Assignment Sample on Mathematics & Business Finance
Introduction
Task 1
- A) The “pound-value of the loan” is £220000000 (200000000*1.1). This can be calculated by multiplying $200m by the “exchange rate” of “1.1 dollars to the pound”.
- B) The “pound-value of the loan” is £320000000 (220000000+ (200000000*0.125*4)) at the end.
- C) The “nominal dollar amount” of the “loan to Beta Capital” would be $266,666,666.67 (320000000/1.2) if Sigma had set its “forward exchange rate” at 1.2 “dollars to the pound” at the end of the given loan period.
- D) If Beta had not locked in its forward exchange rate, its actual loan value would increase if the final exchange rate was higher than the starting rate of “1.1 dollars to the pound”.
- E) Beta’s real loan value would decrease if the “exchange rate” at the conclusion of the loan period was lower than the original “exchange rate of 1.1 dollars to the pound”, which would have happened if “Beta had not fixed its forward exchange rate”.
- F) The following two scenarios are anticipated:
Default risk: If bigbytes Limited “defaults on the loan”, Sigma may not be able to fetch the overall amount of the loan. This would result in a lower return for Beta.
Interest rate risk: If interest rates in the UK decrease during the loan period, the return on the loan may be lower than anticipated. This is because Sigma would be receiving a fixed interest rate of 12.5%, which would become less attractive if interest rates in the UK decrease.
Task 2
A)
| 30th June 2022 | 30th June 2021 | Percentage change | |
| £’s | £’s | ||
| Sales | 3,520,000 | 3,045,000 | 16% |
| Gross profit | 800,000 | 845,000 | -5% |
| Overheads | 570,000 | 600,000 | -5% |
| Net profit | 230,000 | 245,000 | -6% |
| Overdraft | 56,000 | 50,000 | 12% |
| Long term loans | 750,000 | 735,000 | 2% |
Table 1: Percentage change
(Source: MS- EXCEL)
B)
It would be advise Magpie to exercise caution when contemplating lending to this new customer based on the percentage changes. Despite a 16% increase in sales for the business, the “gross profit” and “net profit” both fell by 5-6%, suggesting a possible decline in efficiency or rise in costs. Additionally, the 12% rise in the overdraft indicates possible cash flow problems, which could make the business a higher-risk borrower.
C)
(i) Typical basket of food would cost £141.70, calculated by dividing the current cost (£156.30) by the inflation rate (1 + 10.3% = 1.103).
(ii) Typical basket of food would cost £154.97, calculated by dividing the current cost (£156.30) by the inflation rate for one month (1 + 10.3%/12 = 1.0086).
Task 3
A)
| Product | Units | Price per item (£) | Total cost (£) |
| Mangotango | 700 | 1.54 | 1078 |
| Bluberrysurprise | 1,300 | 0.92 | 1200 |
| Sunorange | 2,510 | 1.05 | 2635.50 |
| Total | 4510 | 4 | 4914 |
Table 2: Calculation
(Source: MS-EXCEL)
B)
If the supermarket accepts the new Chinese supplier’s offer of 45% less than the overall price they have paid, the equivalent price from the new supplier would be £2702.43. This can be calculated by multiplying the total cost the supermarket paid for the products (£4914) by 0.55 (100% – 45%), which gives £2702.43. Therefore, the new supplier would offer the same products for £2702.43, which is 45% less than what the supermarket has paid previously.
C)
| (4p – 3r)(3p – 7r) |
| = 4p * (3p – 7r) – 3r * (3p – 7r) |
| = 12p2 – 28pr -9pr + 21r2 |
| = 12p2 – 37pr + 21r2 |
| = 12p2 + 21r2 – 37pr |
Table 3: Factorization
(Source: MS-Excel)
D)
16x3y2 – 4x2y3 + 12x2y
To factorize the expression “16x^(3)*y^(2) – 4x^(2)*y^(3) + 12x^(2)*y”,
We can first factor out the greatest common factor, which is “4x^(2)*y:4x^(2)*y (4xy – y^(2) + 3)”
Therefore, the fully factorized expression is:
4x2*y(4xy – y2 + 3)
Task 4
A)
- The highest mark in the sample is 89. This can be found by using the MAX function in Excel, which would be =MAX(range of marks).
