Question

PotashCorp

The data set in the file ch18_MCSP_PotashCorp contains average quarterly share prices for PotashCorp and prices for potash mineral. Investigate the relationship between these variables. (a) Some people think that if the share price of a mining company is high, that is because investors expect high mineral prices for thecorresponding quarter. Can the potash price be estimated from the PotashCorp share price? The data includes a period when the price of potash mineral was exceptionally high. If you eliminate the quarters when the price of potash was over CDN$600/tonne, does that affect your analysis? (b) Other people think that if the price at which a mineral can be sold is high, then the share price of the companies producing that mineral will also be high. Is that the case for PotashCorp? That is, can PotashCorp’s share price be estimated from the potashmineral price? If you eliminate the quarters when the price of potash was over CDN$600/tonne, does that affect your analysis? (c) Compare your answers to (a) and (b) including R-squared, P-value for slope, and the regression lines themselves.

Share Buy-Backs and Special Dividends in Canada

PotashCorp announced a program to buy back up to 5% of its common shares between August 2013 and July 2014.

When a company has a strong balance sheet with surplus cash, it needs to find a use for that cash consistent with its strategic goals and the current business environment. When economic conditions aren’t favourable for spending the cash to pay off debt, acquire another company or expand operations, it can use its cash in two other ways: (1) announcing a special dividend, and (2) buying back shares, otherwise known as stock repurchase agreements. Both of these options return value to shareholders. The difference between them is that share buy-backs can be done gradually over several quarters and the amount of the buy-back can be adjusted to the surplus cash available in future quarters; special dividends, on the other hand, require the company to be pretty certain that a base level of surplus cash will continue to be available in future quarters.

Suppose you’re advising the board of directors of a major company that needs to decide between a share buy-back and a special dividend. Surplus cash during the past eight quarters is given in the table. (Quarter 8 is the most recent.)

Quarter	1	2	3	4	5	6	7	8
Surplus Cash ($ billion)	1.2	0.8	1.4	1.3	0.9	1.4	1.3	1.1

The board will issue a special dividend if it can be both 95% certain that surplus cash will exceed $1.15 billion in quarter 9 and 95% certain that it will exceed $1.2 billion in quarter 10. It will announce a share buy-back program if it can be both 90% certain that the total surplus cash from quarter 9 will exceed $1.15 billion and that the surplus cash from quarter 10 will exceed $1.2 billion. Use linear regression to advise the board of directors about its options.

The data is given below

Year	Quarter	Potash mineral price (CDN$/tonne)	PotashCorp share price (CDN$)
2008	1	490	45
	2	510	65
	3	665	58
	4	955	33
2009	1	1070	27
	2	845	33
	3	605	31
	4	475	35
2010	1	340	37
	2	320	35
	3	340	39
	4	350	48
2011	1	360	57
	2	400	56
	3	430	53
	4	480	46
2012	1	480	45
	2	465	42
	3	475	43
	4	440	42
2013	1	405	41
	2	400	41
	3	400	34
	4	375	31
2014	1	350	33
	2	320	36
	3	310	36
	4	350	34
2015	1	385	35

Answer 1

Please find the solution below:

All the parts of the question are explained below...

A regression equation is calculated below based on the data provided:

Here,

Dependent Variable: Potash Mineral Price (Y)

Independent Variable: Share Price (X)

Plot of the Regression Equation:

Though there is a regression equation formed, but the model is not a good fit. Refer the Excel output below:

In the above output, refer the Refer the value of R squared. The value of R squared is not closer to 1. Generally, if the value of R squared is closer to 1, it means that maximum variation of the data is explained by the regression line in the model. But in this regard, as the value is very small, i.e. 0.036, it means that only 3.6% of the variations are explained be the regression line which doesn't signifies a good fit.

Thus it can be concluded that there is no such strong relationship between the Price of the Potash and its Share Price.

P Value Analysis:

For the intercept, the P value is very small and is less than 0.05. It means that there is a significant difference in it. This signifies that the null hypothesis is rejected and the alternate is accepted.

Here, the hypothesis are:

H₀: β = 0

H_a: β is not equal 0

As a significant difference is obtained, so null hypothesis is not accepted and hence the intercept can't be 0.

But for the slope (Share Price), it can become 0 as the P value is more than 0.05 in this case. here, the null hypothesis is accepted.

End of the Solution...