than others from leasing or buying outright depending on the specific needs of that sector.

Freda Automobile (Freda), an emerging automobile company has taken a decision to provide a new Toyota Land Cruiser for its Chief Executive Officer (CEO). The company is considering whether to buy or lease. The Toyota Land Cruiser has a useful life of six years and will cost GH¢1,000,000 to buy and will be funded with a bank loan. The Finance Director provided the borrowing interest rate for the loan at 22% per annum. The annual repairs and maintenance cost when the V8 is bought is GH¢18,000. The corporate tax rate is currently 25% paid in the same year the profit is made. The capital allowance on the V8 is 25% per annum on reducing balance basis.

Alternatively, the Toyota Land Cruiser could be leased at a rental cost of GH¢250,000 per annum for six years payable at the beginning of each year.

Required:
i) Explain TWO (2) reasons why Freda will prefer leasing option to outright buy. (4 marks)
ii) Calculate the Net Present Value (NPV) for the buy option. (5 marks)
iii) Calculate the Net Present Value (NPV) for the lease option. (4 marks)
iv) Based on your computations in ii) and iii) above, advise management which option should be considered. (2 marks)

b) The Ghana Stock Exchange (GSE) market has recently been intensifying its public education for Ghanaian companies to list on the stock market to raise the needed capital for expansion and growth. You have been approached by owners of Asafo Ghana Ltd who have expressed interest in getting listed on the stock market but have limited knowledge on what they stand to benefit by listing their company on the market.

Required:
Explain FOUR (4) advantages Asafo Ghana Ltd could derive from listing on GSE. (5 marks)

a)
i) Reasons why leasing is preferred to buying:

  • Lower Initial Cash Outlay: Leasing prevents high initial cash outlay upfront compared to buying, which can be beneficial for cash flow management, especially for a growing company like Freda Automobile.
  • Risk of Obsolescence: Leasing helps reduce the risks of holding obsolete equipment since it is owned by the lessor, especially in fast-changing industries where assets may quickly become outdated.
  • Maintenance Costs: Depending on the lease terms, leasing can transfer the cost of maintenance to the lessor, further reducing the financial burden on the lessee.
  • Credit Score Consideration: Leasing may provide a better option to access and use assets or equipment if the company’s credit score is not strong enough to secure a favorable loan for purchasing the asset.

ii) Buying Option – Net Present Value (NPV) Calculation:

Computation of Capital Allowance @ 25%

Tax benefits @ 25%

EVALUATION
Cost of borrowing 22%
Cost of borrowing net of tax benefit = 75% x22% = 16.5%

NPV =(1,000,000)+42,042+24,597+13,686+6,987+2,926+18331
= (891,431)

iii) Leasing Option

NPV= (250,000)+(160,875)+(138,188)+(118,500)+(101,813)+(87,375)+25000
= (831,750)

Alternative
Annuity factor for 5 years = 3.2365
Year 1-5 (187,500) x 3.236 = (606,750)
Year 6 62,500 x 0.400 = 25,000
Year 0 x 1 = (250,000)
(831,750)

iv) Based on the analysis above the LEASE OPTION should be taken to provide the
V8 for the CEO.

b) Advantages of listing on the Ghana Stock Exchange (GSE):

  • Access to Long-Term Capital: Listing on the GSE allows Asafo Ghana Ltd to raise long-term capital through the issuance of shares, which can be used for expansion and growth.
  • Enhanced Corporate Image: Being listed on the stock exchange can enhance the company’s brand, status, and prestige, increasing its visibility and reputation.
  • Increased Liquidity: Listing provides shareholders with liquidity, as they can easily buy or sell shares in the open market.
  • Tax Incentives: Listed companies often benefit from tax incentives provided by the government, reducing the overall tax burden.
  • Transferability of shares provides access to liquidity to the shares
  • Realization of investment proceeds and public trading enhances valuation of
    shares
  • Provision of incentives to employees and investing public

 

  • 20 Marks

FM – MAR 2024 – L2 – Q4 – Introduction to investment appraisal

This question involves calculating the NPV of a project, advising on whether to undertake the project, and explaining why NPV is preferred over the payback period as an investment appraisal method.

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.

  • 10 Marks

FM – NOV 2015 – L2 – Q3b – Introduction to financial management

Calculate the NPV for God is King Ltd's project and advise management on whether to accept or reject the project.

God is King Ltd has been printing all its magazines from Dubai due to the comparative cost advantage. The company is considering establishing its own printing department, and the R&D team has identified a printing machine which will meet the quality and cost specifications of God is King Ltd. The machine also has the capacity to print to meet the market needs of the company. The machine, which has a useful life of 5 years, will cost GHS800,000 and immediate installation cost will be GHS50,000. Fixed cost for maintaining the machine will be 170,000 per annum over the machine’s useful life and additional working capital of GHS30,000 will be introduced in year 2. The use of this machine will generate a contribution of GHS500,000 per annum for five (5) years. Corporate income tax rate, payable in arrears, is 25% and the company’s after-tax cost of capital is 20%. No capital allowance is permitted.

Required:
Calculate the NPV for the project and advise management on whether to accept or reject the project. (10 marks)

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