Chapter 19
Answers to Examples
Chapter 1 - 2
No examples
Chapter 3
Example 1
Fixed Budget | Flexed Budget | Actual | Variances | ||
Sales | 100,000 | 120,000 | 122,000 | 2,000 | (F) |
Materials | 50,000 | 60,000 | 60,000 | - | |
Labour | 25,000 | 30,000 | 28,500 | 1,500 | (F) |
Variable o/h | 12,500 | 15,000 | 15,000 | - | |
Fixed o/h | 10,000 | 10,000 | 11,000 | 1,000 | (A) |
97,500 | 115,000 | 114,500 | 500 | (F) | |
Profit | $2,500 | $5,000 | $7,500 | 2,500 | (F) |
Original budgeted profit | 2,500 | |
Sales volume variance | 2,500 | (F) |
Flexed budget profit | 5,000 | |
Sales price variance | 2,000 | (F) |
Labour variance | 1,500 | (F) |
Fixed overhead variance | 1,000 | (A) |
Actual profit | $7,500 |
Chapter 4 - 5
No examples
Chapter 6
Example 1
X | Y | Z | |
|---|---|---|---|
$’000 | $’000 | $’000 | |
Gross margin | 897 | 1,070 | 1,056 |
Less: Customer specific costs | |||
Sales visits (80/100/140 × $420) | (33.6) | (42) | (58.8) |
Order processing (200/320/700 × $190) | (38) | (60.8) | (133) |
Despatch costs (200/320/700 × $350) | (70) | (112) | (245) |
Billing and collections (200/320/700 × $97) | (19.4) | (31.04) | (67.9) |
Profit | 736 | 824.16 | 551.3 |
Ranking | 2 | 1 | 3 |
Example 2
Gollum | Sam | |
|---|---|---|
$ | $ | |
Revenue | 25,000 | 21,000 |
Less: discount | 2,500 | 3,150 |
Net revenue | 22,500 | 17,850 |
Less: cost of shoes | (12,500) | (10,500) |
customer transport cost | (5,000) | – |
customer administration cost | (250) | (500) |
Net gain | 4,750 | 6,850 |
The difference on a unit basis is considerable. | ||
Number of pairs of shoes sold | 500 | 420 |
Net gain per pair of shoes sold | $9.50 | $16.31 |
Example 3
Total fixed costs must have been budgeted as: $30 x 1,000 + $60 x 200 = $42,000.
These are now split as 1/3 = $14,000 for set-up costs and the rest, $28,000 for other costs
The cost driver/causer for set-up costs will be the activity of setting-up. There are 1,000/500 + 200/100 = 4 set-ups in the period, so the cost per set-up = $14,000/4 = $3,500.
For one set-up, 500 units of A are made, so the cost per unit = $3,500/500 = $7.
For one set-up, 100 units of B are made, so the cost per unit = $3,500/100 = $35.
$ | Product A | Product B |
|---|---|---|
Marginal cost | 50 | 80 |
Set-up costs | 7 | 35 |
Other fixed costs $28,000/(1000 + 2 x 200) = $20 for A, $40 for B | 20 | 40 |
Total absorption cost | 77 | 155 |
50% mark-up | 38.5 | 77.7 |
Selling price | 115.5 | 232.5 |
It can now be more clearly seen that set-up costs are a major component of Product B. These could be reduced if it were possible to have longer production runs.
Chapter 7 - 8
No examples
Chapter 9
Example 1
Begin with a review of the summary information - notable points
Growth in turnover
Growth in PBIT
Growth in PAT
Growth in total assets, debtors approx. in line with turnover, creditors at a higher rate.
Reduction of gearing (result of rights issue?) and reduced interest charge
Dividend growth
P/E ratio has overtaken industry average.
