Dear Students,
Hope all are doing well.
I am posting the Week 4_ Assignment taken from – Chapter 8. The questions are as follows;
– Chapter 8: Questions and Problems (page 288): Questions 1, 8, 13, 16, 18
This assignment is due on Thursday at 11:59pm.
Thank you so much.
See you soon.
Best regards,
Sujatha (She/Her)
Answers
QUESTION ONE
Stopperside Wardrobe Co. current price of its dividends can be calculated by use of the Gordon Growth Model. Under this model, the stock price is arrived at after dividing the current dividend with the required return and the dividend growth rate difference.
- Price= Current dividend/ (Required Return- Growth Rate)
= 1.45/ (0.11-0.06)
= 1.45/0.05
= $29
- Price in three years = current price*(1+gworth rate) ^ n
= 29*(1+0.06) ^3
= 29*(1.06) ^3
= 29*1.191016
= $ 34.54
- Price in 15 years= current price*(1+gworth rate) ^ n
= 29*(1+0.06) ^15
= 29*(1.06) ^15
= 29*2.39655819
= $ 69.50
QUESTION TWO
Value of stock paying perpetuity dividends= Dividend/ Required Return
Therefore, Required return= Dividend/ Value of the stock
= 4.75/93
= 0.0511
= 5.11%
QUESTION THREE
| PARTICULARS | TIME (years) | AMOUNT=d*(1+g) | PV=d/(1+r) ^n |
| Dividend(cashflow) | 1 | 3.20*(1+0.05) = 3.36 | 3.36/ (1+0.15) = 2.92 |
| Dividend(cashflow) | 2 | 3.36*(1+0.05) = 3.528 | 3.528/ (1+0.15) ^2=2.67 |
| Dividend(cashflow) | 3 | 3.528*(1+0.05) =3.7044 | 3.7044/ (1+0.15) ^3= 2.44 |
| Dividend(cashflow) | 4 | 3.7044*(1+0.05) =3.88962 | 3.88962/ (1+0.13) ^4= 2.39 |
| 5 | 3.88962*(1+0.05) =4.1 | 4.1/ (1+0.13) ^5=2.23 | |
| 6 | 4.1*(1+0.05) =4.305 | 4.305/ (1+0.13) ^6=2.07 |
Thus, the stock price at the end of the sixth year using the Gordon growth model
P= d/ (r-g)
= 4.305/ (0.11-0.05)
=$ 71.75
Present value of the stock price at the end of the sixth year will be calculated by use of the present value of future cashflows formula.
PV= d/(1+r) ^n
=$ 71.75/ (1+ 0.13) ^6
= $ 34.46
The current share price= sum of all the dividends present values for the first six years + present value of the stock price at the end of the sixth year
=2.92+2.67+2.44+2.39+2.23+2.07+34.46
= $49.18
QUESTION FOUR
Dividend value at end of year 4= D4 / Required Return- Growth Rate
= 2.50/ (0.12-0.05)
= $ 35.71
Present Value (PV)= d/(1+r) ^n
= 35.71/ (1+0.12) ^4
= $ 22.69
Present values from year 1 to 4 (PV= d/(1+r) ^n)
Year 1 12/ (1+0.12) = 10.71
Year 2 8/ (1+0.12) ^2= 6.38
Year 3 7/ (1+0.12) ^3 = 4.98
Year 4 2.5/ (1+0.12) ^4= 1.59
The current price = 10.71+6.38+4.98+1.59+22.69
= $ 46.35
QUESTION FIVE
Step 1: Computation of dividend in year 3
D3= D0 * (1+g1) ^3
Where g1=30%
= D0*(1+0.3) ^3
= D0*2.197
Step 2: Computation of year 4 dividend
D4=D0*(1+G1) ^3*(1+G2)
Where, g1=30%, g2=20%
= D0*(1+0.3) ^3*(1+0.2)
= D0*2.197*1.2
Step 3: D0 computation when the stock price is constant
R=10%, SP= $76, g3= 6%
76=D0*2.1970*1.2*(1+0.06) / (0.1-0.06)
76=D0*69.8646
D0=76/69.8646
= 1.0878 or 1.09
Step 4: Computation of dividend for the next year(D1)
D1= D0*(1+g1)
= 1.09*(1+0.3)
= 1.417 or 1.42
