Managerial Accounting

Managerial Accounting — 2020

KNEC Diploma in Supply Chain Management, Module III. Original examination questions with explained answers for revision. Answers are independently prepared for study and are not an official KNEC marking scheme.

July 2020

Paper codes: 2903/305; 2906/305; 2907/305; 2926/305; 3103

Question 1(a) — 8 marks

Explain four production related decisions made in Managerial Accounting.

Answer

1. Make or buy: compare avoidable internal production costs and capacity opportunity costs with the price of purchasing externally.
2. Product mix: allocate scarce materials, machine time or labour to products with the best contribution per limiting resource.
3. Continue or discontinue: assess the contribution lost and costs actually saved when a product or production line is closed.
4. Capacity and production method: compare the relevant costs and benefits of machinery, overtime, subcontracting or process changes needed to meet output requirements.

Question 1(b) — 12 marks

Tamara Limited manufactures a single product, TM. The following is the extract of the budgeted income statement for the year 2021.

Item	Ksh
Sales (80,000 units)	8,000,000
Variable costs	3,200,000
Fixed costs	3,600,000
Total costs	6,800,000
Net profit	1,200,000

Determine the:

(i) break-even point in units and in shillings;

(ii) margin of safety in units and in percentage;

(iii) the number of units to be sold in order to make a profit of Ksh 3,300,000;

(iv) selling price required to make a profit of Ksh 3,600,000, based on the current sales of 80,000 units.

Answer

Question 2(a) — 8 marks

Explain each of the following transfer pricing methods:

(i) Full cost transfer pricing.

(ii) Marginal cost transfer pricing.

(iii) Market based transfer pricing.

(iv) Negotiated transfer pricing.

Answer

1. Full cost: charge the receiving division the production cost including allocated fixed overhead; a profit mark-up may be added if specified.
2. Marginal cost: use the variable or incremental cost of supplying the transferred units; if capacity is constrained, the minimum acceptable price also includes contribution forgone.
3. Market based: use a comparable external market price, adjusted for selling or distribution costs avoided on internal transfers.
4. Negotiated: divisional managers agree a price within a range acceptable to both, subject to group objectives and capacity constraints.

Question 2(b) — 12 marks

Cosmetics Limited intends to introduce a new perfume in the market. Three types of perfumes have been proposed by the management; Ryex, Wih and Swi. The following data relates to the expected demand, probabilities and expected annual net profits for the three perfumes:

Demand	Probability	Ryex (Ksh ‘000)	Wih (Ksh ‘000)	Swi (Ksh ‘000)
High	0.40	1,200	1,500	1,800
Moderate	0.30	1,800	1,000	1,600
Low	0.30	600	-500	-300

(i) Draw a decision tree to represent the information above.

(ii) Determine the Expected Monetary Value (EMV) of each perfume.

(iii) Based on the results in (ii) above, advise the management on the perfume to introduce in the market.

Answer

1. Introduce Ryex under the EMV criterion. Its expected annual net profit of Ksh. 1,200,000 exceeds Swi’s Ksh. 1,110,000 and Wih’s Ksh. 750,000. Keep the low-demand losses for Wih and Swi negative.

Question 3(a) — 8 marks

Malipi Transporters owns a fleet of vehicles for logistic purposes. The following data shows the number of years that the vehicles have been used and their respective maintenance costs:

Number of years used	2	4	6	10	12	15
Maintenance cost (Ksh ‘000)	2	3	3	5	8	10

(i) Determine the linear regression equation.

(ii) Using the equation in (i) above, estimate the maintenance cost of a vehicle that has been used for 18 years.

Answer

The estimated maintenance cost is Ksh. 11,218.96. This is an extrapolation beyond the observed 2–15 years.

Question 3(b) — 12 marks

Naxim Limited intends to purchase either machine A or machine B. The cost of each machine is Ksh 1,000,000. The following are the expected net cash inflows from each of the machines.

Year	Machine A (Ksh)	Machine B (Ksh)
1	200,000	200,000
2	390,000	400,000
3	300,000	330,000
4	330,000	540,000

Additional information: The cost of capital is 14%. The scrap values at the end of the four years are Ksh 80,000 for A and Ksh 100,000 for B.