Profitability | Year 1 | Year 2 | Year3 | Year 4 |
|---|---|---|---|---|
ROCE | 26% | 0.27 | 0.2 | 22% |
Profit Margin | 0.199 | 0.198 | 0.172 | 0.192 |
Asset Turnover | 1.3 | 1.4 | 1.2 | 1.2 |
Gearing | ||||
Gearing (book values) | 50% | 34.6% | 6% | 3.9% |
Interest cover (times) | 7.25 | 9.5 | 48.5 | 75.3 |
Liquidity | ||||
Debtor days | 73 | 76 | 71 | 70 |
Creditor days | 68 | 76 | 81 | 83 |
Investor ratios | ||||
Share Price* $ | 9.63 | 11.40 | 9.66 | 11.95 |
Market Capitalisation $m | 86.67 | 102.6 | 115.92 | 143.4 |
Divi per share (p) | 22.2 | 24.4 | 21.65 | 30.0 |
Divi yield | 2.3% | 2% | 2.2% | 2.5% |
EPS = 5,100,000/9,000,000 = $0.5666; P/e = 17. Therefore price = 17 x 0.5666 = $9.63
Chapter 10
Example 1
Return from new project = | 17,000 | = 17% |
100,000 |
(a) For company:
17% > 15% (target)
Therefore company wants to accept
(b) For division
ROI (without project) | 82,000 | = 16.4% |
500,000 | ||
ROI (with project) | 82,000 + 17,000 | = 16.5% |
500,000 + 100,000 |
ROI of division increases; therefore, the divisional manager is motivated to accept.
Example 2
Return from new project = | 16,000 | = 16% |
100,000 |
(a) For company: 16% > 15%
Company wants to accept
(b) For division:
ROI (without project) | =16.4% | |
ROI (with project) | 82,000 + 16,000 | = 16.3% |
500,000 + 100,000 |
Example 3
(1) | RI (without project) | |
Profit | 82,000 | |
Less: Interest | ||
15% × 500,000 | (75,000) | |
7,000 |
RI (with project) | |
Profit | 99,000 |
Less: Interest | |
15% × 600,000 | 90,000 |
9,000 |
$9,000 > $7,000 manager motivated to accept
(2) | RI (without project) | 7,000 |
ROI (with project) | |
Profit | 98,000 |
Less: Interest | |
15% × 600,000 | 90,000 |
8,000 |
$8,000 > $7,000 manager motivated to accept
In both cases the decisions are goal congruent
Example 4
(a) | d.f. at 10% | P.V. | ||
|---|---|---|---|---|
0 | (250,000) | 1 | (250,000) | |
1 – 5 | 72,500 | 3.791 | 274,847 | |
24,847 |
NPV positive: company accepts
(b) | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
Bal sheet value | 250,000 | 200,000 | 150,000 | 100,000 | 50,000 | |
Net cash flow | 72,500 | 72,500 | 72,500 | 72,500 | 72,500 | |
Less: Depreciation | (50,000) | (50,000) | (50,000) | (50,000) | (50,000) | |
Profit | 22,500 | 22,500 | 22,500 | 22,500 | 22,500 | |
Less: Interest at 10% | (25,000) | (20,000) | (15,000) | (10,000) | (5,000) | |
Residual value | (2,500) | 2,500 | 7,500 | 12,500 | 17,500 |
If manager thinks short-term, may reject project
(c) | Annual depreciation + interest | 250,000 | = $65,946 |
3.791 |
1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|
Bal sheet value | 250,000 | 209,054 | 164,013 | 114,468 | 59,969 |
Net cash flow | 72,500 | 72,500 | 72,500 | 72,500 | 72,500 |
Less: Depreciation | (40,946) | (45,041) | (49,545) | (54,499) | (59,949) |
Profit | 31,554 | 27,459 | 22,955 | 18,001 | 12,551 |
Less: Interest at 10% | (25,000) | (20,905) | (16,401) | (11,447) | (5,997) |
Residual value | 6,554 | 6,554 | 6,554 | 6,554 | 6,554 |
Even if manager thinks short-term, he is motivated to accept.
