Question

5. Farah’s Fashions (FF) makes designer clothes. FF’s factory can produce 10,000 garments for $14. FF can produce another 20,000 garments, but it will have to operate two more shifts increasing the per unit price to $22 each for these garments. There is a 10% chance the fashions will be a hit and FF can sell garments for $50 each. There is a 20% chance the fashion will flop and the garments will have to be heavily discounted and sold for $5 each. There is a 70% chance the fashion will be moderately successful and the garments can be sold for $20 each. The garments will all be sold in one year and, for simplicity, assume FF’s cost of capital is zero. What is the expected selling price for a garment, how many garments would FF produce to sell at this price and what is the NPV at this sells level? What is the value (NPV) of the project if you can wait to decide how much to produce next year?

6. A firm with a current value (cost) of $800 and will return $1,000 next year. The firm also has a potential project that costs $500 and will return $550 next year, but the firm does not have the money to invest and must raise it from outside investors. However, outside investors mistakenly believe the firm will be worth $820 in one year without the project and $13,030 with the project. For simplicity, assume a zero discount rate. Does the project have a positive NPV? Acting on behalf of existing shareholders, should you take the project?

7. An automated machine costs $1,000 and has a 20% probability of breaking irreparably at the end of each year (assuming it was working in the previous year). The machine has a maximum five-year life and will be disposed of with zero value at the end of five years. The machine produces $400 of cashflow at the end of each year and the discount rate is 10% per year. What is the most likely number of years the machine will last and what would the machines value be?

13. Crazy Cliff’s Car Coral (CCCC) is considering buying a company van for $50,000. CCCC expects the van to last 5 years and be disposed of at the end of 5 years for $5,000. CCCC will fully depreciate the van over 5 years using straight-line depreciation. CCCC expects the van to increase sales by $30,000 per year over the life of the van. CCCC also expects maintenance costs to be $4,000 per year. CCCC’s tax rate is 25% and its cost of capital is 10%. What are CCCC’s net income and cashflow in each year? What is the NPV of the van?

Answer 1

Answer to 5

Current Capacity: 10000 units

Current Cost: $ 14

Additional Output: 20000 units

Potential Cost: $ 22

Total Cost for 30000 Units:

(10000*14)+(20000*22)/30000

= $ 19.33

Expected Selling Price:

(0.10)*(50) + (0.20)*(5) + (0.70)*(20)

=$ 20

NPV of additional 20000 Units:

CF0 = 19.33 * 30000 = -579900

CF1= 20 * 30000 = 600000

I/Y = 0

NPV = $ 20100

The project has a positive NPV till the time cost of producing does not increase to $ 20

Max Cost Price = (Current Capacity * current cost) + (additional capacity * potential cost) / Total Capacity

Assuming Max Cost Price = $ 20

Additional Capacity = x

Total Capacity = x + 10000

Hence:

20 = (10000*14) + (x * 22) / (x + 10000)

20 * (x + 10000) = 140000 + 22x

20x + 200000 = 140000 + 22x

200000-140000 = 22x - 20x

2x = 60000

X = 30000

At 30000 Additional units, i.e 40000 Total Units, the NPV will be 0

Answer to 6

CF0 = 500

CF1= 550

I/Y: 0

NPV = $ 50

The project has a Positive NPV

On Behalf of existing shareholders:

CF0 = 500

CF1 = 13030

I/Y = 0

NPV = $ 12530

Assuming the shareholders do not rectify their mistake the project should be taken and even if they do rectify the mistake, it is still a positive NPV project.

Answer to 7

Most likely number of years of machine life = 1 + (probability of breaking down in 1^st year) *

         1 + (probability of breaking down in 2^nd year) *

         1 + (probability of breaking down in 3^rd year) *

         1 + (probability of breaking down in 4^th year) *

         1 + (probability of breaking down in 5^th year) *

= (1 + 0.2) * (1 + 0.2) * (1 +0.2) * (1+ 0.2) * (1 + 0.2)

= 2.48

Most likely number of years of machine life = Round off to = 2.5 years

Machine’s Value =

NPV of the Machine

CF0 = -1000

CF1 = 400

F1 = 5

I/Y = 10

NPV = $ 516.31

Answer to 13

Net Income of van:

= Increase in Sales – Depreciation – Maintenance Cost – Cost of Capital – Tax

Pre Tax Income = 30000 – (50000/5) – 4000 - ( 50000* 0.10)

= 30000 – 10000 – 4000 - 5000

=11000

Tax = 10000 * 0.25 = 2750

Net Income = 10000 – 2750

Net Income = $ 7250

Annual Cash Flow = Increase In sales – maintenance cost – tax + depreciation tax savings

Pre-Tax Cash Flow= 30000 – 4000 = 26000

Tax = 26000 * 0.25= 6500

Depreciation Tax Saving = 10000 * 0.25 = 2500

Annual Cash Flow = 26000 – 6500 + 2500

Annual Cash Flow = 22000

NPV

CF0 = -50000

CF1 = 22000

F1 = 5

I/Y = 10%

NPV = 33397.31