(i) For each of the projects, calculate the Net Present Value (NPV).

(ii) Based on the results in (i) above, advise the management on the machine to purchase.

Answer

1. Add scrap proceeds to the final-year operating inflow only: A’s year-4 cash flow is Ksh. 410,000 and B’s is Ksh. 640,000.
2. Purchase machine B. NPV B is Ksh. 84,897.59, compared with NPV A of Ksh. -79,224.70; B has the higher positive NPV.

Machine A, including scrap: discount rate 14%. PV = cash flow ÷ (1 + r)ⁿ. All amounts are Ksh.

Machine B, including scrap: discount rate 14%. PV = cash flow ÷ (1 + r)ⁿ. All amounts are Ksh.

Question 4(a) — 8 marks

Hitoch Computers Limited intends to hire 4 computer technicians; John, Jane, Joyce and Joseph. They are to offer computer maintenance services to their four clients; K, L, M and N. The amount chargeable, in thousands of shillings, by each of the computer technicians to each of the clients is as shown below:

Technician	K	L	M	N
John	4	7	8	2
Jane	10	8	12	10
Joyce	5	8	10	14
Joseph	16	10	12	13

Determine the:

(i) assignment schedule that will minimize total cost;

(ii) minimum total cost.

Answer

Apply the Hungarian method. Reduce each row by its smallest entry, then reduce each column by its smallest entry.

After row reduction:

After column reduction:

Choose four independent zeros, with one assignment in every row and column. Read the values from the original table:

Minimum total cost = Ksh. 27,000.

Question 4(b) — 12 marks

Alexip Company has three factories: A, B and C which supply refrigerators to four supermarkets: D, E, F and G, on a monthly basis. The monthly factory capacities are as shown below:

Factory	Refrigerators available
A	80
B	100
C	115

The monthly requirements for each supermarket are as follows:

Supermarket	Refrigerators required
D	50
E	60
F	80
G	105

The cost of transporting one unit, in Kenya shillings, from each factory to each supermarket is as follows:

Factory	D	E	F	G
A	170	200	130	120
B	160	210	260	250
C	150	140	180	170

Using the least cost method, determine the:

(i) basic transportation schedule;

(ii) minimum cost of transportation.

Answer

Least cost allocation steps:

Initial basic feasible schedule:

Initial transportation cost = Σ(quantity × unit cost) = 52,150 Ksh.

The initial allocation method produces a feasible schedule, but does not by itself prove minimum cost. Apply MODI: uᵢ + vⱼ = cᵢⱼ on basic cells and Δᵢⱼ = cᵢⱼ − uᵢ − vⱼ on nonbasic cells. A negative Δ permits a cost reduction; adjust alternating +/− cells by θ. Zero basic allocations may be used for degeneracy.

Optimal schedule:

Final reduced costs (all are nonnegative, proving optimality):

Cost working: 80 × 130 + 50 × 160 + 50 × 210 + 10 × 140 + 105 × 170 = 48,150 Ksh.

Question 5(a) — 8 marks

Muliku Limited produces and sells 3 products: X, Y and Z. The following data relates to the products for the month of October 2019:

Item (Ksh)	X	Y	Z
Sales	300,000	230,000	200,000
Total costs	250,000	250,000	150,000
Net profit / loss	50,000	-20,000	50,000

The total costs comprise of 80% variable costs and 20% fixed costs. The management is contemplating dropping product Y. Advise the management on whether to drop product Y or not.

Answer

1. Keep Y if its fixed costs remain. Y contributes Ksh. 30,000 towards fixed costs, despite an allocated loss of Ksh. 20,000. Dropping it reduces total profit from Ksh. 80,000 to Ksh. 50,000.
2. A different conclusion would require avoidable fixed costs above the lost contribution, or a more profitable alternative use of capacity; neither is stated.

Question 5(b) — 12 marks

Napon Limited manufactures and sells a single product, Km. The following costs relate to the production of 10,000 units of the product for the year 2018:

Cost	Ksh
Raw materials	2,000,000
Managers salaries	2,500,000
Factory rent	1,000,000
Administration cost (60% variable)	1,500,000
Direct labour	1,000,000
Electricity (40% fixed)	600,000

(i) Using the accounts analysis method, determine: I total fixed costs; II variable cost per unit. (ii) Based on the results in (i), formulate the linear cost function in the form y = a + bx. (iii) Determine the increase in total cost when 12,000 units are produced in a year.

