1. Ilana Industries Inc. needs a new lathe. It can buy a new high-speed lathe fo

Question

1. Ilana Industries Inc. needs a new lathe. It can buy a new high-speed lathe for $1 million. The lathe will cost $35,000 per year to run, but it will save the firm $125,000 in labor costs and will be useful for 10 years. Suppose that for tax purposes, the lather will be depreciated on a straight line basis over its 10-year life to a salvage value of $100,000. The actual market value of the lathe at the time will also be about $100,000. The discount rate is 8%, and the corporate tax rate is 35%. What is the NPV of buying the new lathe?

3. The most likely outcomes for a particular project are estimated as follows: Unit Price: $50 Variable Cost: $30 Fixed Cost: $300,000 Expected Sales: 30,000 units/year However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 10% higher or 10 lower than the original estimate. The project will last for 10 years and requires an initial investment of $1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 35%, and the required rate of return is 12%. What is the project’s NPV in the most likely scenario? What is the project’s NPV in the best-case scenario? What is the project’s NPV in the worse-case scenario? If the probability of the three scenarios above are 20%, 60%, and 20%, what is the expected NPV of the project? Would you accept it given this estimate?

4. Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The material cost for a standard diamond is $40. The fixed costs incurred each year for factory upkeep and administrative expenses are $200,000. The machinery costs $1 million and is depreciated straight-line over 10 years to a salvage value of zero. What is the accounting break-even level of annual sales in terms of number of diamonds sold? What is the NPV break-even level of sales assuming a tax rate of 35%, a 10-year project life and a discount rate of 12%?

5. You estimate that your cattle farm will generate $1 million of profits on sales of $4 million under normal economic conditions. The degree of operating leverage of your farm is 8. What will your profits be if sales turn out to be $3.5 million? What will your profits be if sales turn out to be $4.5 million?

6. A stock is selling today for $40 a share. At the end of the year, it pays a dividend of $2 per share and sells for $44. What is the total rate of return on the stock for the year? What are its dividend yield and percentage capital gain? Now suppose the year-end stock price after the dividend is paid is $36. What are the dividend yield and percentage capital gain in this case? Why is the dividend yield the same in parts b) and c)?

Explanation / Answer

Question 6) The Total Rate of Return on the Stock for the year = [(44 - 40) + 2 ] / 40

= 6 / 40

= 0.15 i.e. 15 %

Dividend Yield = 2 / 40 = 0.05 i.e., 5 %

Capital Gain Percent = 44 - 40 / 40

= 4 / 40

= 0.10 i.e., 10 %

Now suppose the year-end stock price after the dividend is paid is $36

Dividend Yield = 2 / 40

= 0.05 i.e., 5 %

Capital Gain Percent = 36 - 40 / 40

=(-) 4 / 40

= (-) 0.10 i.e.,(-) 10 %

Divided Yield is same when the year end stock price is either $ 44 or $ 36 because the Dividend Yield is calculated on the beginning price of the stock / current price of stock which is $ 40 in the instant question.

Question 5)

Degree of Operating Leverage = % Change in Profit / % Change in Sales

If sales turn out to be $3.5 million, then the amount of profits would be:-

Firstly, we will compute % change in sales.

% Change in Sales = (3.5 - 4) / 4

= (-) 0.5 / 4

= (-) 0.125

% Change in Profits = 8 * (-) 0.125 = (-) 1 or 1 * 100 = (-) 100 %

The amount of profits when sales turn out to be $ 3.5 Million = 1 Milllion - 100 % of 1 Million = $ 0

If sales turn out to be $4.5 million, then the amount of profits would be:-

Firstly, we will compute % change in sales.

% Change in Sales = (4.5 - 4) / 4

= 0.5 / 4

= 0.125

% Change in Profits = 8 * 0.125 = 1 or 1 * 100 = 100 %

The amount of profits when sales turn out to be $ 4.5 Million = 1 Milllion + 100 % of 1 Million = $ 2 Million

Conclusion:-

Question 1)

Caculation of Operating Cash inflow for Year 1 to Year 10

Saving in Labor Cost

(-) Running Cost

125000

35000

Earning before Depreciation

(-) Depreciation [ 1000000 - 100000 / 10 = 9000000 / 10 = 90000]

90000

  90000

Earning before Tax

(-) Tax

0

0

Earnings after Tax

(+) Depreciation

0

90000

Present Value of Cash inflow = 90000 * Cumulative Present Value Factors for 10 years @ 8 % + 100000 * Present Value Factor for Tenth Year @ 8 %.

Present Value of Cash inflow  = 90000 * 6.710 + 100000 * 0.463

Present Value of Cash inflow  = $ 650200

Present Value of Cash Outflow = $ 1000000 (Initial Investment)

Net Present Value = 650200 - 1000000 = (-) 349800

Conclusion:- The NPV of buying the new lathe is (-) $ 349800. New lathe should not be bought because the NPV of buying the new lathe is negative.

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