[FM/F9: Tài liệu ôn thi] Part B: Investment Appraisal

Part B sẽ ôn lại 6 dạng bài tập quan trọng môn Financial Management (F9) với chủ đề Investment Appraisal.

1. Tổng quan:

 

Topic	Question types	Question index
		MCQ	Cases
Investment appraisal	NPV	1-5
	Capital rationing	6
	Lease or buy	7	8
	Asset replacement	9
	Risk & Uncertainty	10-12
	Basic techniques	13, 14
Reference: BPP ACCA F9 - Financial Management StudyText Knowledge Base: [FM/F9: Tóm tắt kiến thức] Lesson 7: Các phương pháp thẩm định đầu tư cơ bản (Basic investment appraisal techniques)

2. Dạng bài tập chi tiết

Mức độ: Quan trọng

2.1. Dạng 1: Net present value

Trắc nghiệm

Câu 1: (intermediate)

Question: Which TWO of the following statements are correct?

A.	Tax allowable depreciation is a relevant cash flow when evaluating borrowing to buy compared to leasing as a financing choice
B.	Asset replacement decisions require relevant cash flows to be discounted by the the after-tax cost of debt
C.	If capital is rationed, divisible investment projects can be ranked by the profitability index when determining the optimum investment schedule
D.	Government restrictions on bank lending are associated with hard capital rationing

Answer: C, D

Tax saving on the tax allowable depreciation (TAD) is relevant cash flow, not depreciation itself => A is false.

The cost of capital is used for asset replacement decisions. The after-tax cost of debt would be used in a lease vs buy => B is false.

Profitability index (PI) is used to rank divisible projects. => C is true.

Government restrictions on bank lending would represent hard capital rationing. => D is true

Câu 2: Intermediate

Jones Ltd plans to spend $95,000 on an item of capital equipment on 1 January 20X2. The expenditure is eligible for 25% tax-allowable depreciation, and Jones pays corporation tax at 30%. Tax is paid at the end of the accounting period concerned. The equipment will be sold for $25,000 on 31 December 20X5. Jones has a 31 December year end and has a 10% post-tax cost of capital.

What is the present value (PV) at 1/1/20X2 of the tax savings from the TAD?

A. $16,991

B. $15,828

C. $16,018

D. $19,827

Guidance:

Note: 2 areas often cause problems with tax: tax timing & tax savings CF.

Pay attention to tax timing to find the exact discount factor (DF).
If T0 is now, assumed at 1/1/20X2, then T1 is in 1 years’ time which is 31/12/20X2 or 1/2/20X2. (T1 is both the end of Year 1 and the start of Year 2).

“Tax is paid at the end of the accounting period concerned” => pay in 1 years’ time.

It is the tax savings on the depreciation, is the relevant cash flow considered to find the PV.

The answer, effectively used for OT or case questions, could be presented as below:

Tax period	Narrative	($)	Tax saved at 30% ($)	Timing (T)	DF	PV ($)
	Initial investment TAD	x (x)
		x
	Initial investment TAD	(x)
	Balancing allowance

Answer: A. $16,991

Tax period	Narrative		Tax saved at 30% ($)	Timing	DF at 10%	PV ($)
31/12/X2	Initial investment  TAD	95,000 (23,750)	7,125	0 1	0.909	6,477
31/12/X3	TAD	71,250 (17,813)	5,344	2	0.826	4,414
31/12/X4	TAD	53,438 (13,359)	4,008	3	0.751	3,010
31/12/X5	Disposal Balancing allowance	40,078 (25,000) 15,078	4,523	4	0.683	3,090
						16,991

Câu 3: Basic

Data of relevance to the evaluation of a particular project are given below.

Cost of capital in real terms	10% per annum
Expected inflation	8% per annum
Expected increase in the project’s annual cash inflow	6% per annum
Expected increase in the project’s annual cash outflow	4% per annum

Which of the following sets of adjustments will lead to the correct NPV being calculated?

