ASSIGNMENT

Financial Mathematics, Statistical Modelling and Regulatory Frameworks

Financial Mathematics and Statistical Modelling

Question 1

BoE interest rate

0.500%

HSBC interest rate

4.990%

(a)

75% of 650000 will be £ 487,500.00

Total amount paid will be £ 511,826.25

Total number of months

300

Monthly Payments for 25 years

£ 1,706.09

(b)

BoE interest rate increases to

4.00%

HSBC interest rate increase to

8.49%

Total amount paid will be

£ 528,888.75

Monthly payments increases to

£ 1,762.96

Total maximum amount Jeff can pay

£ 960,000.00

Rate at which Jeff will not be able to pay

1.969230769

(c )

Total amount paid will be £ 511,826.25

Maximum Amount Jeff can pay

£ 3,200.00

Shortest Length for Repaying (in Months)

160

months

Result

The rate at which Jeff shall not be able to pay the mortgage is 96.92%

Question 2

(a)

Let

x1 = Quantity of Basic type Microwave ovens

x2 = Quantity of Average type Microwave ovens

x3 = Quantity of Premium type Microwave ovens

Quantity

Profit

Basic

2000

15

Average

14

28.63

Premium

800

104.88

Maximum Profit for Microwave ovens

£ 114,304.82

Subject to the following constraints

Forming

4421

<=

4500

Machining

17498

<=

17500

Assembly

3821

<=

6500

Testing

3014

<=

4750

Demand for Basic model

2000

<=

2000

Demand for Average model

14

<=

1200

Demand for Premium model

800

<=

800

Question 2.2 (1)

Quantity

Profit

Basic

1285

15

Average

0

28.63

Premium

1000

104.88

Maximum Profit for Microwave ovens

£ 124,155.00

Subject to the following constraints

Forming

4285

<=

4500

Machining

17497.5

<=

17500

Assembly

4142.5

<=

6500

Testing

3142.5

<=

4750

Demand for Basic model

1285

<=

1000

Demand for Average model

0

<=

1200

Demand for Premium model

1000

<=

1000

Result

The profit maximizing level of Basic quality, average and premium quality are found to be 114,304.82 but because the profit margin in the premium level quality is significantly higher than the other two so if there is an increase in the demand of premium quality will certainly leads to an increase revenue as well as profit. Similarly, a decrease in the demand for Basic model left over with the maximum available hours which can be utilized to manufacture.

Question 3

Question 3

For sensitivity Analysis

7.5% UP

7.5% DOWN

Annual Demand (in units)

250000

268750

231250

Ordering Cost (in pounds)

20

21.5

18.5

carrying cost for 1 unit (in pence)

0.55

0.59125

0.50875

Carrying cost Annual

137500

147812.5

127187.5

(a)

Economic order quantity

9

units per order

(b)

EOQ (Annual Demand 7.5% UP)

9

units per order

EOQ (Annual Demand 7.5% DOWN)

8

units per order

EOQ(Ordering Cost 7.5% UP)

9

units per order

EOQ(Ordering Cost 7.5% DOWN)

8

units per order

EOQ(Carrying Cost 7.5% UP)

8

units per order

EOQ(Carrying Cost 7.5% DOWN)

9

units per order

Results

The EOQ when there is an increase or decrease in the annual demand and ordering cost to 7.5% does not imposing any change in the optimal quantity ordered. However when the carrying cost is down to 7.5%, the optimal ordering quantity is the highest i.e. with the decreasing cost same number of units can be ordered leading to higher revenues and therefore higher profits at the end. Thus, the company should initiate to lower its cost to increase the EOQ.

Question 4

Year

Country A

Country B

(in £'000)

(in £'000)

1

300

800

2

550

800

3

1,250

800

4

2,300

1,700

NPV (Country A)

$3,123.40

NPV (Country B)

$3,056.31

Discount rate

11.25%

Result

If the cost of capital remains same at 111.25% level, then Alen Inc. should go for their operations in Country A as its NPV is comparatively higher than the Country B.

Changes in Cost of Capital

Time

Discount rate

Country (A)

Country (B)

-3

8.25%

$3,406.93

$3,290.46

-2

9.25%

$3,308.54

$3,209.38

-1

10.25%

$3,214.09

$3,131.38

0

11.25%

$3,123.40

$3,056.31

1

12.25%

$3,036.27

$2,984.03

2

13.25%

$2,952.54

$2,914.40

3

14.25%

$2,872.03

$2,847.30

Result

If the discount rates are increased or even decreased in the near future, still the NPV of country A remains higher than country B. So Alen Inc should open a new facture in Country ...