$\text{NPV} = \sum \frac{CFAT_t}{(1+k)^t} - \text{Initial outlay}, \quad k = 12\%$

(a) Net present value

PVIF at 12%: year 1 = 0.8929, year 2 = 0.7972, year 3 = 0.7118, year 4 = 0.6355, year 5 = 0.5674.

Project A

$\text{NPV}_A = 5{,}96{,}508 - 4{,}00{,}000 = \text{Rs } 1{,}96{,}508$

Project B (equal inflows, so use the annuity factor)

$\text{PVIFA}_{12\%,5} = \frac{1-(1.12)^{-5}}{0.12} = 3.6048$

$\text{PV of inflows} = 1{,}64{,}000 \times 3.6048 = \text{Rs } 5{,}91{,}183$

$\text{NPV}_B = 5{,}91{,}183 - 4{,}00{,}000 = \text{Rs } 1{,}91{,}183$

(b) More profitable project

Project A is more profitable because its NPV (Rs 1,96,508) is higher than that of Project B (Rs 1,91,183) by about Rs 5,325, so it adds more to the wealth of the firm. If the projects are mutually exclusive, select A; if independent, both are acceptable as both NPVs are positive.

Given:

• Selling price per unit (SP) = Rs 60
• Variable cost per unit (VC) = Rs 40
• Break-even point (BEP) = 8,000 units

Contribution per unit: $C = SP - VC = 60 - 40 = Rs\ 20$

1. Break-even point in rupees: $\text{BEP (Rs)} = \text{BEP units} \times SP$ $= 8{,}000 \times 60 = Rs\ 4{,}80{,}000$

2. Operating fixed cost: At break-even point, total contribution equals fixed cost. $\text{Fixed cost} = \text{BEP units} \times \text{Contribution per unit}$ $= 8{,}000 \times 20 = Rs\ 1{,}60{,}000$

Answer:

• Break-even point in rupees = Rs 4,80,000
• Operating fixed cost = Rs 1,60,000

Given:

• Selling price per unit (S) = Rs 40
• Variable cost per unit (V) = Rs 25
• Break-even point in units = 10,000 units

Required:

1. Break-even point in rupees
2. Fixed cost

Solution:

Contribution per unit = S − V
= Rs 40 − Rs 25
= Rs 15 per unit

1. Break-even point in rupees:

$BEP \text{ (Rs)} = BEP \text{ (units)} \times \text{Selling price per unit}$

$= 10,000 \times 40$

$= \text{Rs } 4,00,000$

2. Fixed cost:

$BEP \text{ (units)} = \frac{\text{Fixed Cost}}{\text{Contribution per unit}}$

So,

$\text{Fixed Cost} = BEP \text{ (units)} \times \text{Contribution per unit}$

$= 10,000 \times 15$

$= \text{Rs } 1,50,000$

Answer:

• Break-even point in rupees = Rs 4,00,000
• Fixed cost = Rs 1,50,000

(a) Contribution margin (P/V) ratio

At the break-even point, contribution equals fixed cost.

$\text{CM ratio} = \frac{\text{Fixed cost}}{\text{BEP (Rs)}} \times 100 = \frac{1{,}20{,}000}{4{,}80{,}000} \times 100 = \mathbf{25\%}$

(b) Selling price per unit

$\text{CM ratio} = \frac{S - V}{S} \;\Rightarrow\; 0.25 = \frac{S - 3}{S} \;\Rightarrow\; 0.75S = 3 \;\Rightarrow\; S = \textbf{Rs } 4$

Check: Contribution per unit = Re 1; BEP units = 1,20,000 ÷ 1 = 1,20,000; BEP sales = 1,20,000 × 4 = Rs 4,80,000.