Guidance: Different rates of inflation => use 'money approach', i.e. the cash flows must be inflated at their specific rates and discounted at the money cost of capital.

Answer: B
(1 + Money rate) = (1 + Real rate) × (1 + Inflation rate) = 1.1 × 1.08 = 1.188

Câu 4: A project has an initial outflow at time 0 when an asset is bought, then a series of revenue inflows at the end of each year, and then finally sales proceeds from the sale of the asset. Its NPV is £12,000 when general inflation is zero % per year. 

If general inflation were to rise to 7% per year, and all revenue inflows were subject to this rate of inflation but the initial expenditure and resale value of the asset were not subject to inflation, what would happen to the NPV?

A.	The NPV would remain the same
B.	NPV would rise
C.	NPV would fall
D.	NPV could rise or fall

Answer: C

The NPV impact of the initial outflow is unaffected.
The revenue flows will be subject to inflation, but then should be discounted at a money rate which includes this inflation => The net effect is no change in the PV.
The sales proceeds represent a flow of money, not affected by inflation, but this will now
be discounted at a higher money rate, lowering NPV of the project.

Câu 5: 

Spotty Ltd plans to purchase a machine costing $20,000 to save labour costs. Labour savings would be $8,000 in the first year and labour rates in the second year will increase
by 10%. The estimated average annual rate of inflation is 8% and the company’s real cost of
capital is estimated at 12%. The machine has a two-year life with an estimated actual
salvage value of £5,000 receivable at the end of year 2. All cash flows occur at the year end.

What is the NPV (to the nearest $) of the proposed investment?

Guidance: Calculate the 

 (I)   money cost of capital 
 (II)  present in cash flow table to get the NPV.

How to get money cost of capital?

	i: nominal interest rate
Use Fisher formula: (1+i) = (1+r)*(1+h)	r: real interest rate
	h: inflation rate
The real rate (r) and the general inflation rate (h) must be expressed as decimals when using the Fisher formula.

 

Important:	Pay attention to the correct timing of each cash flow
	Discount factor = 1(1+r)n (r: cost of capital; n: period)

Answer: $ (3,954)

  (I)   Money cost of capital = [(1.08 × 1.12) – 1] × 100 = 20.96%
  (II)  Answer presenting:

Timing	T0	T1	T2
Initial investment ($)	(20,000)
Labour ($)		8,000	8,800
Salvage ($)			5,000
DF at 20.96%	1	0.8627	0.6835
	(20,000)	6,613.6	9,432.3
NPV = (3,954.1)

2.2. Dạng 2: Capital Rationing

Trắc nghiệm

Câu 6: Four projects, I, II, III, and IV, are available to a company which is facing shortages of capital over the next year but expects capital to be freely available thereafter.

	I	II	III	IV
	$’000	$’000	$’000	$’000
Total capital required over lifetime of the project	20	30	40	50
Capital required for next year	20	10	30	40
NPV of the project at company cost of capital	60	40	80	80

In what sequence should the projects be selected if the company wishes to maximise net present values?

Guidance: “facing shortages of capital over the next year but expects capital to be freely available thereafter” => Capital rationing in single period with divisible projects => Profitability Index application.

PI = NPV/Investment => Investment priority base on ranking in order of highest to lowest PI.

Answer: Investment sequence: II, I, III, IV.

	I	II	III	IV
PI (NPV/Investment)	=60/20 =3	=40/10 =4	=80/30 = 2.67	=80/40 =2
Ranking	2	1	3	4

3.3. Dạng 3: Lease or buy

Trắc nghiệm

Câu 7: B Co is considering whether to buy or lease two following assets:

Asset 1: 10-year economic life, 0 residual value. It can be bought by paying $80,000 immediately or leasing with 10 lease rentals of $12,000 per year payable annual in advance.

Asset 2: 5-year economic life. It can be bought by paying $81,000 immediately and it will have $40,000 residual value after 5 years. Or, it can be leased with 5 lease rentals of $14,000 per year payable in arrears.

How should B Co finance these assets?