Ii. The lowest mark in the sample is 30. This can be found by using the MIN function in Excel, which would be =MIN(range of marks).
Iii. The range of marks in the sample is from 30 to 89. This can be calculated by subtracting the lowest mark from the highest mark, which would be =MAX(range of marks) – MIN(range of marks).
Iv. The mode of the sample is 56. This is the most frequently occurring value in the sample. In Excel, the MODE function can be used to find the mode of a sample, which would be =MODE(range of marks).
- The median of the sample is 57. This is the middle value when the sample is arranged in order. In Excel, the MEDIAN function can be used to find the median of a sample, which would be =MEDIAN(range of marks).
Vi. The mean of the sample is 57.65. This is the average of all the values in the sample. In Excel, the AVERAGE function can be used to find the mean of a sample, which would be =AVERAGE(range of marks).
Vii. The standard deviation of the sample is 16.17103971. This is a measure of how spread out the data is. In Excel, the STDEV function can be used to find the standard deviation of a sample, which would be =STDEV(range of marks).
- B)
| Lower limit | Upper Limit | Frequency |
| 30 | 40 | 15 |
| 40 | 50 | 18 |
| 50 | 60 | 22 |
| 60 | 70 | 18 |
| 70 | 80 | 14 |
| 80 | 90 | 13 |
| Total | 100 |
Table 4: Use of Count If function
(Source: MS-Excel)
Indeed, the programme director is correct that the majority of students received scores below 60%. Of of 100 pupils, 55 (15+18+22) had scores below 60, which represents the majority of the students. The management is anxious about the kids, and for good reason.
Task 5
the sales for three different tourist age groups during the first quarter of 2022 for three different types of service bookings offered by South Pacific Cruises: Boarding Party, Dolphin Splash, and Northern Lights.
Looking at the data, we can see that Northern Lights is the most popular service, with a total of 103 bookings during the first quarter. Dolphin Splash is the second most popular service, with 99 bookings, followed by Boarding Party with 40 bookings.
In terms of age groups, the Silver Sunsets group had the most bookings for Northern Lights with 58 bookings, followed by the Mid Lifers with 20 bookings and the Under 30s with 25 bookings. For Dolphin Splash, the Under 30s group had the most bookings with 16, followed by the Silver Sunsets with 35 bookings and the Mid Lifers with 48 bookings. For Boarding Party, the Under 30s group had the most bookings with 34, followed by the Mid Lifers with 5 bookings and the Silver Sunsets with 1 booking.
From these results, we can see that the Northern Lights service is the most popular among customers, and the Under 30s age group is the best market for South Pacific Cruises for Boarding Party, Dolphin Splash, and Northern Lights services. The Silver Sunsets group had the most bookings for Northern Lights and Dolphin Splash services, indicating that they may be a good market for these services as well. However, these results are based on sales during the first quarter of 2022 and may not necessarily be representative of future trends or customer behavior.
Task 6
- A) COUNTIF function
The COUNTIF function’s implications lead to an estimated 72 automobiles being produced by BMW.
- B) COUNTIF function
The COUNTIF function’s implication determines that there were 6 Toyota vehicles sold in Japan.
- C) XLOOKUP function
The body type of the Z4 model produced by BMW is determined by the use of the XLOOKUP feature to be a sporty compact /roadster automobile.
- D) VLOOKUP function
The VLOOKUP function assessment identifies the production years of the ATS produced by FORD as 2012 to 2019.
Task 7
- A) The formula “A = P(1 + r/n)(nt)” can be used to determine the investment’s final value, where A stands for the investment’s “final value,” P stands for the investment’s “principal amount,” r stands for the “interest rate”, n stands for the “number of times the interest” is compounded annually, and t stands for the time period. Using the indicated numbers as a plug-in, we arrive at A = £85,000(1 + 0.0327/1)(1*5) = £99836.61. So, the final value would be £99836.61.
