K2 Management Accounting

E1. Short-term decision making

Relevant costing. A relevant cost is a future cash flow that changes because of the decision. Costs that have already been spent (sunk costs), commitments that cannot be avoided, non-cash items such as depreciation, and general fixed overheads that would be incurred anyway are not relevant. An opportunity cost, which is the benefit given up by choosing one use of a resource instead of the next best, is relevant. For materials already in inventory, the relevant cost is the replacement cost if the material is in regular use, or the higher of its resale value and its use in another job if it is not. For labour, the relevant cost is the variable pay rate if more workers must be hired or paid, plus any contribution lost if workers are moved from other work, and it is nil if the workers are idle and paid anyway.

Limiting factor analysis. When one resource is scarce, the firm should maximise the contribution from each unit of that resource. Calculate the contribution per unit of the scarce resource for each product, rank the products, and allocate the resource to the best product first, up to its maximum demand, then to the next. In a make or buy decision with one scarce resource, compare the extra cost of buying per unit of scarce resource saved: the product with the lowest extra cost per unit of resource should be bought first. A shadow price is the increase in contribution from having one more unit of the scarce resource, and it equals the contribution per unit of resource of the marginal product.

Cost-volume-profit (CVP) analysis. The contribution per unit is the selling price less the variable cost, and the contribution to sales (C/S) ratio is contribution divided by sales. The break-even point is where the contribution equals the fixed costs, so break-even units = fixed costs / contribution per unit and break-even revenue = fixed costs / C/S ratio. The margin of safety is the amount by which sales can fall before break-even is reached. Units needed for a target profit = (fixed costs + target profit) / contribution per unit. A higher selling price or lower costs reduce the break-even point. A break-even chart plots total cost and total revenue and a profit/volume chart plots profit against volume. CVP assumes costs and revenue are linear, fixed costs stay the same, there is one product or a constant mix and all production is sold.

Worked figures

CVP: price $40, variable cost $24 and fixed costs $64,000. Contribution per unit is $16, the C/S ratio is 40%, break-even is 4,000 units or $160,000 of revenue. With budgeted sales of 5,000 units the margin of safety is 20%. A target profit of $32,000 needs (64,000 + 32,000) / 16 = 6,000 units.

Limiting factor: product X earns $12 contribution and uses 2 labour hours, and product Y earns $15 and uses 3 hours. Contribution per hour is $6 for X and $5 for Y. With 1,000 hours and demand of 300 units of X and 200 of Y, X uses 600 hours and the other 400 hours go to Y, which makes 133.3 units. Contribution = 300 x 12 + 133.3 x 15 = $5,600. The shadow price of an hour is $5, the contribution of the marginal product Y.

Key terms

• Relevant cost: A future cash flow that will change as a result of a decision.
• Opportunity cost: The benefit given up by choosing one use of a resource instead of the next best.
• Margin of safety: The amount by which sales can fall before the break-even point is reached.
• Shadow price: The extra contribution from one more unit of a scarce resource.

Study tip: For relevant costing, ask of every item: is it a future cash flow, and does it change because of this decision?

Practice questions for section E1

E2. Long-term decision making

Interest. Simple interest is calculated on the original sum only. Compound interest is calculated on the sum plus interest already earned, so the future value is the present value x (1 + r) to the power n. A nominal rate is the quoted annual rate, and the effective annual rate allows for compounding within the year. Discounting is the reverse of compounding: the present value is the future value divided by (1 + r) to the power n. The present value of an annuity (a level payment each year) uses an annuity factor, and a perpetuity (a level payment for ever) is the payment divided by the interest rate.

Cash flow and profit differ. Investment appraisal uses relevant cash flows, so depreciation and sunk costs are left out and the timing of cash is included. The relevant costing rules from short-term decisions apply to the cash flows of an investment.

The methods are net present value (NPV), internal rate of return (IRR), return on capital employed (ROCE) and payback. NPV is the sum of the discounted cash flows less the investment, and a project is acceptable if it is positive. The IRR is the discount rate at which the NPV is zero. It is found by interpolation between two rates, and a project is acceptable if the IRR is higher than the required return. ROCE compares average annual profit with the capital invested, and different books define the capital figure as the initial or the average investment, so use the definition given in the question. Payback is the time to recover the investment from cash flows, and discounted payback uses discounted cash flows. Payback is easy to understand and shows risk and liquidity, but it ignores cash flows after the payback period and, in its basic form, the time value of money.

NPV is usually seen as the best method because it uses cash flows, takes account of the time value of money and measures the increase in wealth. Its limits are that it needs a discount rate and forecasts, which are uncertain. IRR is a percentage that is easy to compare, but it can be misleading when comparing projects of different sizes.

Worked figures

An investment of $200,000 returns $80,000 a year for 4 years. At 12 percent the annuity factor is 3.0373, so the present value is $242,988 and the NPV is $42,988. Payback is $200,000 / $80,000 = 2.5 years. At 20 percent the NPV is $7,099 and at 25 percent it is $-11,072, so the IRR is about 20 + (7,099 / (7,099 + 11,072)) x 5 = 22.0 percent.

A nominal rate of 12 percent compounded monthly gives an effective annual rate of (1.01)^12 - 1 = 12.68%. A perpetuity of $5,000 a year at 8 percent has a present value of $62,500.

ROCE (using initial investment): total profit over 4 years is $80,000 x 4 - $200,000 = $120,000, an average of $30,000 a year, so ROCE is 15.0% on the initial $200,000.

Key terms

• Effective annual rate: The annual rate that allows for compounding within the year.
• Annuity: A level payment each year for a fixed number of years.
• Internal rate of return: The discount rate at which the NPV of a project is zero.
• Payback: The time taken for cash inflows to recover the initial investment.

Study tip: Draw a timeline of the cash flows first. Most mistakes in NPV questions come from timing, not arithmetic.

Practice questions for section E2