Answer

Question 6(a) — 8 marks

Highlight four limitations of the cost-volume-profit (CVP) analysis.

Answer

1. Constant selling price is assumed, although discounts and market changes may alter revenue per unit.
2. Costs are treated as linear, with constant variable cost per unit and fixed costs within a relevant range; overtime or capacity steps can break this assumption.
3. Costs must be separated reliably into fixed and variable elements, which is difficult for mixed costs.
4. A single product or constant sales mix is assumed; changes in the mix alter the average contribution and break-even point.

Question 6(b) — 12 marks

Bingwa Limited manufactures and sells two types of products Jx and Kx, using two types of materials; M1 and M2.

The following are the estimates for the month of January 2022:

Expected sales	Units	Selling price/unit (Ksh)
Jx	600	200
Kx	400	250

Standard material kg/unit	Jx	Kx
M1	4	1
M2	2	2

Material	Cost/kg (Ksh)
M1	100
M2	150

Finished goods inventory	Jx	Kx
1 January	50	80
31 January	40	50

Raw materials inventory (kg)	M1	M2
1 January	40	50
31 January	60	70

For the month of January 2022, prepare:

(i) sales budget in shillings;

(ii) production budget in units;

(iii) material usage budget in units;

(iv) material purchases budget in shillings.

Answer

Sales budget:

Production = sales + closing finished goods − opening finished goods:

Material usage budget (kg):

Purchases = usage + closing raw material − opening raw material:

Question 7(a) — 8 marks

The management of Adepa Petrol station has ascertained that the arrivals and services at their facility follow a Poisson distribution. The average time between arrival of cars is 5 minutes while the average time taken to fuel a car is 2.5 minutes.

I. Determine: (i) expected average queue length; (ii) average number of cars in the queuing system. II. Mary is late for a meeting and has no time to wait in the queue. Determine the probability that the station will be busy on her arrival.

Answer

1. For a Poisson arrival process, an arriving customer sees the long-run busy proportion. Therefore the probability that Mary finds the station busy is ρ = 0.5, or 50%.

λ = 60/5 = 12 cars per hour; μ = 60/2.5 = 24 cars per hour.

Use the stable M/M/1 model: one server, Poisson arrivals, independent exponential service times and λ < μ. Service completions are counted per time interval; service durations are exponential.

Question 7(b) — 12 marks

Sandimix Limited has four storage sites for construction sand: S1, S2, S3 and S4. Four clients, C1, C2, C3 and C4 require to be supplied with sand. The quantities of sand available from each site is shown below:

Site	Tonnes available
S1	800
S2	700
S3	500
S4	600

The quantities required by each client are as shown below:

Client	Tonnes required
C1	500
C2	1,000
C3	700
C4	400

The cost of transporting one tonne of sand, in thousands of Kenya shillings, from each site to each client, is as shown below:

Site	C1	C2	C3	C4
S1	2	4	6	8
S2	4	6	7	5
S3	9	3	6	7
S4	6	8	4	6

Using the Vogel’s approximation method (VAM), determine the:

(i) basic transportation schedule;

(ii) minimum cost of transportation.

Answer

VAM allocation steps:

Initial basic feasible schedule:

Initial transportation cost = Σ(quantity × unit cost) = 10,000 Ksh ‘000.

The initial allocation method produces a feasible schedule, but does not by itself prove minimum cost. Apply MODI: uᵢ + vⱼ = cᵢⱼ on basic cells and Δᵢⱼ = cᵢⱼ − uᵢ − vⱼ on nonbasic cells. A negative Δ permits a cost reduction; adjust alternating +/− cells by θ. Zero basic allocations may be used for degeneracy.

No improving negative reduced cost exists in the initial schedule.

Optimal schedule:

Final reduced costs (all are nonnegative, proving optimality):

Cost working: 500 × 2 + 300 × 4 + 200 × 6 + 100 × 7 + 400 × 5 + 500 × 3 + 600 × 4 = 10,000 Ksh ‘000.

The minimum total cost in shillings is Ksh. 10,000,000.