Features of Investment Decision

Investment decision (also called capital budgeting decision) refers to the decision relating to the selection of long-term assets or projects in which funds are invested with the expectation of earning returns over a period of time. Its main features are explained below:

1. Long-term effect: The investment decision affects the earning capacity and growth of the firm over the long run. Once funds are invested in fixed assets, they are blocked for years and cannot be easily reversed without heavy loss. Hence, such decisions have a lasting impact on the firm's profitability and value.

2. Large amount of funds involved: Investment decisions require a huge amount of funds compared to working capital decisions. For example, setting up a new plant, purchasing machinery or launching a new product line needs substantial capital. Therefore, such decisions are taken at the top level of management after careful analysis.

3. Irreversible in nature: Most investment decisions are irreversible, or reversible only at a significant loss. Fixed assets cannot be disposed of without incurring loss, and a wrong decision may prove fatal for the survival of the firm. Hence, these decisions are taken after thorough investigation and evaluation.

4. Risk involved: Investment decisions involve high risk and uncertainty because returns are expected over a long period and future conditions (demand, cost, technology, government policy) cannot be predicted with certainty. The greater the uncertainty, the greater the risk attached to the decision.

5. Impact on cash flow and profitability: A sound investment decision increases the firm's cash inflows and profitability, while a wrong decision may result in heavy losses and cash outflow. Thus, investment decisions directly influence the liquidity and earning capacity of the business.

6. Difficult and complex decision: Investment decisions are among the most difficult and complex decisions of financial management. They require consideration of many factors such as availability of funds, cost of capital, expected returns, risk, legal formalities and the overall objectives of the firm.

7. Affects the cost and capital structure: The funds required for investment are raised from various sources such as equity shares, debentures and loans. Hence, the investment decision affects the cost of capital and the capital structure of the company.

8. Basis of other decisions: Investment decisions provide the basis for other financial decisions. For instance, the amount and nature of fixed assets determine the requirement of working capital and the financing pattern of the firm.

Conclusion: In short, investment decisions are long-term, high-risk, large-value and irreversible decisions that determine the future growth, profitability and survival of a business enterprise. Therefore, they must be taken with great care and proper evaluation.

Minimum rate of return = 10%, so the discount factors at 10% are 0.9091, 0.8264, 0.7513, 0.6830 and 0.6209 for years 1 to 5 (annuity factor for 5 years = 3.7908).

(a) NPV of Project A

$NPV_A = 3{,}41{,}498 - 3{,}00{,}000 = \text{Rs } 41{,}498$

(b) NPV of Project B

The cash flow is an annuity of Rs 1,50,000 for 5 years.

$PV = 1{,}50{,}000 \times 3.7908 = \text{Rs } 5{,}68{,}620$

$NPV_B = 5{,}68{,}620 - 5{,}00{,}000 = \text{Rs } 68{,}620$

Conclusion: Both projects have positive NPV, so both are acceptable. Project B has the higher NPV (Rs 68,620 against Rs 41,498), so it is preferable if only one can be chosen.

Investment decision refers to the decision regarding how much funds should be invested in long-term assets or projects and which specific assets or projects the firm should invest in. It involves evaluating and selecting investment proposals on the basis of expected return and risk so as to maximise the wealth of shareholders.

Investment proposals are the alternative capital expenditure projects placed before the financial manager for evaluation and selection. Five common types are as follows.

1. Replacement investment proposal This relates to replacing worn-out, obsolete or damaged plant and machinery with new ones. Its aim is to maintain the existing level of operations and reduce operating costs, for example replacing an old machine with a more efficient model. The risk is relatively low because the firm's earnings are already known.

2. Expansion investment proposal This relates to increasing the existing capacity of the firm, such as adding a production line or opening new branches to meet growing demand. It is taken up when existing facilities are fully used and the market can absorb more output. It raises sales and profits but carries more risk than replacement.

3. Diversification investment proposal This relates to entering a new line of business different from the firm's existing products or industry, for example a textile company starting cement production. Its purpose is to spread risk over unrelated activities and earn higher returns. It is the riskiest type because the firm has no prior experience in the new field.

