# Sales in Managerial Economics

Problems

Question One

A machine cost $ 4,000. It lasts 2 years and has no scrap value (that is, it has no value at the end of those two years of use). In each year, it produces $ 2400 in income. Should the firm invest in the machine if the interest rate is 10%? Should the firm invest in the machine if the interest rate is 20%? Why? What if the machine's scrap value was $350?

Question Two

Wiley Coyote has been retained to analyze two new projects for the Acme Company. Each project has a cost of $10,000, and the cost of capital for both projects is 12%. The projects net cash flows are as follows:

Year Project 1 Project 2

0 (10,000) (10,000)

1 6,500 3,500

2 3,000 3,500

3 3,000 3,500

4 1,000 3,500

a) Calculate each project's nominal payback period, net present value (NPV), and internal rate of return (IRR)

b) Should both projects be accepted if they are interdependent?

c) Which project should be accepted if they are mutually exclusive?

d) Why does a conflict exist between NPV and IRR rankings?

Question 3

In the first year, Bubba's Pork Rind factory sold $ 100,000. A mere 13 years later, Bubba sold $ 475,000. What is the compound growth rate? If Bubba's sales growth continued unabated, what would Bubba's sales be after the next 13 years?

If, in the above, the initial period had been 10 years, what would the compound growth rate have been then? What would you expect the sales to be after 16 more years?

https://brainmass.com/economics/economic-growth/sales-in-managerial-economics-294323

#### Solution Summary

Predict the amount of sales in the case.

Managerial Economics: Appalachian Coal Mining, Twenty-first Century Electronics, Vanguard Corporation and more...

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Managerial Economics

(1) Appalachian coal mining believes that it can increase labor productivity and, therefore, net revenues by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is

MC= 40P

Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution the marginal increase in revenue ( MR) is

MR= 1,000- 10p

How much pollution reduction should Appalachian Coal Mining undertake?

(2) Twenty first century electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the number of radios stolen per week.

Number of security guards-------------- Number of radios stolen per week

0--------------------------------------50

1---------------------------------------30

2----------------------------------------20

3----------------------------------------14

4-----------------------------------------8

5-----------------------------------------6

(a) If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?

(b) If the cost of a stolen radio is $25, what is the most firm would be willing to pay to hire the first security guard?

(c) If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security guards should the firm hire?

(3) The director of Marketing at Vanguard Corporation believes that sales of the company's bright side laundry detergent(s) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents ®. The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation:

S= a + bA + cR

Where S, A and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better.

(a) What sign does the marketing director expect a, b, and c to have?

(b) Interpret the coefficients a, b, and c.

The regression output from the computer is as follows:

Dependent Variable: S-------- R- Square F- Ratio p-Value on F

OBSERVATIONS: 36 0.2247 4.781 0.0150

PARAMETER STANDARD

VARIABLE ESTIMATE ERROR T-RATIO P-VALUE

INTERCEPT 175086.0 63821.0 2.74 0.0098

A 0.8550 0.3250 2.63 0.0128

R - 0.284 0.164 -1.73 0.0927

(c) Does Vanguard's advertising expenditure have a statistically significant effect on the sales of bright side detergent? Explain, using the appropriate p-value.

(d) Does advertising by its three largest rivals affect sales of bright side detergent in a statistically significant way? Explain, using the appropriate p-value

(e) What fraction of the total variation in sale of bright side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation?

(f) What is the expected level of sales each week when Vanguard spends $40,000 per week and the combined advertising expenditure for the three rivals are $100,000 per week?