Simple Linear Regression Keynes’ Explanation of Consumption

John Maynard Keynes hypothesized that household income was the primary determinant of household spending.  To test his theory, 9 regions were selected within the United States based upon average disposable income levels.

 

 

The scale income levels for these regions were 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 and 5.0. Per capita household spending was recorded for each region.  The results are given in Table 1.

Average Disposable Income Levels	Per Capita Household Spending
X	Y
.5	4.21
1.0	5.93
1.5	7.30
2.0	8.32
2.5	10.64
3.0	11.50
3.5	11.80
4.0	11.95
5.0	11.90

 

1.      Verify that the least square regression line for predicting consumer spending from income is:

 

                                                                       Ÿ = 4.563 + 1.847X

 

2.      Verify that the correlation coefficient between consumer spending and income is 0.9234.

 

 

 

3.      The analysis of variance table is of the form:

Source	Degrees of Freedom	Sum of Squares	Mean Squares
Regression	1	58.748	58.748
Error	7	10.143	1.449
Total	8	68.891

 

 

 

 

 

 

Complete the table and test at the  significance level that there is a linear regression relation between consumer spending and income.  Discuss.

 

1.      What is the percentage of variation in consumer spending that is explained by income?

 

2.      Compute the standard error of the estimated regression line and interpret.

 

3.      Compute the predicted spending when income is 0, 3, 5, and 6 units.

 

4.      Plot the data and comment on the use of the linear model to fit this data.

 

 

5.      Consider the following data set where Y represents per capita household spending expressed in terms of year 31 dollars and X is disposable income after taxes.

 

Year	Disposable Income X	Household Spending Y
27	3319	3042
28	3421	3124
29	3404	3108
30	3276	2994
31	3271	2971

 

The predictor equation using all 31 data points is:

 

                        Y-circumflex = -227 + 0.98X

 

a.     What would be the effect upon consumer spending if Congress introduces a tax cut in year 32 that increases per capita disposable income by $100?

 

 

b.     How would consumer spending in year 32 been effected by a tax increase that would have lowered per capita disposable income by $100?

You’ve borrowed $20,000 on margin to buy shares in Disney, which is now selling at $40 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price falls to $35 per share.

Will you receive a margin call?
How low can the price of Disney shares fall before you receive a margin call?

During the campus Spring Fling, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair. Repair personnel can be hired at the rate of $20 per hour. One repairer can fix cars in an average time of 25 minutes. While a car is disabled or being repaired, lost income is $40 per hour. Cars tend to break down at the rate of two per hour. Assume that there is only one repair person, the arrival rate follows a Poisson distribution and the service time follows an exponential distribution.

a) On average, how long is a disabled bumper car waiting to be serviced?
b) On average, how many disabled bumper cars are out of service waiting to be serviced or being serviced?
c) When a bumper car becomes disabled, what is the probability that it will find that there are at least three cars already waiting to be repaired? 
d) The amusement part has decided to increase its repair capacity by adding either one or two additional repair people. These will not work individually but they only work as one team. Thus if two or three people are working, they will work together on the same repair. One repair worker can fix cars in an average time of 25 minutes. Two repair workers working as a team take 20 minutes and three repair workers working as a team take 15 minutes. What is the cost of the repair operation for the two repair strategies (adding 1 or 2 repair workers) that it is considering?

Week 3 Problem Set

Answer the following questions and solve the following problems in the space provided. When you are done, save the file in the format flastname_Week_3_Problem_Set.docx, where flastname is your first initial and you last name, and submit it to the appropriate dropbox.

Chapter 7 (pages 225–228):

1.

Your brother wants to borrow $10,000 from you. He has offered to pay you back $12,000 in a year. If the cost of capital of this investment opportunity is 10%, what is its NPV? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

 

8.

You are considering an investment in a clothes distributor. The company needs $100,000 today and expects to repay you $120,000 in a year from now. What is the IRR of this investment opportunity? Given the riskiness of the investment opportunity, your cost of capital is 20%. What does the IRR rule say about whether you should invest?

 

19.

You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost $5,000 and will be posted for one year. You expect that it will generate additional revenue of $500 per month. What is the payback period?

 

21.

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $10 million. Investment A will generate $2 million per year (starting at the end of the first year) in perpetuity. Investment B will generate $1.5 million at the end of the first year and its revenues will grow at 2% per year for every year after that.

• a. Which investment has the higher IRR?
• b. Which investment has the higher NPV when the cost of capital is 7%?
• c. In this case, for what values of the cost of capital does picking the higher IRR give the correct answer as to which investment is the best opportunity?

 

 

 

Chapter 8 (260–262)

1.

Pisa Pizza, a seller of frozen pizza, is considering introducing a healthier version of its pizza that will be low in cholesterol and contain no trans fats. The firm expects that sales of the new pizza will be $20 million per year. While many of these sales will be to new customers, Pisa Pizza estimates that 40% will come from customers who switch to the new, healthier pizza instead of buying the original version.

a. Assume customers will spend the same amount on either version. What level of incremental sales is associated with introducing the new pizza?

b. Suppose that 50% of the customers who will switch from Pisa Pizza’s original pizza to its healthier pizza will switch to another brand if Pisa Pizza does not introduce a healthier pizza. What level of incremental sales is associated with introducing the new pizza in this case?

 

6.

Cellular Access, Inc. is a cellular telephone service provider that reported net income of $250 million for the most recent fiscal year. The firm had depreciation expenses of $100 million, capital expenditures of $200 million, and no interest expenses. Working capital increased by $10 million. Calculate the free cash flow for Cellular Access for the most recent fiscal year.

 

12.

A bicycle manufacturer currently produces 300,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $2 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $250,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require $50,000 of inventory and other working capital upfront (year 0), but argues that this sum can be ignored because it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are $20,000.

If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?