Question

1. Given the information in the table, what is the dividend yield from t=0 to t=1?

Today’s Dividend	$3.98
Discount Rate	5.97%
Growth rate in dividends 0 to 1	6.37%
Growth rate in dividends 1 to 2	8.88%
Growth rate in dividends 2 to 3	8.46%
Growth rate in dividends 3 onward	4.30%

2.

Given the information in the table, what is TODAY’s price of the stock?

Today’s Dividend	$2.80
Discount Rate	5.00%
Growth rate in dividends 0 to 1	5.00%
Growth rate in dividends 1to 2	2.00%
Growth rate in dividends 2 to 3	3.00%
Growth rate in dividends 3 onward	3.00%

Answer 1

1. Dividend Year 1 =3.98*(1+6.37%) =4.2335
Dividend Year 2 =3.98*(1+6.37%)*(1+8.88%) =4.6095
Dividend Year 3 =3.98*(1+6.37%)*(1+8.88%)*(1+8.46%) =4.9994
Dividend Year 4 =3.98*(1+6.37%)*(1+8.88%)*(1+8.46%)*(1+4.30%)=5.2144
Terminal value =Dividend Year 4/Required Rate =5.2144/(5.97%-4.30%) =312.2395
Price of stock =D1/(1+r)+D2/(1+r)^2+D3/(1+r)^3+Terminal Value/(1+r)^3
=4.2335/(1+5.97%)+4.6095/(1+5.97%)^2+4.9994/(1+5.97%)^3+312.2395/(1+5.97%)^3=274.69
Dividend Yield =Dividend Year 1/Price of stock =4.2335/274.69 =1.54%

2. Dividend Year 1 =2.80*(1+5%) =2.94
Dividend Year 2 =2.80*(1+5%)*(1+2%) =2.9988
​​​​​​​Dividend Year 3 =2.80*(1+5%)*(1+2%) *(1+3%) =3.0888
Dividend Year 4 =2.80*(1+5%)*(1+2%) *(1+3%)*(1+3%)=3.1814
Terminal value =Dividend Year 4/Required Rate =3.1814/(5.00%-3%) =159.07
Price of stock =D1/(1+r)+D2/(1+r)^2+D3/(1+r)^3+Terminal Value/(1+r)^3
=2.94/(1+5%)+2.9988/(1+5%)^2+3.0888/(1+5%)^3+159.07/(1+5%)^3=145.60
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