Financial Mathematics and Business

QUESTION NO. 5

A.

The Barbosa Plc. can use four investment appraisal methods. These methods are divided into two groups based on their complexity and accuracy.

Low Accuracy Methods

These are easy methods that require simple calculations. These methods are not reliable in terms of accuracy, but they can be used in the basic appraisal analysis for screening out bad investment options from a very long list

These methods involve two test for anlaysis

Payback Period

Average rate of return

High Accuracy Methods

These methods are more accurate and precise. They are used in large businesses and when the investment amount is quite big. The heavy calculations involved in these methods lower the risk of bad decision using a poor appraisal tool. The projects which are subjected to these methods are more complex and involve huge investments.

These methods also involve two tests for analysis

Discounted Cashflow ( DCF)

Net Present Value (NPV)

B.

If Barbosa Plc. has a rule that the investment has to payback within three (3) years then the decision will be based on the review of the following data

The amount of NPV

The payback period

For option A the NPV is 2764000 and the payback period is 1.6 years.

For option B the NPV is 5411000 and the payback period is 3.2 years.

The option B is clearly giving high NPV but the payback period is 3.2 years. The option A is has NPV of 2764000 and the payback period is 1.6 years.

Since Barbosa's rule is to make investments that would payback within three (3) years the choice will be option A, because its payback period is 1.6 years as compared to the payback period of option B which is 3.2 years.C.

Based the current cash flows the NPV of the Barbosa's investment is calculated below for each option

For Option A

Discounted Factor

10%

Year

0

1

2

3

4

5

Net Cashflow

(2,000.00)

1,300

1,750

2,150

800

0

Cumulative Cashflow

(2,000.00)

(700.00)

1,050.00 3,200.00 4,000.00 4,000.00

Discounted Cashflow

(2,000.00)

1179.14

1439.73

1604.36

541.47

0.00

6

7

8

9

10

0

0

0

0

0

4,000.00 4,000.00 4,000.00 4,000.00 4,000.00

0.00

0.00

0.00

0.00

0.00

NPV

2,764.70

payback period

3

1.6

0

The net present value calculated for this option on the basis of the cashflows and initial investment has been found to be 2764000.

Since this value of NPV is positive Barbosa may consider making investment according to the option A plan. A positive NPV implies that the investment may result in adding value to the firm in future.

For Option B

Discounted Factor

10%

Year

0

1

2

3

4

5

Net Cashflow

(7,500.00)

500

1,700

3,000

3,000

3,000

Cumulative Cashflow

(7,500.00)

(7,000.00)

(5,300.00)

(2,300.00)

700.00 3,700.00

Discounted Cashflow

(7,500.00)

453.51

1398.59

2238.65

2030.52

1841.74

6

7

8

9

10

3,000

2,300

2,000

1,800

1,200

6,700.00 9,000.00 11,000.00 12,800.00 14,000.00

1670.51

1161.66

916.22

747.94

452.27

NPV

5,411.61

payback period

3

3.233333333

0

The net present value calculated for this option on the basis of the cashflows and initial investment of 7.5m has been found to be 5411000.

Since this value of NPV is positive Barbosa may consider making investment according to the option B plan. A positive NPV implies that the investment may result in adding value to the firm in future.

Recommendation: Both the options would add value to the firm because both options have generated positive NPV. Still if option A is considered then it would generate cashflows for Barbosa for ...