(a) The Better Shoe Company is considering a major investment in a new product area, novelty umbrellas. It hopes that this product will become a fashion icon. The following information has been collected:

1. The project will have a limited life of 11 years.

2. The initial investment in plant and machinery will be Sh. 10 million and a marketing budget of Sh. 2 million will be allocated to the first year.

3. The net cash flows before depreciation of plant and machinery and before marketing expenditure for each umbrella will be Sh. 100.

4. The products will be introduced both in Kenya and Uganda.

5. The marketing costs in years 2 to 11 will be Sh. 5 million per annum.

6. If the product catches the imagination of the customers in both countries, then sales in the first year are anticipated at 1 million umbrellas.

7. If the fashion press ignores the new products in one country but become enthusiastic in the other, sales ill be 700,000 umbrellas in year 1.

8. If the marketing launch is unsuccessful in both countries, first year sales will be 200,000 umbrellas.

The probability of each of these events occurring is:

1 million sales = 0.3

0.7 million sales = 0.4

0.2 million sales = 0.3

9. If the first year is successful in both countries then two possibilities are envisages.

• Sales levels are maintained at 1 million units per annum for the next 10 years – probability of 0.3.

• The product is seen as a temporary fad and sales fall to 100,000 units for the remaining 10 years

– probability of 0.7.

10. If success is achieved in only one country in the first year, then for the remaining 10 years there is:

• A 0.4 probability of maintaining the annual sales at 700,000 units and

• A 0.6 probability of sales immediately falling to 50,000 units per year.

If the marketing launch is unsuccessful in both countries, the production will cease and the project will be scraped with zero value. The annual cash flows and marketing costs will be payable at each year end.

Assume:

• Cost of capital is 10 per cent per annum.

• No inflation or taxation.

• No exchange rate charges.

Required:

(i) Calculate the expected net present value for the project.

(ii) Calculate the standard deviation for the project.

(iii) If the project produces a net present value of less that Sh. 10 million, the directors fear that the

company will be vulnerable to a hostile takeover. Calculate the probability of the firm avoiding a hostile takeover. Assume normal distribution.

(b) As a firm operating in a mature industry, Orchard Farms is expected to maintain a constant dividend pay out ratio and constant growth rate of earnings for the foreseeable future. Earnings were Sh. 4.50 per share in the recently completed fiscal year. The dividend pay out ratio has been a constant 55% in recent years and is expected to remain so. Orchard Farms‟ return on equity (ROE) is expected to remain at 10% in the future, and you require an 11% return on the stock.

Required:

(i) Using the constant dividend growth model, calculate the current value of Orchard Farms‟ share.

(ii) After aggressive acquisition and marketing programme, it now appears that Orchard Farms‟ earnings per share and ROE will grow rapidly over the next two years. Assuming the Orchard Farms‟dividend will grow at a rate of 15% for the next two years, returning in the third year, to the historical growth and continuing at the historical rate of the foreseeable future.

Calculate Orchard Farms‟ current market rate.

**ANSWER**

(a) The various sales revenue are as follows

Marketing costs

Year 0 Year 1 Year 1 Year 2 – 11

Normal distribution table not given