4. Research and development (R&D) proposal This relates to spending on developing new products, improving existing ones or introducing new production techniques. It is made for long-term survival and growth. The benefits are uncertain and arise only in the future, so the risk is high.

5. Strategic or intangible investment proposal This relates to investment in items such as brand building, advertising, employee training, welfare schemes and pollution-control equipment. These may not give immediate, measurable returns but are necessary to meet legal requirements, improve the firm's image and create goodwill.

Thus, proposals may be replacement, expansion, diversification, R&D or strategic in nature, and each is evaluated on its expected return and risk.

Steps Involved in the Evaluation of an Investment

Evaluation of an investment means examining whether a proposed project is financially and economically worthwhile before committing funds to it. The main steps are as follows:

1. Identification of Investment Proposals The first step is to identify and list all possible investment proposals available to the firm. Proposals may come from various departments, expansion plans, replacement needs, or new product ideas. Each proposal is given a clear description of its nature and purpose.

2. Estimation of Cash Flows After identifying the proposal, the cash inflows and outflows associated with it over its whole life are estimated. This includes:

• Initial investment (cash outflow at the beginning),
• Annual net cash inflows during the project's life,
• Terminal value or salvage value at the end of the project.

These cash flows are estimated on an after-tax basis, since tax affects the real return of the project.

3. Determination of the Required Rate of Return (Discount Rate) The firm decides the minimum rate of return it expects from the investment. This rate reflects the cost of capital and the risk of the project. It is used to discount future cash flows to their present value.

4. Selection of Evaluation Techniques The firm chooses suitable capital budgeting techniques to judge the proposal. The main techniques are:

• Payback Period (PBP): Time taken to recover the initial investment.
• Net Present Value (NPV): Present value of cash inflows minus present value of cash outflows.
• Internal Rate of Return (IRR): The discount rate at which NPV equals zero.
• Profitability Index (PI): Present value of inflows divided by initial investment.
• Accounting Rate of Return (ARR): Average profit divided by average investment.

5. Evaluation and Comparison of Proposals Each proposal is evaluated using the selected techniques. The results are compared with the acceptance criteria:

• PBP should be less than the standard period.
• NPV should be positive.
• IRR should be greater than the required rate of return.
• PI should be greater than one.

6. Ranking of Proposals When several proposals are acceptable, they are ranked from best to least attractive. Under capital rationing (limited funds), the firm selects the proposals that give the highest return per rupee invested.

7. Final Selection and Implementation The best proposal or group of proposals is finally selected. Funds are then allocated and the project is implemented. After implementation, actual performance is reviewed against the estimates to check whether the expected benefits are achieved.

Conclusion Thus, investment evaluation moves from identifying proposals, estimating cash flows, fixing the discount rate, applying evaluation techniques, comparing and ranking results, to final selection and review. This systematic process helps the firm choose the most profitable investment and avoid wasteful use of scarce capital.

Given:

• Fixed operating cost (FC) = Rs 200,000
• Variable cost per unit (V) = Rs 20
• Selling price per unit (P) = Rs 30

Contribution per unit: $C = P - V = 30 - 20 = \text{Rs }10$

1. Operating break-even point in units: $BEP \text{ (units)} = \frac{FC}{C}$ $= \frac{200,000}{10} = \mathbf{20,000 \text{ units}}$

2. Operating break-even point in rupees: $BEP \text{ (Rs)} = BEP \text{ (units)} \times P$ $= 20,000 \times 30 = \mathbf{Rs\ 600,000}$

Alternatively, using contribution margin ratio: $\text{CM ratio} = \frac{10}{30} = \frac{1}{3}$ $BEP \text{ (Rs)} = \frac{200,000}{1/3} = \text{Rs }600,000$

Answer:

• Annual operating break-even point = 20,000 units
• Annual operating break-even sales = Rs 600,000

Importance of Investment Decision

Investment decision (also called capital budgeting decision) refers to the decision regarding the selection of long-term assets or projects in which the firm's funds are to be invested. It involves committing large funds for a long period with the expectation of future returns. Its importance can be explained as follows:

1. Long-term growth and survival: Investment decisions determine the future earning capacity and growth of a firm. A firm can expand, diversify, or modernise only by investing in new plant, machinery, and projects. Wrong decisions may threaten the very survival of the firm.