Example 5
2,014 | 2,013 | |
$m | $m | |
Profit after tax | 88 | 71 |
Non-cash expenses | 15 | 20 |
Research and development | 11 | 10 |
After tax interest (0.7 × 8); (0.7 × 6) | 5.6 | 4.2 |
Adjusted profit | 119.6 | 105.2 |
Adjusted Capital Employed
2,014 | 2,013 | |
Capital employed at start of the year | 400 | 350 |
Non cash expenses | 20 | |
Research and development | 10 | |
Non-capital leases | 16 | 16 |
446 | $366 |
Weighted average Cost of Capital:
2013: (15% × 0.7) + (9% × 0.7 × 0.3) = 12.39%
2014: (17% × 0.7) + (10% × 0.7 × 0.3) = 14.00%
EVA 2013 = 105.2 – (366 × 0.1239) = $59.85m
EVA 2014 = 119.6 – (446 × 0.14) = $57.16m
Chapter 11 - 12
No examples
Chapter 13
IRR and MIRR are retained here as background material, although they are not specifically listed in the APM syllabus for September 2026 to June 2027.
Example 1
Net present value of the Rome plc project
All figures in the schedule are $000.
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Sales | - | 2,000 | 2,140 | 2,290 | 2,450 | 2,622 |
Materials | - | (864) | (933) | (1,008) | (1,088) | (1,175) |
Labour | - | (735) | (772) | (810) | (851) | (893) |
Net operating cash flow | - | 401 | 435 | 472 | 511 | 554 |
Tax on operating cash flow | - | (100) | (109) | (118) | (128) | (139) |
Machine cost | (1,800) | - | - | - | - | - |
Scrap value | - | - | - | - | - | 1,000 |
Tax saving/(charge) on capital allowances | - | 113 | 84 | 63 | 47 | (107) |
Working capital | (200) | - | - | - | - | 200 |
Net cash flow | (2,000) | 414 | 410 | 417 | 430 | 1,508 |
Discount factor at 10% | 1.000 | 0.909 | 0.826 | 0.751 | 0.683 | 0.621 |
Present value | (2,000) | 376 | 339 | 313 | 294 | 936 |
NPV = -2,000 + 376 + 339 + 313 + 294 + 936 = $258,000.
The NPV is positive, so the project should be accepted.
Example 2
Internal rate of return of the project in Example 1
Using a second discount rate of 15% (figures in $000):
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Net cash flow | (2,000) | 414 | 410 | 417 | 430 | 1,508 |
Discount factor at 15% | 1.000 | 0.870 | 0.756 | 0.658 | 0.572 | 0.497 |
Present value | (2,000) | 360 | 310 | 274 | 246 | 749 |
NPV at 10% = +$258,000.
NPV at 15% = approximately -$61,000.
IRR ≈ 10% + [258 ÷ (258 + 61)] × (15% - 10%) = 14.0%.
Example 3
Modified internal rate of return
Cash flows are measured in $000.
Time | Cash flow |
0 | (1,000) |
1 | 600 |
2 | 700 |
3 | (200) |
Present value of the investment-phase outflows
Outflow | Present value |
Time 0: 1,000 × 1.000 | 1,000 |
Time 3: 200 × 0.751 | 150 |
Total present value of outflows | 1,150 |
Terminal value of the return-phase inflows at time 3
Inflow | Terminal value |
Time 1: 600 × 1.10² | 726 |
Time 2: 700 × 1.10 | 770 |
Total terminal value of inflows | 1,496 |
For the MIRR, the present value of investment outflows is equated with the discounted terminal value of the inflows:
1,150 × (1 + MIRR)³ = 1,496
MIRR = (1,496 ÷ 1,150)^(1/3) - 1 = approximately 9.1% (about 9%).
Chapter 14
No examples
Chapter 15
Example 1
Target cost per unit
Calculation | $ per unit |
Selling price | 20.00 |
Less: required profit (40% × $20) | (8.00) |
Target cost | $12.00 |
The maximum cost that will allow Packard plc to earn its required 40% gross profit is $12 per unit.
Example 2
Target cost per unit
Annual calculation | $m |
Expected revenue (40,000 × $67.50) | 2.70 |
Less: required annual profit (30% × $5.00m) | (1.50) |
Annual target cost | $1.20m |
Target cost per unit = $1,200,000 ÷ 40,000 units = $30 per unit.
Chapter 16-17
No examples