- B) The formula “A = P(1 + r/n)(nt)”, where A is the final sum, P is the initial sum, r is the “interest rate”, n is the “number of times” the interest is compounded annually, and t is the time period, can be used to determine the initial sum that Boxroom Ltd invested. In this situation, A = £37,245, r = 0.031, n = 1 (since interest is compounded annually), and t = 8. Plugging in the values and solving for P, we get P = £ 29,174.18. Therefore, the original amount that Boxroom Ltd invested was ££ 29,174.18.
- C) To calculate the “average annual interest rate” using the “geometric mean method”, formula used is r = (A/P)^(1/t) – 1, where r is the annual interest rate, A is the “final amount”, P is the “principal amount”, and t is the “time period”. In this case, we are given P = £35,000, A = £64,555, and t = 10. We can calculate the annual interest rate for each year by dividing the final amount by the initial amount and taking the 10th root of the product. Using this method, we get r = [(64555/35000)^(1/10)] – 1 = 0.0631 or 6.31% (to two decimal places). Therefore, the average annual interest rate using the geometric mean method is 6.31%.
Task 8
- A) Discount rate is 3.5%
| Discounting rate 3.5% | Present value @ 3.5% discount |
| 0.01 | -700,000 |
| 0.965 | 144927.5362 |
| 0.931225 | 275385.6566 |
| 0.898632125 | 126271.9788 |
| 0.867180001 | 214374.788 |
| 3% | |
| Formula | IRR(D2:D6) |
Table 5: Quantification of the IRR
(Source: Self-developed)
Discount rate is 6%
| Discounting rate 6% | Present value@6% discount |
| 1 | -700000 |
| 0.94 | 141509.434 |
| 0.8836 | 262548.9498 |
| 0.830584 | 117546.6996 |
| 0.780749 | 194855.0412 |
| 1% | |
| Formula | IRR(F2:F6) |
Table 6: Calculation of the IRR
(Source: Self-developed)
B)
IRR(-700000:214374.788)
IRR(-700000:194855.0412)
C)
According to the facts provided, it is concluded that the project is appropriate if the IRR rate above the hurdle rate. On the reverse hand, it is also established that the project cannot be allowed if the IRR rate is lower than the hurdle rate. In other words, it can be claimed that now the new proposal would be very advantageous for the corporation if the hurdle rate is lower than the IRR.
In addition, it can also be seen as the target rate that stakeholders expect to get or acquire at when they make an investment. Another interpretation is that the capital cost is used to access, analyse, or set the rate of the obstacle. In addition to the cost of capital, it is concerned with the risk that is involved, the rates of return, the existing chances for business expansion, and other pertinent aspects. According to the described case study, it is established that Birkbeck Ltd.’s hurdle rate is assessed as being 6.5%. .So it can be noticed that the IRR that is been evaluated is less in comparison to the anticipated rate of hurdle.
The project should not be approved by Birkbeck Ltd in light of the appraisal and computation of the value of IRR, it can be concluded based on the collected knowledge and further interpretation. Moreover, analysis has shown that the value of IRR is 3% at a discount rate of 3.5%. On the reverse hand, the value of IRR is 1% at a 6% rate of discount. Hence, it may be claimed that the IRR value in both cases of discount rates is lower than the specified or given rate of a barrier. This further indicates that the project would not be advantageous if the corporation accepts it at the rate of the 6.5% hurdle rate.
- D)
One advantage of the “internal rate of return (IRR)” technique of “investment appraisal” is that it considers the time value of money by taking into account the timing and magnitude of cash flows over the project’s life (Yan and Zhang, 2022, p. 1474). IRR provides a single measure of project profitability that can be easily compared with a company’s minimum required “rate of return” or the “cost of capital”. It is also useful for evaluating projects with different cash flow patterns and determining the maximum amount of capital that a firm can commit to a project.
The IRR technique has the drawback of assuming “cash flows” are reinvested at the project’s IRR, which is not necessarily a reasonable assumption. Furthermore, it makes the unavoidable assumption that financial flows be “received and reinvested” at regular intervals. Additionally, IRR may not be able to provide accurate results if the cash flow pattern has multiple sign changes or if the project has non-conventional cash flows, such as mutually exclusive projects (Wang, 2021, p. 24).
