Question

Suppose you valuate a firm by discounting the future dividends from the firm. Assume the dividend will be paid only once a year at the end of the year. Today is the first day of the year. There are two different scenarios about the future dividends. Scenario #1: You believe the first next dividend is, on average, ??[????+1 ] = $36. The dividend growth rate ?? is 3%. You believe the expected dividend amount is growing with the rate ?? in the future forever so that ??[????+2] = ??[????+1 ](1 + ??) ??[????+3] = ??[????+1 ](1 + ??) 2 … Scenario #2: The dividend for the next 7 years will be $30 per year. Then the dividend will grow at the rate ?? = 5% after that. Assume you believe the CAPM and ?????? = 1.4, ??[????] = 0.09, and ???? = 0.02. If you believe the probability on the scenarios #1 and #2 are 20% and 80%, respectively, what would be your valuation on this firm?

Answer 1

??[????+1 ], d0 = $36

growth rate , g = 3% = 0.03

required return, r = rf + ( beta*( E[rm]-rf ) = 0.02 + (1.4*(0.09-0.02)) = 0.118

( expected dividend) d1 = d0*(1+g) = 36*1.03 = 37.08

Value of frim , v1 = d1/(r-g) = 37.08/(0.118-0.03) = 421.3636364

scenario 2

growth rate after 7 years , g = 5% = 0.05

d1=d2=d3=d4=d5=d6=d7 = 30

value of firm, v2 = [d1/(1+r)] + [d2/(1+r)²] + [d3/(1+r)³] + [d4/(1+r)⁴] + [d5/(1+r)⁵] + [d6/(1+r)⁶] + [d7/(1+r)⁷] + [d8/((1+r)⁷*(r-g))]

= [30/(1.118)] + [30/(1.118)²] + [30/(1.118)³] + [30/(1.118)⁴] + [30/(1.118)⁵] + [30/(1.118)⁶] + [30/(1.118)⁷] + [(30*(1.05))/((1.118)⁷*(0.118-0.05))]

= 349.967610

valuation of firm = (0.20*v1)+(0.80*v2) = (0.20*421.3636364) + (0.80*349.967610) = $364.2468 or $364.25 ( rounding off to 2 decimal places)