IB Business Management HL 3.8 Investment Appraisal Questions

Evaluate investment-appraisal evidence, risk and returns to justify project recommendations in IB Business Management HL cases.

Exam points

Define and identify the key concepts and tools in 3.8 Investment appraisal.
Apply 3.8 Investment appraisal to business calculations, case evidence or management decisions where relevant.
Analyse and evaluate 3.8 Investment appraisal using case context, stakeholder impacts and business trade-offs.

Covered syllabus points

3.8.1—Investment appraisal methods 3.8.2 (HL)—Net present value

[Maximum number: 8]

Solar Soccer Academy Ltd. (SSA)

Solar Soccer Academy Ltd. (SSA) is a private limited company set up five years ago by Stephen Murdock. It provides top-quality soccer (football) skills and technique coaching. So far, SSA has been a success, and Stephen is deciding whether to open another academy in a neighbouring city.
The cost of building a second academy is $ 500000. Stephen has produced forecasted financial information for the second academy's first five years of operation (see Table 1).

Table 1: Forecasted financial information for a second academy

Stephen estimates cash outflow to be 25 % of the total cash inflow in years 1,2 and 3 and 20 % of the total cash inflow in years 4 and 5.

(a)

Using Table 1 and other information provided, calculate for SSA's second academy:

[ 6 ]

(i)

the payback period (show all your working);

[ 2 ]

Payback period for SSA's second academy.

Payback occurs between years 3 and 4:
$\frac{\$300000}{12}=\$25000 \text{ per month}$ $\frac{\$50000}{\$25000}=2 \text{ months}$

Payback period = 3 years 2 months.

Alternative answers using only cash inflows: 2 years 7 months, 2.58333 years, 2.58 years or 31 months.

Award [1] if a candidate who has shown working provides a correct procedure but has made an error in calculation, or the answer does not include years/months.
Award [1] if a candidate does not show any working and simply writes the answer.
Award [2] if a candidate provides the correct answer with working. A correct answer must include years/months.
N.B. award a maximum of [1] if net cash inflows are used.

Year	Cash inflow	Cash outflow	Net cash flow	Cumulative cash flow
0	0	(500000)	(500000)	(500000)
1	160000	(40000)	120000	(380000)
2	200000	(50000)	150000	(230000)
3	240000	(60000)	180000	(50000)
4	375000	(75000)	300000	250000
5	700000	(140000)	560000	810000

(ii)

the average rate of return (ARR) for the first five years of operation (show all your working);

[ 2 ]

Average rate of return (ARR) for the first five years of operation.

Total returns:
$\$120000+\$150000+\$180000+\$300000+\$560000=\$1310000$

Capital cost $=\$500000$

Years of use =5

Total return over 5 years minus capital cost:
$\$1310000-\$500000=\$810000$

Average annual profit:
$\frac{\$810000}{5}=\$162000$

ARR:
$\frac{\$162000}{\$500000}\times100=32.4\%$

Accept 47% if only cash inflows are used.

Award [1] if a candidate who has shown working provides a correct procedure but has made an error in calculation, or the answer does not include the percentage sign.
Award [1] if a candidate does not show any working and simply writes the answer.
Award [2] if a candidate provides the correct answer with working. A correct answer must include the percentage sign.
Award [0] merely for writing the formula.
Apply candidate own figure rule (OFR) if the candidate uses an incorrect net cash flow figure from part (b)(i).

(iii)

the net present value (NPV) at a discount rate of 4 % (see Table 2) (show all your working).

Table 2: Discount rates

[ 2 ]

Net present value (NPV) at a discount rate of 4%.

Using discount tables:

Total present value:
$\$1130794$

NPV:
$\$1130794-\$500000=\$630794$

Accept $948000 if only cash inflows are used.

Some candidates may add the $500000 as Year 0 and calculate it that way. Award full marks if the correct answer is arrived at.
Full headings and full calculations are not expected for each year. Full marks can be awarded if there is some evidence of calculation, especially the movement from total DCF to NPV.
N.B. allow candidate own figure rule (OFR) if using incorrect net cash flow from part (b)(i).

Award [2] if a candidate provides the correct answer with working. A correct answer must include the $ sign. Award [1] for working and [1] for the correct answer.
Award [1] if a candidate who has shown working provides a correct procedure but has made an error in calculation, or the answer does not include the $ sign.
Award [1] if a candidate does not show any working and simply writes the answer.
Award [0] for writing the formula.

