Financial Math Answers

DICT has sh. 5 million available for immediate investment and wishes to maximize the interest earned on its investments over the next year. The specifics of possibilities are shown in the table below:

INVESTMENT

INTEREST EARNED

RISK SCORE

Trade Credits

7%

1.7

Corporate bonds

10%

1.2

Gold stocks

19%

3.7

Platinum stocks

12%

2.4

Mortgage securities

8%

2.0

Construction loans

14%

2.9

For each type of investment, the table shows expected return over the next year as well as a score that indicates the risk associated with investment (a lower score implies less risk). 

To encourage a diversified portfolio, several limits have been placed on the amount that can be committed to any one type of investment:

(1) No more than 25% of the total amount may be invested in any single type of investment.

(2) At least 30% of the funds invested must be in precious metals.

(3) At least 45% must be invested in trade credit and corporate bonds, and

(4) The average risk score of the total investment must be 2 or less.

Halwings Company Ltd who manufactures and retails products A, B and C employ sixty direct workers who work under a group of bonus scheme. The company engages three grades of workers who are paid a bonus of the excess of time allowed over time taken. The bonus paid is 75% of the workers‘ base rate and is shared by the workers in proportion to the time spent on the work. The following production data has been extracted from the company‘s records for April 2000.                               

Product

Units produced

Time allowed per unit

A

320

63

B

640

120

C

1200

100

Grade of worker

Number of direct workers

Base rate per hour (sh)

Hours worked per worker

1

20

30

30

2

8

27

64

3

32

24

50

Required:

a) Percentage of hours saved to hours taken.                                                        (6 marks)

b) Bonus due to the group.                                                                                   (7 marks)

c) Gross earnings due to the group.                                                                      (7 marks)                                                                                                           

QUESTION 2 (TOPIC: OVERHEAD COSTING)

Given: Total budgeted overheads = Shs.240, 000 and the Production budget is given as follows:

Product A B

i) Units 20,000 10,000

ii) Labour hours 20,000 20,000

iii) Labour cost Shs.17,500 Shs.22,500

iv) Machine hours 45,000 15,000

v) Material cost Shs.15,000 Shs.25,000

Required;

The overhead absorption rate per unit of A and B using the following methods:

a) Unit method

b) Percentage on material cost.

c) Percentage on labour cost.

d) Percentage On prime cost.

e) Labour hour rate.

f) Machine hour rate.

Consider a perpetuity whose payments at the end of each year are R, R+p, R+2p,..., R+(n-1)p, R+np, R+np,... . The payments increase by a constant amount p until they reach R+np, after which they continue without change. Show that the discounted value A of such a perpetuity at rate i per annum is given by:

A = (R+pa(n)i) / i

A perpetuity paying 1.000$ at the end of each month is replaced with an annuity paying X$ each month for 10 years. Calculate X if j4 = 7%

If the annuity paid 2.500$ at the end of each month, how long would the annuity last and what would be the size of the final, smaller payment?

Determine the present value of future contributions to a pension plan for a person aged 35, earning 30.000$ per year and expecting to retire at 65. The pension plan requires contributions of 5% of salary and the employee expects to receive average annual salary increases of 3%. Use an annual effective rate of interest of 7% and assume contributions are made at the end of each year.

a) Differentiate between bad debt written off and provision for doubtful debt (5mks)

b) Why do you think that cash flow statement is necessary to any business (5mks)

c) Explain the cost which should not be included in the initial cost of property plant

and equipment (10 marks)

Differentiate between purchased goodwill and internally generated goodwill. (

Upendo ltd wishes to take advantage of the new commercial paper now popular. It

wishes to issue two debenture papers. Both bear coupons of 12% and the effective yield

required on each is 20%. Paper A has a maturity of 10 years and paper B a maturity of

20 years. Both will be paying interest annually and Kshs. 100,000 at maturity. What is

the price of each paper? If the effective yield on each paper rises to 24%, what is the

price of each paper?

a) Differentiate between purchased goodwill and internally generated goodwill. (5 marks)

b) Upendo ltd wishes to take advantage of the new commercial paper now popular. It

wishes to issue two debenture papers. Both bear coupons of 12% and the effective yield

required on each is 20%. Paper A has a maturity of 10 years and paper B a maturity of

20 years. Both will be paying interest annually and Kshs. 100,000 at maturity. What is

the price of each paper? If the effective yield on each paper rises to 24%, what is the

price of each paper? (15 mks)