Asset 1	Buy	= -80,000
	Lease	= (AF1-9 at 10%+1)*-12,000
		= (5.759 + 1) * -12,000 = -81,108 => Buy
Asset 2	Buy	= -81,000 + (40,000/1.15)
		= -56,163
	Lease	= (AF1-5 at 10%) * -14,000
		= 3.791 * -14,000 = -53,074 => Lease

Tự luận

Câu 8: 

ASOP Co is considering an investment in new technology that will reduce operating costs through increasing energy efficiency and decreasing pollution. The new technology will cost $1 million and have a four-year life, at the end of which it will have a scrap value of $100,000.
A licence fee of $104,000 is payable at the end of the first year. This licence fee will increase by 4% per year in each subsequent year.
The new technology is expected to reduce operating costs by $5.80 per unit in current price terms. This reduction in operating costs is before taking account of expected inflation of 5% per year.

Year	1	2	3	4
Production	60,000	75,000	95,000	80,000

If ASOP Co bought the new technology, it would finance the purchase through a four-year loan paying interest at an annual before-tax rate of 8.6% per year. Alternatively, ASOP Co could lease the new technology. The company would pay four annual lease rentals of $380,000 per year, payable in advance at the start of each year. The annual lease rentals include the cost of the license fee.
If ASOP Co buys the new technology it can claim tax allowable depreciation on the investment on a 25% reducing balance basis. The company pays taxation one year in arrears at an annual rate of 30%. ASOP Co has an after-tax weighted average cost of capital of 11% per year.

Required: Based on financing cash flows only, calculate and determine whether ASOP Co should lease or buy the new technology.

Answer:

1. After-tax cost of borrowing = 8.6 × (1 – 0.3) = 6% per year

Evaluation of leasing

Year	CF	Amount ($)	DF at 6%	PV ($)
0-3	Lease rentals	(380,000)	(1+2.673) = 3.673	(1,395,740)
2-5	Tax savings	114,000	3.465 * 0.943 = 3.267	372,438
				(1,023,302)

PV of cost of leasing = $1,023,302

Evaluation of borrowing to buy

(W1) Tax benefit

Year	TA depreciation	Tax benefits $	License fee tax benefits $	Total $
2	1,000,000 * 0.25 = 250,000	75,000	31,200	106,200
3	750,000 * 0.25 = 187,500	56,250	32,448	88,698
4	562,500 * 0.25 =140,625	42,188	33,746	75,934
5	421,875 – 100,000 = 321,875	96,563	35,096	131,659

 

Year	Capital	License fee $	Tax benefits $	Net CF	DF at 6%	PV $
0	(1,000,000)			(1,000,000)	1	(1,000,000)
1		(104,000)		(104,000)	0.943	(98,072)
2		(108,160)	106,200	(1,960)	0.89	(1,744)
3		(112,486)	88,698	(23,788)	0.84	(19,982)
4	100,000	(116,986)	75,934	58,948	0.792	46,687
5			131,659	131,659	0.747	98,349
						(974,762)

PV of borrowing to buy = $974,762.

ASOP Co should buy the new technology since the present cost of borrowing to buy is lower than the present cost of leasing. 

2.4. Dạng 4: Asset replacement

Trắc nghiệm

Câu 9: Basic

 A company buys a machine for $10,000 and sells it for $2,000 at time 3. Running costs of the machine are: time 1 = $3,000; time 2 = $5,000; time 3 = $7,000.

If a series of machines are bought, run, and sold on an infinite cycle of replacements, what
is the equivalent annual cost of the machine if the discount rate is 10%?

Guidance: EAC = NPV/AF 

Answer: 

Timing	$’000	DF	$’000)
0	(10)	1	(10)
1	(3)	0.909	(2.727)
2	(5)	0.826	(4.13)
3	(7)	0.751	(5.257)

NPV = (22, 144) => EAC = 22,144/2.487 = $8,904

2.5. Dạng 5: Risk and Uncertainty

Trắc nghiệm

Câu 10: Intermediate

Arnold is contemplating purchasing for $400,000 a machine to produce 55,000 units of a product per annum for five years. These products will be sold for $15 each and unit variable costs are expected to be $10. Incremental fixed costs will be $80,000 per annum for production costs and $35,000 per annum for selling and administration costs. Arnold has a required return of 10% per annum. 