2. Large amount of funds involved: Such decisions require huge amounts of funds, often a large part of the firm's total capital. Once funds are invested in long-term assets, they become fixed and cannot be withdrawn easily. Hence these decisions must be taken very carefully.

3. Irreversible in nature: Investment decisions are generally irreversible. If a wrong project is selected, it is very difficult and costly to reverse the decision, as the assets cannot be sold without a heavy loss. Therefore, thorough analysis is essential before committing funds.

4. Affects the risk and return of the firm: Every investment carries risk. Investment decisions affect both the profitability (return) and the riskiness of the firm. A firm must strike a proper balance between risk and return so as to maximise the wealth of shareholders.

5. Impact on financing and liquidity: The size of investment determines the amount of funds to be raised from various sources. Heavy investment in fixed assets reduces liquidity and increases the financial burden of the firm. Hence investment decisions are closely linked with financing decisions.

6. Affects the cost and capital structure: Investment decisions influence the debt–equity mix and the overall cost of capital of the firm. A firm investing in risky projects may have to pay a higher cost of capital, which affects its profitability.

7. Maximisation of shareholders' wealth: The basic objective of financial management is to maximise the wealth of shareholders. This is achieved only when the firm invests in projects having a positive net present value (NPV), i.e., projects whose return exceeds the cost of capital.

Conclusion: Thus, investment decisions are of vital importance because they involve large funds, are irreversible, and determine the growth, profitability, risk, and long-term survival of a business. A wrong investment decision can ruin the firm, while a correct one can ensure its prosperity.

Given: Initial cost of machinery = Rs 600,000
Required rate of return = 15%
Life = 5 years

a. Payback Period

Since cash inflows are unequal, cumulative cash inflows are calculated as:

Initial investment is recovered between Year 2 and Year 3.

Remaining amount after Year 2:

$600,000 - 500,000 = 100,000$

Cash inflow of Year 3 = Rs 200,000

$\text{Payback period} = 2 + \frac{100,000}{200,000} = 2.5 \text{ years}$

Payback period = 2.5 years = 2 years 6 months.

b. Decision Based on Maximum Cost Recovery Period

Maximum acceptable cost recovery period = 5 years
Actual payback period = 2.5 years

Since 2.5 years < 5 years, the machinery recovers its cost within the company’s maximum acceptable period.

Therefore, the company should purchase the machinery.

c. Net Present Value at 15%

$NPV = \sum_{t=1}^{5} \frac{CF_t}{(1+r)^t} - \text{Initial cost}$

where $r = 15\%$

$\text{NPV} = 793,277.18 - 600,000$

$\text{NPV} = Rs\ 193,277.18$

Since NPV is positive, the project is financially viable.

Conclusion: The company should purchase the machinery.

Discount factors at 8%: $\dfrac{1}{(1.08)^t}$ = 0.9259, 0.8573, 0.7938, 0.7350, 0.6806 for years 1 to 5.

(i) Net present value

Proposal P

$NPV_P = 98{,}222 - 80{,}000 = \text{Rs } 18{,}222$

Proposal Q

$NPV_Q = 1{,}01{,}408 - 80{,}000 = \text{Rs } 21{,}408$

(Using unrounded factors the NPVs are about Rs 18,224 and Rs 21,411.)

(ii) Decision

Both proposals have positive NPV, so both are acceptable. Since the investment is the same and the proposals are mutually comparable, the proposal with the higher NPV is chosen. Proposal Q (NPV about Rs 21,400) is more suitable than P (NPV about Rs 18,200), because its larger cash flows come in the earlier years.