Question

Personal Finance Problem Common stock value: Constant growth Over the past 6 years, Elk County Telephone has paid the dividends shown in the following table. P7-12 Year 2019 2018 2017 2016 2015 2014 Dividend per share $2.87 2.76 2.60 2.46 2.37 2.25 The firm's dividend per share in 2020 is expected to be $3.02. a. If you can earn 13% on similar-risk investments, what is the most you would be willing to pay per share in 2019, just after the $2.87 dividend? b. If you can earn only 10% on similar-risk investments, what is the most you would be willing to pay per share? c. Compare and contrast your findings in parts a and b, and discuss the impact of changing risk on share value. Common stock value: Variable growth Newman Manufacturing is considering a cash purchase of the stock of Grips Tool. During the year just completed, Grips earned $4.25 per share and paid cash dividends of $2.55 per share (Do 2.55). Grips, earnings and dividends are expected to grow at 25% per year for the next 3 years, after which they are expected to grow at 10% per year to infinity. What is the maximum price per share that Newman should pay for Grips if it has a required return of 15% on investments with risk characteristics similar to those of Grips? P7-13

Answer 1

Considering 13% rate of investment for a dividend of $3.02 in 2020.
D1 = 3.02
k = 13%
growth rate g needs to be estimated as follows
FV = 2.87 , PV = $2.25 and N = 5
FV = PV*(1+g)ⁿ
2.87 = 2.25*(1+g)⁵
1+g = (1.2756)^1/5
g = 1.04988 - 1
g = 0.04988
g = 4.99%

Therefore, Price of the share = D1 / (k-g)
                                                  = 3.02 / (0.13 - 0.04988)
                                                  = $37.69

Price of the share willing to pay is $37.69

b)

With a 10% rate of investment and dividend of $3.02
D1 = 3.02
k = 9%
g = 4.99%

Price = 3.02 / (0.10 - 0.0499)
         = $60.26

Price willing to pay at 10% $60.26

c)

When rate of investment decreases the price of the share increases. Thus, for a low risk stock, prices would go up in comparison to high risk stock. This is because the rate of investment demanded will be more for higher risk stocks.

13)

Given

D0 = $2.55
g = 25% for next three years
g2 = 10% perpetuity
k = 15%

price = D1/(1+k) + D2/(1+k)^2 +D3/(1+k)^3 +TV/(1+k)^3

Terminal Value TV = D3*(1+g) / (k -g)
                             = 4.98 * (1+0.10) / (0.15-0.10)
                             = $109.57

Note: calculations done in excel hence no intermediate rounding is done.

Check the table below:

Year	Dividend	Present Value	Calculation
0	2.55
1	3.19	2.77	3.19/1.15
2	3.98	3.01	3.98/1.15^2
3	4.98	3.27	4.98/1.15^3
3	109.57	72.04	109.57/1.15^3
sum		81.10

Maximum price will to pay for the stock is $81.10