By AT LEAST how many units must the estimate of production and sales volume fall for the project to be regarded as not worthwhile?

Guidance: 

Note: Consider from investor’s perspective => Required return is cost of capital => Cash flows needs to be discounted at 10% to present value.

Not worthwhile project means NPV = 0 or worse => Changes from WHICH aspect lead to NPV falling?

Answer: 15,630 units

Timing		Cash flow $’000	10% factor	PV $
0	Initial investment	(400)	1	(400,000)
1-5	Fixed costs	(115)	3.791	(435,965)
1-5	Contribution	= (15-10)*55 000	3.791	1,042,525
	NPV			206,560

The initial NPV is positive and the investment is worthwhile.

In order for this project to be not worthwhile, its contribution must fall by $340,350 or by 206560/1,042,525 = 19.8%. 

Therefore, the sale volume goes in the same manner and must fall by = 19.8% * 55,000 = 10,897 units.

Câu 11: (Basic)

An investment project has a cost of $12,000, payable at the start of the first year of
operation. The possible future cash flows arising from the investment project have the
following present values and associated probabilities:

PV of Year 1 cash flows (CFs)	Probability	PV of Year 2 CFs	Probability
16,000	0.15	20,000	0.75
12,000	0.60	(2,000)	0.25
(4000)	0.25

What is the expected value (EV) of the net present value of the investment project? 

$ 

Guidance: EV = Cash flow value * related probability

Answer: $11,100

EV of PV of year 1 cash flow: $16,000 × 0.15 + $12,000 × 0.6 – $4,000 × 0.25 = $8,600
EV of PV of year 2 cash flow: $20,000 × 0.75 – $2,000 × 0.25 = $14,500
Total PV = ($12,000) + $8,600 + $14,500 = $11,100.

Câu 12: Advanced

 A shop has the following probability distribution of weekly demand for a product.

Demand	Probability
300	0.4
400	0.3
600	0.3

Orders must be made each week in advance, any inventory left is scrapped. Cost per item is $2.5 and each item is sold for $3.

What is the optimum quantity to be ordered each week?

Guidance:

Optimum quantity ordered => gives the highest expected value of returns.

With returns = Revenue – Cost.

Step 1: Draw up a profit/loss matrix:

Probability	0.4	0.3	0.3	EV ($)
Demand	300	400	600
Order quantity
300	(W1)	(W2)	(W2)
400
600

Step 2 (Working – W): Calculate returns (profit/loss) for all scenarios.

For example: 

Order	Cost per unit ($)	Cost	Demand	Selling price	Revenue	Revenue – Cost ($)
300	2.5	750	300	3	900	150
400	2.5	1000	600 (*)	3	1200 (*)	200

Note: Demand > Order => Out of stock because no buffer inventory remained, any item left is scrapped. => Highest return when all ordered quantities are sold.

Step 3: Calculate the total EV for each option of order quantity.

Total EV = Total of (Profit/loss of each ordering scenario * probability in demand)

Step 4: Compare and choose highest EV => Optimum order amount obtained.

Answer:

Step 1: Draw up profit/loss matrix

Probability	0.4	0.3	0.3	EV ($)
Demand	300	400	600
Order quantity
300	(W1)	(W2)	(W2)
400
600

Step 2: Calculate returns (profit/loss) ($) for all scenarios.

Probability	0.4	0.3	0.3	EV ($)
Demand	300	400	600
Order quantity
300	150	150	150
400	(100)	200	200
600	(600)	(300)	300

Step 3: Calculate the total EV of returns for each option of order quantity.

