# Question 3: You have been reading about the Madison Computer Company (MCC), which currently retains 90 percent of its earnings (\$5 a share this year). It earns an ROE of almost 30 percent. a. Assuming a required rate of return of 14 percent, how much would you pay for MCC on the basis of the earnings multiplier model? Discuss your answer and justify with examples. b. What would you pay for Madison Computer if its retention rate was 60 percent and its ROE was 19 percent? Show your work.

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\$1.97 ONLY

(a.) Given the following Information :

Required rate of return = 14% or 0.14

Return on equity = 30% or 0.30

Retention ratio = 90% or 0.90

Dividend Payout Ratio = 1 – 0.90 = 0.10

Earnings per share = \$5.00

Growth rate = Retention Ratio x ROE

= 0 .90 x 0.30 = 0.27 or 27%

Using Earning Multiplier P/E = (Dividend / Equity ) / (Required Return of Return – Growth rate)

= [( 5 * 0.10) / 5 ] / ( 0.14 – 0.27)

The answer is meaningless and can’t be calculated .Since the required rate of return (14 %) is less than the growth rate (27%), the earnings multiplier cannot be used.

As for the calculation of Price which an investor is willing to pay Required rate of Return has to be more than growth rate to facilitate calculation of earning Multiplier.

By taking the data in part (b) only it can be seen how the price can be calculated using earnings model

(b.)

Given the following Information :

Required rate of return = 14% or 0.14

Return on equity = 19% or 0.19

Retention ratio = 60% or 0.60

Dividend Payout Ratio = 1 – 0.60 = 0.40

Earnings per share = \$5.00

Growth rate = Retention Ratio x ROE

= 0 .60 x 0.19 = 0.114 or 11.4%

Using Earning Multiplier P/E = (Dividend / Equity ) / (Required Return of Return – Growth rate)

= [( 5 * 0.40) / 5 ] / ( 0.14 – 0.114)

= 0.40 / 0.026

= 15.384615

Now lets take this

Next year’s earnings is expected to be: \$5.00 x (1 + .114) = \$5.57

Applying the Earning Multiplier calculated above

Price = (15.384615) x (\$5.57) = \$85.69

In this way ,an investor would be willing to pay up to \$85.69 for Madison Computer Company (MCC) stock.