Financial Skills
Question 1
(a) Base-weighted aggregate price index for 2019
Base-weighted aggregate price index = [∑P1 * W0/∑P0 * W0] * 100
| Prices | Volumes (000) | |||||
| 2018 | 2019 | 2018 2019 | ||||
| Basic | 25 | 27 | 32.0 | 33.5 | ||
| Comfort | 39 | 45 | 26.2 | 25.8 | ||
| Luxury | 75 | 70 | 17.7 | 19.2 | ||
| 139 | 142 | 75.9 | 78.50 | |||
Base-weighted aggregate price index = [142*75.9/139*75.9] * 100 = 102.16%
(b) Current weighted aggregate quantity index for 2019
Current weighted aggregate quantity index = [∑Q1 * W1/∑Q0 * W1] * 100
Current weighted aggregate quantity index = [(78.50 * 78.50)/(75.9 * 78.50)] * 100 = 103.43%
(c) Base-weighted relative price index for 2019
Base-weighted relative price index = [(142 * 78.50)/(139 * 75.9)] * 100 = 187.09%
Question 2
(a) Tree diagram
(b) Probability of failing to hit only one = ¾ * 2/3 = 0.5
(c) Probability of hitting at least one = ¾ * 1/3 = 0.25
Question 3
(a) f(x, y) =ax+by+c
Where x are number of buses and y is the cost
(b) Feasible region
(c) Minimizing cost
Total number of attendees = 400
Number of drivers = 9
To minimize cost we need, 5 small buses and 4 big buses
6 small buses capacity = 5 * 40 = 200
3 big buses capacity = 4 * 50 = 200
Total cost = (5*800) * (4*600) = 4,000 + 2,400 = £6,400
Question 4
(a) Scatter graph
The scatter graph that has been demonstrated above depicts that the length of the service has an influence on the annual salary the different designers earn. This observation is reflected by the upward trend of the annual salary as the number of years in service increase. However, the annual salary takes a declining trend after the sixth year of service as demonstrate in the graph above.
(b) A critical reflection on the length of service and the annual salary for the various designers depicts they have a positive relationship. The annual salary has the effect of increasing as the length of services in the company expands. Even though the annual salary for the 12 years designer and 15 years designer are lower compared to that of the 6 years designer, the trend of the scatter graph indicates that salary increases with years of service on average. Consequently, the relationship between the length of service and annual salary has been quantified using the linear function derived using an excel software as demonstrated below.
Y = 1.768X + 39.82
The Y in the function formula represents the annual salary for a given designer while the X variable is the number of years. Consequently, the annual salary of the designers will expand on average as the length of service increase.
Question 5
(a) Net present value (NPV) computation and recommendation
NPV = -C0 + C1/(1+r)1 + C2/(1+r)2 + C3/(1+r)3 + ………+ Ct/(1+t)t
Machine A NPV = -£3,600 + 56,000/(1 + 8%)1 + 59,000/(1 + 8%)2 + 62,000/(1 + 8%)3 + 60,000/(1 + 8%)4 + 58,000/(1 + 8%)5
Machine A NPV = -£3,600 + 51,851.85 + 50,582.99 + 49,217.60 + 44,101.79 + 39,473.83
Machine A NPV = £231,628.06
Machine B NPV = -£3,600 + 47,000/(1 + 8%)1 + 50,000/(1 + 8%)2 + 54,000/(1 + 8%)3 + 59,000/(1 + 8%)4 + 65,000/(1 + 8%)5
Machine B NPV = -£3,600 + 43,518.52 + 42,866.94 + 68,024.45 + 43,366.76 + 44,237.91
Machine B NPV = £238,414.58
The net present value of the two machines demonstrates that they are both viable since they have positive values. However, it is recommendable for Sensorpedic to consider investing through machine B over machine A. The rationale behind the recommendation is informed by the higher positive NPV it promises, which implies it will higher returns in the future compared to machine A.