Probability	0.4	0.3	0.3	EV ($)
Demand	300	400	600
Order quantity
300	150	150	150	150
400	(100)	200	200	80
600	(600)	(300)	300	-240

Step 4: Choose the highest EV

Order quantity of 300 units gives highest EV returns of $150

 => Optimum order quantity = 300 units.

Tự luận

Câu 12: Advanced

Vyxyn Co is evaluating a planned investment in a new product costing $20m, payable at the start of the first year of operation. The product will be produced for four years, at the end of which production will cease. The investment project will have a terminal value of zero. Financial information relating to the investment project is as follows:

Year	1	2	3	4
Sales volumes (units/year)	440,000	550,000	720,000	400,000
Selling price ($/unit)	26.5	28.5	30	26
Fixed cost ($/year)	1,100,000	1,121,000	1,155,000	1,200,000

These selling prices have not yet been adjusted for selling price inflation, which is expected to be 3·5% per year. The annual fixed costs are given above in nominal terms. Variable cost per unit depends on whether competition is maintained between suppliers of key components. The purchasing department has made the following forecast:

Competition	Strong	Moderable	Weak
Probability	45%	35%	20%
Variable cost ($/unit)	10.8	12	14.7

The variable costs in this forecast are before taking account of variable cost inflation of 4·0% per year. Vyxyn Co can claim tax-allowable depreciation on a 25% per year reducing balance basis on the full investment cost of $20m and pays corporation tax of 28% per year one year in arrears.
It is planned to finance the investment project with an issue of 8% loan notes, redeemable in ten years’ time. Vyxyn Co has a nominal after-tax weighted average cost of capital of 10%, a real after-tax weighted average cost of capital of 7% and a cost of equity of 11%.

Required:

(a)   Calculate the expected net present value of the investment project and comment on its financial acceptability.

Guidance:

(a)

Step 1: Inflation - Working 1 (W1):

Note: Question involving tax & inflation and different inflation rate => Fisher formula must be used to find the nominal rate.

Step 2: Calculate inflated sales (W2)

Year	1	2	3	4
Sales volumes (units/year)
Inflated selling price ($/unit)
Inflated sales

Step 3: Calculate inflated variable costs (W3)

Note: In case of risk and uncertainty, mean value is calculated before taking into account of inflation.

 

Step 4: Tax benefits (W4)

Note: Pay attention to tax timing and present the working as following:

Year	Narrative	Value ($)	Tax benefit at ? (%) ($)	Timing (T)
	Initial investment TAD	x (x)
		x
	Initial investment TAD	(x)
	Balancing allowance

Step 5: Working capital needs (W5)

In question of WC needs => cash outflow pay attention to its correct timing.

Step 6: Present the answer using the following pro-forma:

Year	1	2	3	4	5
	$’000 (if needed)
Sales income
Variable costs
Contribution
Fixed costs
Taxble cash flow
Taxation at tax rate
Tax benefits (W2)
WC needs (W3)
After-tax CF
DF at nominal rate
PV

 

Total PV or future CF
Initial investment
ENPV

Answer:

(b)
Step 1: Nominal cost of captail is given = 10%

Step 2: Calculate Inflated sales – W1

Year	1	2	3	4
Sales volumes (units/year)	440,000	550,000	720,000	400,000
Selling price ($/unit) (*)	=26.5 * 1.035 = 27.4	= 28.5*1.035 = 29.5	= 30*1.035 = 31.1	= 26*1.035 = 26.9
Inflated sales ($’000)	12,056	16,225	22,392	10,760

(*) rounded number to 1 decimal.

