Question

1. Smashed Pumpkin Farms (SPF) just paid a dividend of GH¢4.50 on its stock. The growth rate in dividends is expected to be a constant 7.5 percent per year, indefinitely. Investors require a 20 percent return on the stock for the first three years, an 11 percent return for the next three years, and then a 12 percent return, thereafter. What is the current share price for SPF stock?

2. Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next five years because the firm needs to plough back its earnings to fuel growth. The company will pay a GH¢6 per share dividend in six years and will increase the dividend by 5 percent per year, thereafter. If the required return on this stock is 21 percent, what is the current share price?

3. South Park Corporation is expected to pay the following dividends over the next four years: GH¢4.75, GH¢3, GH¢2, and GH¢1. Afterwards, the company pledges to maintain a constant 9 percent growth rate in dividends, forever. If the required return on the stock is 16 percent, what is the current share price?

4. Mega Growth Co. is growing quickly. Dividends are expected to grow at a 30 percent rate for the next three years, with the growth rate falling off to a constant 7 percent, thereafter. If the

the required return is 21 percent and the company just paid a GH¢1.50 dividend, what is the current share price?

5. Janicek Corp. is experiencing rapid growth. Dividends are expected to grow at 20 percent per year during the next three years, 15 percent over the following year, and then 10 percent per year, indefinitely. The required return on this stock is 15 percent, and the stock currently sells for GH¢50.00 per share. What is the projected dividend for the coming year?

Answer 1

1. Price of the share of Smashed Pumpkin can be calculated as below :

Current year dividend = 4.50 & it grows at 7.5% each year

Thus Year 1 dividend = 4.50 x (1+7.50%) = 4.84

Year 2 dividend would be = 4.84 X (1+7.50%) = 5.20. Similar for other dividends

Year 6 dividend is 6.94 and it will grow forever at 7.5%. The discount rate here is 12%

The terminal value of dividend = D0 x (1+g) / (k - g)

The terminal value of dividend at the end of year 6 = 6.94 x (1+7.50%) / (12% - 7.5%) = 165.90

Now we need to discount each year dividend with the discount rate

PV of dividend = Dt / (1+k)^t, where Dt is dividend in t year, k is the discount rate & t = time

PV of terminal value of dividend at year 6 = 165.90 / (1+12%)^6 = 84.05

Price of share = Sum of the PV of all dividends (including the terminal value) = 106.44

Year	0	1	2	3	4	5	6	7
Discount Rate		20%	20%	20%	11%	11%	11%	12%
Dividend	4.50	4.84	5.20	5.59	6.01	6.46	6.94
Terminal Value of Dividend								165.90
Growth Rate		7.50%	7.50%	7.50%	7.50%	7.50%	7.50%	7.50%
Present Value of Dividend		4.03	3.61	3.24	3.96	3.83	3.71	84.05
Price of share		106.44

2. The price of Metallica Bearing share would be 14.46

as given below

The year 6 dividend is 6

The terminal value of dividend = D0 x (1+g) / (k - g)

The terminal value of dividend at the end of year 6 = 6 x (1+5%) / (21% - 5%) = 39.38

We then find the PV of year 6 dividend and the terminal value of dividend

PV of dividend = Dt / (1+k)^t, where Dt is dividend in t year, k is the discount rate & t = time

PV of year 6 dividend =  6/ (1+21%)^6 = 1.91

PV of terminal Value = 39.38/ (1+21%)^6 = 12.55

Metallica Bearing
Year	0	1	2	3	4	5	6	7
Discount Rate								21%
Dividend		0.00	0.00	0.00	0.00	0.00	6.00
Terminal Value of Dividend								39.38
Growth Rate								5.00%
Present Value of Dividend		0.00	0.00	0.00	0.00	0.00	1.91	12.55
Price of share		14.46

C. South Park Corp will have share price = 16.76

The terminal value of dividend = 1 X (1+9%) / (16% - 9%) = 15.57

PV of terminal value = 15.57 / (1+ 16%)^4 = 8.60

South Park Corp
Year	0	1	2	3	4	5
Discount Rate		16%	16%	16%	16%	16%
Dividend		4.75	3.00	2.00	1.00
Terminal Value of Dividend						15.57
Growth Rate						9.00%
Present Value of Dividend		4.09	2.23	1.28	0.55	8.60
Price of share		16.76

D. Mega Growth share price would be 19.42

Mega Growth
Year	0	1	2	3	4
Discount Rate		21%	21%	21%	21%
Dividend	1.50	1.95	2.54	3.30
Terminal Value of Dividend					25.19
Growth Rate		30%	30%	30%	7%
Present Value of Dividend		1.61	1.73	1.86	14.22
Price of share		19.42