Question

Gentry Can Company's (GCC) latest annual dividend of $1.25 a share was paid yesterday and maintained its historic 8 percent annual rate of growth. You plan to purchase the stock today because you believe that the dividend growth rate will increase to 9 percent for the next three years and the selling price of the stock will be $46 per share at the end of that time.

A: How much should you be willing to pay for the GCC stock if you require a 12 percent return? Do not round intermediate calculations. Round your answer to the nearest cent.

B: What is the maximum price you should be willing to pay for the GCC stock if you believe that the 9 percent growth rate can be maintained indefinitely and you require a 12 percent return? Do not round intermediate calculations. Round your answer to the nearest cent.

C: If the 9 percent rate of growth is achieved, what will the price be at the end of Year 3, assuming the conditions in Part b? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Part A:

Price of Stock = PV of Cash flows from it.

Year	Particluars	CF	PVF @12%	Disc CF	Formula	Calculation
1	D1	$      1.36	0.8929	$      1.22	D0(1+g)^1	1.25(1.09^1)
2	D2	$      1.49	0.7972	$      1.18	D0(1+g)^2	1.25(1.09^2)
3	D3	$      1.62	0.7118	$      1.15	D0(1+g)^3	1.25(1.09^3)
3	P3	$   46.00	0.7118	$   32.74	Given
Price of Stock				$   36.29

Part B:

P0 = D1 / ( Ke - g)

D1 from Part A is taken

D1 = $ 1.36 / [ 12% - 9%)

= $ 1.36 / 3%

= $ 45.42

Part C:

P3 = D4 / { Ke - g}

D4 = D0(1+g)^4

= $ 1.25 (1+0.09)^4

= $ 1.25 (1.09)^4

= $ 1.25 * 1.4116

= $ 1.7645

P3 = D4 / { Ke - g}

= $ 1.7645 / [ 12% - 9% ]

= $ 1.7645 / 3%

= $ 58.82