Step 3: Variable costs (VC) – W3

Mean variable cost = 10.8 * 0.45 + 12*0.35 + 14.7*0.2 = $12 per unit

Year	1	2	3	4
Variable cost ($/unit)	12	12	12	12
Infalted 4% per year	=12*1.04 = 12.48	=12*1.042 12.98	=12*1.043 = 13.5	=12*1.044 =14.04
Sales volume (units/year)	440,000	550,000	720,000	400,000
Total variable costs	= 440,000*12.48 = 5,491,000	= 550,000*12.98 = 7,139,000	= 720,000 *13.5 = 9,720,000	= 400,000*14.04 = 5,616,000

Step 4: Tax benefit – W4

Tax timing: Payable in arrears

Year	Narrative	Value ($’000)	Tax benefit at 28% ($)	Timing of benefit (T)
1	Initial investment TAD at 25%	20,000 (5,000)	1,400	2
		15,000
2	TAD at 25%	(3,750)	1,050	3
		11,250
3	TAD at 25%	(2,812.5)	787.5	4
		8437.5
4		(8,437.5)	2362.5	5
	Balancing figure	0

Step 5: Working capitl needs (no needs - ignored in this question) (W5)

Step 6: Present the answer:

Year	1	2	3	4	5
	$’000	$’000	$’000	$’000	$’000
Sales income (W2)	12,069	16,791	23,947	11,936
Variable costs (W3)	(5,491)	(7,139)	(9,720)	(5,616)
Contribution	6,578	9,652	14,227	6,320
Fixed costs	(1,100)	(1,121)	(1,155)	(1,200)
Taxble cash flow	5,478	8,531	13,072	5,120
Taxation at 28%		(1,534)	(2,389)	(3,660)	(1,434)
Tax benefits (W2)		1,400	1,050	788	2,362
After-tax CF	5,478	8,397	11,733	2,248	928
DF at nominal rate	0.909	0.826	0.751	0.683	0.621
PV	4,980	6,936	8,812	1,535	576

 

Total PV or future CF	22,839
Initial investment	(20,000)
ENPV	2,839

Mức độ: Ít quan trọng

2.6. Dạng 6: Basic techniques

Câu 13: Basic

The following information relates to an investment project which is being evaluated by the directors of Fence Co, a listed company. The initial investment, payable at the start of the
the first year of operation is $3.9 million.

Year	1	2	3	4
Net operating CF ($’000)	1,200	1,500	1,600	1,580
Scrap value				100

The directors believe that this investment project will increase shareholder wealth if it achieves a return on capital employed greater than 15%. As a matter of policy, the directors require all investment projects to be evaluated using both the payback and return on capital employed methods. Shareholders have recently criticized the directors for using these investment appraisal methods, claiming that Fence Co ought to be using the academically-preferred net present value method.

(a)  What is the payback period of the investment project? years
(b)  Based on the average investment method, what is the percentage return on capital
employed (ROCE) of the investment project, to one decimal place? %
(c)  Which TWO of the following statements about investment appraisal methods are
correct?

A.	The return on capital employed method considers the time value of money
B.	Return on capital employed must be greater than the cost of equity if a project is to be accepted
C.	Riskier projects should be evaluated with shorter payback periods
D.	Payback period ignores the timing of cash flows within the payback period

Answer:

(a)  A

Payback period = 2 + (1,200/1,600) = 2.75 years.

(b)  26%

Average annual accounting profit = (Total operating cash flows – total depreciation)/life of project = (5,880 – 3,800)/4 = $520,000 per year
Average investment = (3,900 + 100)/2 = $2,000,000
ROCE = 100 × 520/2,000 = 26%.

(c)  C & D

Risk can be taken into account by shortening the required payback period, meaning
that only those cash flow closer to the present (and thus less risky) are considered.
Payback period ignores the timing of cash flows within the payback period is correct.

Câu 14: Which TWO of the following statements are true of the IRR and the NPV methods of
appraisal?

1. IRR ignores the relative sizes of investments
2. IRR is easy to use where there are non-conventional cash flows (eg cash flow
   changes from negative to positive and then back to negative over time)
3. NPV is widely used in practice
4. IRR is technically superior to NPV

Answer:

The IRR ignores the relative sizes of investments. It, therefore, does not measure the absolute increase in company value, and therefore shareholder wealth, which can be created by an investment. => 1 is true

Where cash flows change from negative to positive more than once there may be as many IRRs as there are changes in the direction of cash flows. So IRR is not easy to use in this situation => 4 is false then 3 is true.