Task 9
A)
| Calculation of NPV | ||||
| Year | Cash flow | Discounting rate | Present value | |
| 0 | -£ 20,500,000.00 | 1.00 | -£ 20,500,000.00 | |
| 1 | £ 12,500,000.00 | 0.92 | £ 11,467,889.91 | |
| 2 | £ 12,500,000.00 | 0.84 | £ 10,520,999.92 | |
| 3 | £ 12,500,000.00 | 0.77 | £ 9,652,293.50 | |
| 4 | £ 12,500,000.00 | 0.71 | £ 8,855,315.14 | |
| 5 | £ 12,500,000.00 | 0.65 | £ 8,124,142.33 | |
| Total present value | £ 299,999.78 | |||
| Initial investment | -£ 20,500,000.00 | |||
| Net Present Value | -£ 20,200,000.22 | |||
Table 7: Calculation of NPV
(Source: MS-Excel)
B)
| Payback period | |||
| Year | Cash flow | Cumulative cash flow | |
| 0 | -£ 20,500,000.00 | -£ 20,500,000.00 | |
| 1 | £ 12,500,000.00 | -£ 8,000,000.00 | |
| 2 | £ 12,500,000.00 | £ 4,500,000.00 | |
| 3 | £ 12,500,000.00 | £ 17,000,000.00 | |
| 4 | £ 12,500,000.00 | £ 29,500,000.00 | |
| 5 | £ 12,500,000.00 | £ 42,000,000.00 | |
| Payback period | 7.05 | ||
| 7 years 5 months | |||
Table 8: Calculation of PBP
(Source: MS-Excel)
- C) The “net present value (NPV)” method and simple payback method are both commonly used techniques for evaluating investment projects (Shou, 2022, p. 42). While simple payback is a straightforward method, it has some limitations, making the NPV method a more advantageous approach.
Two advantages of NPV are:
“Takes into account the time value of money”: By utilising a necessary “rate of return” to discount all “future cash flows” to their “present values”, NPV takes the “time value of money” into account. This indicates that due to factors like inflation and the opportunity cost of tying up funds, cash flows received in the future will be worth less than cash flows received today. The simple payback technique, on the other hand, ignores changes in the value of money over time and just takes into account the length of time it takes for a project to repay its initial investment (Bayguzina et al. 2020, p. 27).
Provides a measure of project profitability: By estimating the difference between the “present value” of cash “inflows and outflows”, NPV offers a single indicator of project profitability. This makes it simple to compare various investment opportunities and shows unequivocally whether a project will bring value to the company. The basic payback approach does not account for the project’s continued profitability; it merely calculates the amount of time needed to recover the initial expenditure (Szafranko, 2022, p. 65).
In conclusion, the NPV technique offers a more thorough and precise picture of a project’s profitability, yet simple payback can still be helpful in giving a rapid estimate of how long it would take to return the initial investment. Therefore, it is still worth using the payback technique as part of the investment appraisal process, but it should be supplemented with the NPV method to provide a more comprehensive analysis of the investment opportunity.
References
Wang, Y., 2021, December. The development and usage of NPV and IRR and their comparison. In 2021 3rd International Conference on Economic Management and Cultural Industry (ICEMCI 2021) (pp. 2044-2048). Atlantis Press.
Shou, T., 2022, July. A Literature Review on the Net Present Value (NPV) Valuation Method. In 2022 2nd International Conference on Enterprise Management and Economic Development (ICEMED 2022) (pp. 826-830). Atlantis Press.
Bayguzina, L.Z., Galimova, G.A. and Sukiasyan, A.A., 2020, March. Tools for estimating the risk effect on the investment project efficiency. In International Scientific Conference” Far East Con”(ISCFEC 2020) (pp. 529-536). Atlantis Press.
Szafranko, E., 2022. Assessment of the economic efficiency of energy‐saving projects, methodology based on simple and compound methods. Energy Science & Engineering, 10(2), pp.423-438.
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