3.3. Required return on the S&P 500 index: k = 9% + (4%)(1) = 13.0%.

(a) P/E0 = Payout (1 + g)/(k − g) or k − g = yield (1 + g), where yield = Payout/(P/E0) = 2.9%

g = (k − y)/(1 + y) = (13% − 2.9%)/1.029 = 9.8%

and gReal = (9.8 − 4.5)/1.045 = 5.1% or gReal ≈ 9.8 − 4.5 = 5.3%, versus a compound growth rate of earnings during the post-war period of about 2%.

(b) The long-term nominal growth of earnings and dividends would be about (1.02)(1.045)

− 1 = 6.6%. Hence, P E0

= 1,5 D0(1.16)t E0(1 + k)t

+ 1

(1 + k)5 D0 E0

(1.16)5(1.066)

k − 0.066 where D0/E0 = 0.614 and P/E0 = 21.2. Solving for k, it yields y = 11.17%. This implies a premium over long-term bonds of 2.17%.

3.5. k is the solution to:

15.4 = 0.357(1 + k)

−1 + 0.421(1 + k)

−2 + 0.487(1 + k)

−3 + 0.583(1 + k)

−4

+ 0.680(1 + k)

−5 + 0.725(1 + k)

−6 + 0.765(1 + k)

−7 + 0.799(1 + k)

−8

+ 0.824(1 + k)

−9 + 0.841(1 + k)

−10 + 0.858(1 + k)

−10(k − 0.0202)

k is the prospective required real return equal to 6.32% or (1.0632)(1.025) = 8.98% nominal.

The equity premium is 8.98% − 4.62% = 4.36%.

3.6. The equity premium equals 4.25%.

3.7. βU

= 1.32/(1 + 0.50/0.50) = 0.66.

CHAPTER 4