ABMF4024 BUSINESS FINANCE
Tutorial 3 (Cont) Answer
November Novembe r 1, 2010
Question 1 a) An upward shift shift in interest rates and investors¶ required rates of return would cause (r s)to increase and the price of the firm's stock (Po) to decrease. b) A reduction in the future growth potential of of the firm's earnings and dividends due toincreased foreign competition would lower the firm's future dividends (D1, D2,...) andhence decrease the stock price (Po). c) An increase in the riskiness of the firm's common stock due to larger South Americaninvestments by the firm would increase the (margi (margi nal) investor's required rate of return(r s) and hence decrease the stock price (Po), unless the growth potential of these investments outweighed the increase risk. Question 2 The financial decisions of the firm affect both expected future dividend payments of the firm (D1, D2...) as well as the (marginal) investor's required rate of return (r s). Shareholder wealth (stock price) is a function of these variables and hence is a function of the financial decisions of the firm. Question 3 Hart Enterprises recently paid a dividend, D 0 of $1.25. It expects to have nonconstant growth of 20 percent for 2 years followed by a constant rate of 5 percent thereafter. The firm¶s required return is 10 percent . Question 4 a) How far away is the terminal, or horizon, date? The
terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at the end of Year 2. b) What is the firm¶s horizon, or terminal, terminal, value? b. 0 | 1.25
r s = 10% gs = 20%
1 | 1.50
gs = 20%
2 | g 1.80
n
37.80 =
3 | 1.89
= 5%
1 .89 0.10 0.05
The
horizon, or terminal, value is the value at the horizon date of all dividends expected thereafter. In this problem it is calculated as
follows:
$ . .
( . ) .
!
$ 7.
.
ABMF4024 BUSINESS FINANCE
Tutorial 3 (Cont) Answer
c) What is the firm¶s intrinsic value today,
November Novembe r 1, 2010
P 0 ?
The
firm¶s intrinsic value is calculated as the sum of the present value of all dividends during the supernormal growth period plus the present value of the terminal value. Using your financial calculator, enter the following inputs: CF 0 = 0, CF1 = 1.50, CF 2 = 1.80 + 37.80 = 39.60, I/YR = 10, and then solve for NPV = $34.09.
Question 5 = $25; D1 = $1.25; r s = 0.12 Given P0 = D1/P0 + g Hence r s 0.12 = 1.25/25 + g g = 0.7 (or 7%) Question 6 Present Value of First 4-Year's Dividends: [D0(1 + g1)t/(1 + r s)t]; D0 = $1.50; g1 = .11; r s = .14; t=1 Year (t) 1 2 3 4
Dividend Interest Factor Dt =1.50(1+ 0.11)t PVIF14%,t 1.50(1 1.50(1 + .11)1 =$1.6650 =$1.6650 0.877 1.50(1 1.50(1 + .11)2 =$1.8482 =$1.8482 0.769 1.50(1 + .11)3 =$2.0514 0.675 1.50(1 1.50(1 + .11)4 =$2.2771 =$2.2771 0.592 PV (First 4-Years' Dividends) Dividends) :
Present Value Dt x PVIF14%,t 1.460 1.421 1.385 1.348 $5.614
Value of Stock at End of Year 4: P4= D5/(r sí g2) g2 = .05 D5= D4(1 + g2) = 2.2771(1 + .05) = $2.391 P4 = 2.391/(.14 í .05) = $26.567 Present Value of P4: PV(P4) = P4/(1 + r s)4 = $26.567/(1 + .14) 4 = $26.567(PVIF. 14,4) = $26.567 x 0.592 = $15.728 Value of Common Stock (P 0): P0 = PV(First 4-Years' Dividends) + PV(P4) = $5.614 + $15.728 = $21.34
Question 7 a) FVn = PVo(1+ g) n
ABMF4024 BUSINESS FINANCE
Tutorial 3 (Cont) Answer
November Novembe r 1, 2010
PVo = $2.00; FV6 FV6 = $4.00 ; n = 6 4.00 = 2.00(1 + g) 6 (1 + g) 6 = 2.000 term (1 + g) 6 represents the future value interest factor (FVIF g,6 ) inTable I at the back of the book. Reading across the Period = 6 row, onefinds (1 + g ) 6 in the i 12% column. Therefore g 0.12 (or 12%). The
b) Dt= D0(1 + g)t ; D0 = $2.00 Year t 1 2 3 4 5 6
Dividend* Dt = 2.00(1 + g) t 2.00(1 + .12) 1 = $2.240 2.00(1 + .12) 2 = $2.509 2.00(1 + .12) 3 = $2.8l0 2.00(1 + .12) 4 = $3.147 2.00(1 + .12) 5 = $3.525 2.00(1 + .12) 6 = $3.948
*Note: The (1 + 0.12) t factors can be obtained from Table I, i.e., (1 + 0.12) t = FVIF.12,t Earnings per year will be exactly two times the projected dividends. c) P0 = D1/(r s - g) r s= 0.18; g = 0.12; D1 = $2.240 P0= 2.240/(0.18 í 0.12) = $37.33
Question 8 The dividend at the end of two years = $1 (FVIF0.20, 2) = $1.44 D3 = $1.44(1.06) = $1.526 D4 = $1.53(1.06) = $1.618 D5 = $1.62(1.06) = $1.715 The
price of the stock at the beginning of year 5 is the same as at the end ofyear 4, orP4 = $1.715/ (0.15 í 0.06) = $19.06
