**4-2**

**What is an opportunity cost rate? How is this rate used in discounted cash flow analysis, and where is it shown on a time line? Is the opportunity rate a single number that is used all situations?**

Opportunity cost rate is rate of return that investor could earned on an alternative investment of similar risk.

An opportunity cost is the difference in return between an investment that has chosen for investment and one that is inevitably gave up. For example, if a person invests in equity and get 3% return over a period of time then by investing his/her money on stock that person gave up the opportunity of another investment. Let’s assume a treasury bond yielding 5%. In the above situation that person’s opportunity costs are 2% (5% - 3%) (Tatum, September 2010).

Opportunity cost rate is used as an interest rate (discounting factor) to calculate present value of future cash flow. To compute present value, future value is divided by (1 + r) in each year. Therefore, in time line opportunity cost is shown in between two cash flows.

No the opportunity cost is not the single number that is used in all situation. As per the risk associated with investment the alternatives as well as opportunity cost will be different.

**4-3**

**An annuity is defined as a series of payments of a fixed amount for a specific number of periods. Thus, $100 a year for 10 years is an annuity, but $100 in year 1, $200 in year 2, and $400 in years 3 through 10 does not constitute an annuity. However, the second series contains an annuity. Is this statement true or false?**

Answer: The above statement is true because annuity is a series of payment at fixed intervals over a fixed number of years or over a life time. To be annuity it is necessary to be fixed amount. The second series is irregular cash flow but still constitute series of an annuity.

**4-4**

**If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100%, but the annual growth rate would be less than 10%. True or false? Explain.**

The above statement is true because annual growth rate is 7.18%.

In calculation:

FV= PV (1+r)

_{}^{n}or, 2 = 1 (1+r)

^{10}or, 2/1 = (1+r)

^{10}or, (1+r)

^{10 }= 2or, (1 + r) = 2

^{(1/10)}or, (1 + r) = 2

^{(0.1)}or, (1 + r) = 1.0718

or, r = 1.0718 – 1

or, r = 0.0718 = 7.18%

**4-5**

**Would you rather have a saving account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain.**

Answer: I would rather have a saving account that pays 5% interest compounded daily than compounded semiannually because effective rate of semiannual interest rate is 5.063% while effective rate of daily compounding is 5.13%.

Calculation of interest compounded semiannually

= (1+ I

_{nom })^{M }- 1.0 M

= (1 + 0.05/2)

^{2 }- 1= (1.025)

^{2 }- 1= 1.050625 - 1

^{}= 5.063%

Calculation of interest compounded daily

= (1+ I

_{nom })^{M }- 1.0 M

= (1 + 0.05/365)

^{365 }- 1= (1.0001369)

^{365 }- 1= 1.05126 - 1

^{}= 5.13%

**3-2**

**Financial ratio analysis is conducted by managers, equity investors, long-term creditors, and short-term creditors. What is the primary emphasis of each of these groups in evaluating ratios?**

Answer: Analysis of financial ratio helps equity investors to know whether their investment earnings some return or not. Is company earning higher or lower return compared to previous year, industry average and the biggest competitors within the same industry?

Analysis of financial ratios assists Short term creditors to know the ability of company to pay their short term obligation. Calculation of Current ratio, receivable turnover and accounts payable are some of the ratios that helps short term creditors to analyze company’s credit history.

Financial ratios analysis helps long term creditors to know company’s ability to meet interest expenses and long term obligations on time. Times interest earned ratio, debt to total assets turnover ratio, debt to shareholders equity ratio are some of the ratios that are helpful for long term creditors.

**3-3**

**Over the past years, M. D. Rryngaert & Co. has realized an increase in its current ratio and drop in its total assets turnover ratio. However, the company’s sales, quick ratio, and fixed assets turnover ratio have remained constant. What explains these changes?**

Answer: The above changes explain that company was not able to successfully manage their inventories. Due to the increase in inventory both current assets and current ratio increased where as total assets turnover decreased. Since inventory does not included on quick ratio and fixed assets turnover, these ratios remain constant. Company’s sales have remained constant but inventory has increased. This situation shows that company is losing their money.

**3-4**

**Profit margins and turnover ratios vary from one industry to another. What differences would you except to find between a grocery chain such as Safeway and steel company? Think particularly about the turnover ratios, the profit margin, and Du Pont equation.**

Answer: Profit margin is the ratio between revenue and income. Business with higher profit margin have lower cost of sales and hence high profit while business with lower profit margin have higher cost of sales. Thus business with low margin needs to have high volume to sales to make up for the low margin. Turnover ratios show how many times a year company is replacing their inventories or collecting their debtors. Higher turnover indicates that company is producing and selling their products quickly and lower turnover ratio indicates that company is producing and selling their products late (Averkamp, 2004).

Grocery chains like Safeway are business having lower profit margin, high turnover ratio and hence higher volume of business transaction where as Steel company is a business having higher profit margin, low turnover ratio and hence lower volume of business transactions.

**3-6**

**Why is it sometimes misleading to compare a company’s financial ratios with those of other firms that operate in the same industry?**

Answer: Within the same industry some of the firm may operate in their growth stage of business life cycle and some may operate in maturity and introduction stage. The size of the firm may also vary from company to company within the same industry. Some firm may diversified their product all around the globes and some may operate locally. All these differentiations affect the company’s financial performance. A growing company may have negative cash flow and negative return because of huge investment in fixed assets but a matured company may have positive cash flow. In the above example even though growing company looks weaker it will grow in the future and earned highest return but currently when investor compare these two they will definitely make wrong decision. Therefore comparing financial ratios without considering other forces within the same industry is some time misleading.

References

Averkamp, 2004. Accounting Coach. Retrieved September 15, 2010 from

**Ehrnhardt and Brigham, CORPORATE FINANCE, 4th Ed., 2010, Mason, OH: Thomson-Southwestern Publishing.**

Tatum, 2010.

*What is opportunity cost*. Retrieved September 13, 2010 from
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