The following is an estimated demand function:
Q = 875 + 6XA + 15Y − 5P (125) (2) (−1.2)
Where Q is quantity sold, XA is advertising expenditure (in thousands of dollars), Y is income (in thousands of dollars), and P is the good's price. The standard errors for each estimate are in parentheses. The equation has been estimated from 10 years of quarterly data. The R2 was 0.92; the F-statistic was 57; the Standard Error of the Estimate (SEE) is 25. Suppose the values of the explanatory variables next period are: Advertising = $100,000; Income = $10,000; and Price = $100.
Required:
Using the above fitted regression, what is the predicted value of sales?
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Ответ:
$38,208.04
Explanation:
The amount is constant which means that it is an annuity.
It is based on the past so to find the value today, take the future value of the annuity from 5 years ago to find out the value today.
As this is paid at the beginning of the period, it is an annuity due.
Future value of annuity due = Annuity * (1 + r) * ( ( 1 + r)^n - 1 / r)
Rate = 9%/ 4 quarters = 2.25%
Periods = 5 * 4 quarters = 20 periods
Future value of annuity = 1,500 * (1 + 2.25%) * ( ( 1 + 2.25%)²⁰ - 1 / 2.25%)
= $38,208.04