Question

Integrative—Risk and Valuation Hamlin Steel Company wishes to determine the value of Craft​ Foundry, a firm that it is considering acquiring for cash. Hamlin wishes to determine the applicable discount rate to use as an input to the​ constant-growth valuation model. ​ Craft's stock is not publicly traded. After studying the required returns of firms similar to Craft that are publicly​ traded, Hamlin believes that an appropriate risk premium on Craft stock is about 9%. The​ risk-free rate is currently 6​%.

Craft's dividend per share for each of the past 6 years is shown in the following​ table:

2019   $2.85
2018   $2.69
2017   $2.54
2016   $2.39
2015   $2.26
2014   $2.13

a. Given that Craft is expected to pay a dividend of $3.023.02 next​ year, determine the maximum cash price that Hamlin should pay for each share of Craft. ​(Hint: Round the growth rate to the nearest whole​ percent.)

b. Describe the effect on the resulting value of Craft​ from:

​(1) A decrease in its dividend growth rate of​ 2% from that exhibited over the 2014​-2019 period.

​(2) A decrease in its risk premium to 8​%.

Answer 1

Answer a:

Dividend growth rate:

Annual growth rate = (Ending value /Beginning Value) ^{(1 / Number of years)} - 1

= (2.85 / 2.13) ^(1/5) - 1

= 5.997%

= 6%

Risk premium on Craft stock is about 9%. The​ risk-free rate is currently 6​%.

Hence Required rate = 6% + 9% = 15%

Maximum cash price that Hamlin should pay for each share of Craft = Dividend next year / (Required rate - Constant growth rate)

= 3.02 / (15% - 6%)

= $33.56

Maximum cash price that Hamlin should pay for each share of Craft = $33.56

Answer b (1):

Effect on the resulting value of Craft​ from a decrease in its dividend growth rate of​ 2% from that exhibited over the 2014​-2019 period.

Growth rate = 6% - 2% = 4%

Share price (if dividend next year increases by 4%) = Dividend next year / (Required rate - Constant growth rate) = 2.85 * (1 + 4%) / (15% - 4%) = $26.95

Share price (if dividend next year remains as given in a) = Dividend next year / (Required rate - Constant growth rate) = 3.02 / (15% - 4%) = $27.45

Answer b (2):

A decrease in its risk premium to 8​%:

Hence Required rate = 6% + 8% = 14%

Share price = Dividend next year / (Required rate - Constant growth rate) = 3.02 / (14% - 6%) = $37.75

Resulting value of Craft share will from $33.56 to $37.75