(b) Even the NPV results indicate that machine B is recommendable that the company should consider acquiring, it is essential to consider other essential information in making an informed recommendation. One element of the information to seek is the sustainability of the third product machine B has a comparative advantage over machine A. The sustainability of the third product will inform if it is still rational to invest in machine B instead of machine A. The second set of information to seek is the pattern of the expected cash flows after the fifth year under consideration in the analysis. The future expected cash flow for both machines after the fifth year is critical in determining if machine B still will promise higher and positive discounted cash flows for it to remain recommendable one.
Question 6
(a) The null hypothesis to employs is that an increase in age does not influence one to pay more for a luxury pillow.
(b) Expected values
| Employee age band | Would pay more | Would Not pay more | Total |
| 18-39 | 19 | 53 | 72 |
| 40-49 | 61 | 16 | 77 |
| 50-65+ | 68 | 23 | 91 |
| Total | 148 | 92 | 240 |
| Observed | Expected Values |
| 19 | (72 * 148)/240 = 44.40 |
| 53 | (72 * 92)/240 = 27.60 |
| 61 | (77 * 148)/240 = 47.48 |
| 16 | (77 * 92)/240 = 29.52 |
| 68 | (91 * 148)/240 = 56.12 |
| 23 | (91 * 92)/240 = 34.88 |
(c) Chi-squared
Chi-square = ∑[(observed – expected)2/expected]
| Observed | Expected Values | (Observed – Expected values) | (Observed – Expected values)2 | (Observed – Expected values)2/Expected value |
| 19 | (72 * 148)/240 = 44.40 | -25.4 | 645.16 | 14.53063 |
| 53 | (72 * 92)/240 = 27.60 | 25.4 | 645.16 | 23.37536 |
| 61 | (77 * 148)/240 = 47.48 | 13.52 | 182.7904 | 3.84984 |
| 16 | (77 * 92)/240 = 29.52 | -13.52 | 182.7904 | 6.192087 |
| 68 | (91 * 148)/240 = 56.12 | 11.88 | 141.1344 | 2.514868 |
| 23 | (91 * 92)/240 = 34.88 | -11.88 | 141.1344 | 4.046284 |
| Total | 54.50907 |
Consequently, the chi-square = 54.51
Question 7
(a) Three point averages, the trend and seasonal differences using additive model
(i). Three point averages
1st three point averages = (124 + 111 + 129)/3 = 121.33
2nd three point averages = (122 + 130 + 119)/3 = 123.67
3rd three point averages = (127 + 128 + 118)/3 = 124.33
4th three point averages = (126 + 119 + 134)/3 = 126.33
(ii) trend and seasonal differences using additive model
| Months | Batches sold | Moving total of three months | Trend = Moving total of three months/3 | Seasonal differences = batches sold – trend |
| Jan | 124 | |||
| February | 111 | |||
| March | 129 | 364 | 121.33 | 7.67 |
| April | 122 | 362 | 120.67 | 1.33 |
| May | 130 | 381 | 127.00 | 3.00 |
| June | 119 | 371 | 123.67 | -4.67 |
| July | 127 | 376 | 125.33 | 1.67 |
| August | 128 | 374 | 124.67 | 3.33 |
| September | 118 | 373 | 124.33 | -6.33 |
| October | 126 | 372 | 124.00 | 2.00 |
| November | 119 | 363 | 121.00 | -2.00 |
| December | 134 | 379 | 126.33 | 7.67 |
(c) Expected sales in January and February
Trend value of January = 125
Thus, total moving of three months = 125 * 3 = 375
375 = 134 + 119 + expected sales in January
Expected sales in January = 375 – (134 + 119) = 122
Trend values of February = 120
Thus, total moving of three months = 120 * 3 = 360
360 = 120 + 134 + expected sales in February
Expected sales in February = 360 – (120 + 134) = 106