Size Effect

1. c

2. d. The size premium is calculated as tlie realized return in excess of the riskless rate minus the CAPM-estimated return in excess of the riskless rate.

True or False Questions

3. False, The distinction is the beta for the security.

4. False. The S&P CVC studies use 25 size categories and start in 1963, when COMPUSTAT started, because they use COMPUSTAT data.

Fill-in-the-Blank Questions

5. Higher; higher

6. Tenth (lOlh)or 10b, the bottom half of Lhe 10th decile

Exercises

7. The size premium as computed by ftahotson equals tlie realized return in excess of the riskless rate minus tlie CAPM-estimated return in excess of the riskless rate (see also about investment opportunities).

So, 16%-- 11% = 5%

8. According to CAPM, the CAPM-estimated return in excess of tlie risk-free rate can be expressed as:

E(R,) - Rf=Bx (RPJ 11%= 1.5 xRPm RPKl=ll%n.5 = 133%

9. The equity risk premium for the 10th decile, according to CAPM, is equal to tlie return above the risk-free rate, or 10.67%, rounded to 11%.

10. According to CAPM:

E(R,)^Rf+Bx(RPj = 6% +1-5x733% = 6% +11% = 17%

11. To compute this, we will use the realized return in excess of the riskless rate, instead of the
CAPM-estimated return in excess of (lie riskless rate.

From CAPM:

E(R,) = Rf + Bx(RPj E(Rt) Rf = BxRPm 16% = 5x7.33% B = 2.18

d. CAPM assumes that rational investors seek to hold efficient portfolios hut the DCF method of estimating cost of capital does not make this assumption.

4. False. Most published esLimales come from "sell-side" analysis.

5. True. This is generally true because single-stage models rely on short- to intermediate-term earnings forecasts, which may not represent sustainable growth.

6. a. Single-stage model

b. MulLisLage model

7. TbboLson's Cost of Capital Yearbook

k=NCFoq + g) PV

= $1.00(1 + 0.05) $10.00

= il^ + 0.05 $10.00

= 0.105+0.05 = 0.155 or 15.5%

9. Company XYZ's cost of equity capital equals 0.098083 or 9.81% .

PV=l	561.70
NCFn	= $1.60
NCF5	= $2.24
NCF1(	, = $3.73
gl = 0	.070
ft. = 0.107
£3 = 0	.065

75 = NCF0 x (1 + g{f and NCF1Q = NCF0 x (1 + grf x (1 + glf

+

NCFJl+g,)
[NCF0(l+glT] ^[NCF5(l + g2r5] k-g3

10

(1 + kT tt (1 + kT (i + *)

Using modern spreadsheet applications, one can estimate the cost of equity capital by ilcra-tively solving the tliree-stage DCF model for PV, With the exception of PV, set one cell equal to each of the values (arguments) indicated above and one cell equal to a preliminary estimate of k. Finally, enter the three-stage DCF formula into one cell with each of the for­mula's arguments referring to the appropriate ceil containing that argument. Then simply enter in di fferent values for k until the indicated PV is equal to that of the current stock price.

The following formula was created using Microsoft Excel® and solves the three-stage DCF model for PV where the value for the foil owing arguments are entered in the indicated cells:

o

B3 NCF5 = E2 NCF10 = K3 *i=B4 ft=B5 & = B6 k = E2

=(((B3*(POWER(l+B41l)))/(POWER(l+E4,l)))+((B3*(POWER(l+B4,2)))/(POW:

E4?2)))+((B3-nPOWER(l+B4,3)))/(POWER(l+E43)))+((B3*(POWER(l+B4!4)))/"CPOW RR(l+M,4)))+(m3*(POWRRri+B4,5)))/(POWRRri+FA5))))+((rR2*(POWRR(l+B5,l)) )/(POWER(l+E4,6)))+((E2*(POWER(l+B5,2)))/(POWER(l+E4,7)))+((n2*(POWER(l+ B53))V(POWER(1+E4)8)))+C(E2*0>OWER(1+B5,4)))/(POWER(1+E4,9)))+((E2*(POW ER( 1 +B5,5)))/(POW ER (1+E4,10))))+(((E3*(l +B6))/(E4-B6))/(POW ER( 1+E4,1 ())))

To help you better understand the Microsoft Excel® statement, the following presents the same statement in its algebraic form:

>[B3(X+B*y] " [E2(l+B5r5] ~^Z^~

^ n-i- FAY ^

10

(l + E4)a ti. (l + E4)n (1 + E4)

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