Year	Discounted cash flow
1: $\$120000 \times 0.9615$	\$115380
2: $\$150000 \times 0.9246$	\$138690
3: $\$180000 \times 0.8890$	\$160020
4: $\$300000 \times 0.8548$	\$256440
5: $\$560000 \times 0.8219$	\$460264

(b)

Explain one disadvantage for SSA of only using the payback period method in making its decision to open a second academy.

[ 2 ]

[Maximum number: 8]

Urban Express Ltd. (UE), a private limited company, owns and operates city buses in an economically unstable country. Interest rates are forecasted to increase in the next few years. The government of the country has approached UE to set up a public- private partnership (PPP) to purchase electric buses.

Urban Express (UE)
Urban Express Ltd. (UE), a private limited company, owns and operates city buses in an economically unstable country. Interest rates are forecasted to increase in the next few years. The government of the country has approached UE to set up a public-private partnership (PPP) to purchase electric buses. UE has forecasted the following annual net cash flows for UE's first purchase of electric buses.

Table 2: Forecasted annual net cash flows for UE's first purchase of electric buses

$Table 3: Discount rates at 8\%$

Table 3: Discount rates at 8\%

(a)

Using Table 2, for UE's first purchase of electric buses, calculate:

[ 4 ]

(i)

the average rate of return (ARR) (show all your working);

[ 2 ]

ARR = ((total returns - capital cost) / years of use) / capital cost x 100.
Total returns over 4 years = $\$7500000$ .
Total returns over 4 years minus capital cost = $\$7500000$ - $\$5000000$ = $\$2500000$ .
Average annual profit = $\$2500000$ / 4 years = $\$625000$ per year.
ARR = ( $\$625000$ / $\$5000000$ ) x 100 = 12.5%.

Award [1] for correct working and [1] for the correct answer.
Award up to a maximum of [2].
Award a maximum of [1] if % sign is omitted in working or final answer.

(ii)

the payback period (show all your working).

[ 2 ]

Capital investment = $\$5000000$ .

Net cash flows:

Year	Net cash flow ($)	Cumulative net cash flow ($)
1	2200000	2200000
2	1800000	4000000
3	2400000	6400000
4	1100000	7500000

Alternative cumulative presentation:

Year	Net cash flow ($)	Cumulative net cash flow ($)
0	(5000000)	(5000000)
1	2200000	(2800000)
2	1800000	(1000000)
3	2400000	1400000
4	1100000	2500000

The payback period occurs between years 2 and 3.
By the end of year 2, there is a shortfall of $\$1000000$ to recover the investment cost of $\$5000000$ .
In year 3, the net cash flow is $\$2400000,$ or $\$200000$ a month ( $\$2400000$ / 12 months).
The shortfall of $\$1000000$ is recovered in 5 months ( $\$200000$ x 5 months).
Also, ( $\$1000000$ / $\$2400000$ ) x 12 months = 5 months.
The payback period is 2 years and 5 months, or 2.42 years (2.41666 years), or 2 years and 152 days, or 2 and 5/12 years.

Award [1] for correct working and [1] for the correct answer.
Award up to a maximum of [2].
Accept any other method of calculation.
Accept answer discrepancies due to decimal rounding.

(b)

Using Table 2 and Table 3, calculate the net present value (NPV) at a discount rate of 8 % (show all your working).

[ 2 ]

Using the discount table:

Year	Net cash flow ($)	Discount factor at 8%	Present value ($)
1	2200000	0.9259	2036980
2	1800000	0.8573	1543140
3	2400000	0.7938	1905120
4	1100000	0.7350	808500

Total present value = $\$6293740$ .
NPV = TPV - capital cost.
NPV = $\$6293740$ - $\$5000000$ = $\$1293740$ .

Alternative presentation:

Year	Net cash flow ($)	Discount factor at 8%	Present value ($)
0	(5000000)	1	(5000000)
1	2200000	0.9259	2036980
2	1800000	0.8573	1543140
3	2400000	0.7938	1905120
4	1100000	0.7350	808500
NPV			$\$1293740$

N.B. Allow candidate's own figure rule (OFR).
Award [1] for correct working and [1] for the correct answer.
Award up to a maximum of [2].
Award up to [1] if TPV is correctly calculated but NPV is omitted.
Deduct [1] if either the $ sign is missing (unless already in table heading or working) OR units such as 000's are not specified.
Accept any other method of calculation.

(c)

Explain one factor that may have influenced UE's choice of the discount rate of 8 %.

[ 2 ]

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Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (b)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)