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# Quantitative Methods of Analysis

1) The following table shows nominal GDP and an appropriate price index for a group of selected years. Compute real GDP. Indicate in each calculation whether you are inflating or deflating the nominal GDP data.
Year Nominal GDP, Price Index
1960 \$ 527.4 22.19
1968 911.5 26.29
1978 2295.9 48.22
1988 4742.5 80.22
1998 8790.2 103.22

2) Suppose an economy's real GDP is \$30,000 in year 1 and \$31,200 in year 2. What is the growth rate of its real GDP? Assume that population is 100 in year 1 and 102 in year 2. What is the growth rate of GDP per capita?

3) If the CPI was 110 last year and is 121 this year, what is this year's rate of inflation? What is the "rule of 70"? How long would it take for the price level to double if inflation persisted at (a) 2, (b) 5, and (c) 10 percent per year?

4) A firm has fixed costs of \$60 and variable costs as indicated in the table on the following page. Complete the table.
a. Graph total fixed cost, total variable cost, and total cost. Explain how the law of diminishing returns influences the shapes of the variable-cost and total-cost curves.
b. Graph AFC, AVC, ATC, and MC. Explain the derivation and shape of each of these four curves and their relationships to one another. Specifically, explain in nontechnical terms why the MC curve intersects both the AVC and the ATC curves at their minimum points.
c. Explain how the location of each curve graphed in question 7b would be altered if (1) total fixed cost had been \$100 rather than \$60 and (2) total variable cost had been \$10 less at each level of output.

5) ROI analysis using DuPont model.
a. Firm D has net income of \$27,900, sales of \$930,000, and average total
assets of \$465,000. Calculate the firm's margin, turnover, and ROI.
b. Firm E has net income of \$75,000, sales of \$1,250,000, and ROI of 15%.
Calculate the firm's turnover and average total assets.
c. Firm F has ROI of 12.6%, average total assets of \$1,730,159, and turnover
of 1.4. Calculate the firm's sales, margin, and net income.

6) Basic CVP Exercises
Each problem is unrelated to the others.

1. Given: Selling price per unit, \$20; total fixed expenses, \$5,000; variable expenses per unit, \$15.
Find break-even sales in units.
2. Given: Sales, \$40,000; variable expenses, \$30,000; fixed expenses, \$7,500; net income, \$2,500.
Find break-even sales in dollars.

3. Given: Selling price per unit, \$30; total fixed expenses, \$33,000; variable expenses per unit, \$14.
Find total sales in units to achieve a profit of \$7,000, assuming no change in selling price.

4. Given: Sales, \$50,000; variable expenses, \$20,000; fixed expenses, \$20,000; net income,
\$10,000. Assume no change in selling price; find net income if activity volume increases 10%.

5. Given: Selling price per unit, \$40; total fixed expenses, \$80,000; variable expenses per unit, \$30.
Assume that variable expenses are reduced by 20% per unit, and the total fixed expenses are increased
by 10%. Find the sales in units to achieve a profit of \$20,000, assuming no change in selling price.

#### Solution Preview

Please refer attached files for graphs and better clarity of formulas.

Solutions:

1.
Year Nominal GDP Billions, Price Index (1996 = 100) Real GDP, Billions
1960 \$527.40 22.19 527.40*100/22.19=\$2,376.75 Inflate
1968 911.5 26.29 911.5*100/26.29=\$3,467.10 Inflate
1978 2295.9 48.22 2295.9*100/48.22=\$4,761.30 Inflate
1988 4742.5 80.22 4742.5*100/80.22=\$5,911.87 Inflate
1998 8790.2 103.22 8790.2*100/103.22= \$8,515.99 Deflate
We deflate GDP when prices rise (CPI is more) and inflate GDP when prices fall (CPI is less) compared to a base year.

2. Growth in real GDP=(31200-30000)/30000=4%
Real GDP per capital in year 1 =Real GDP/Population=30000/100=\$300
Real GDP per capital in year 2 = Real GDP/Population 31200/102=\$305.8824
Growth in Real GDP per capita=(305.8824-300)/300=1.96%

3. Rate of Inflation is the rate of change of general price level and is measured as under:

Rate of inflation for year(t)= [{Price level(year t)-Price level (year t-1)}/ Price level (year t)]*100

Inflation = [{CPI(this year)-CPI(last year)}/CPI (last year)]*100
...

#### Solution Summary

There are six problems. Solutions to these problems explain calculating real GDP, inflation rate, and growth rate. Solutions also explain calculations based upon Dupont Model and CVP Analysis.

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