Shares in Brothers Grimm, Inc., manufacturers of gingerbread houses, are expected to pay a dividend of $5.00 in one year and to sell for $100 per share at that time. How much should you be willing to pay today per share of Grimm under the following circumstances? A) If the safe rate of interest is 5 percent and you believe that investing in Grimm carries no risk?
B) If the safe rate of interest is 10 percent and you believe that investing in Grimm carries no risk?C) If the safe rate of interest is 5 percent, but your risk premium is 3 percent?
D) Repeat parts a to c, assuming that Grimm is not expected to pay a dividend, but the expected price is unchanged..

(a) $100.00

(b) $95.45

(c) $97.22

(di) $95.24

(dii) $90.91

(diii) $92.59

Explanation:

Brothers Grimm corporation is responsible for the manufacturing of gingerbread houses. During a one year period, they are expected to pay a dividend of $5 and to sell each shares for $100. The share value for different safe interests is calculated as follows

a) If the safe interest is 5%, then the share value for today is

= ( 5+100)/( 1+5/100)

= 105/ ( 1+0.05)

= 105/1.05

= $100.00

b) If the safe interest is 10%, the share value for today would be

= (5+100)/(1+10/100)

= 105/( 1+0.1)

= 105/1.1

= 95.454

= $95.45( to 2 decimal places)

c) If the safe interest is 5% and the risk premium is 3%, then the share value for today is

= (5+100)/(1+(5+3)/100)

= 105/( 1+8/100)

= 105/(1+0.08)

= 105/1.08

= $97.222

= $97.22 (to 2 decimal places)

d) Since Grimm is not expected to pay dividend, the share values for each safe interest can be calculated as follows:

i) If the safe interest is 5% and there is no payment of dividend, then the share value for today is

= 100/( 1+5/100)

= 100/( 1+0.05)

= 100/1.05

= $95.238

= $95.24 ( to 2 decimal places)

ii) If the safe interest is 10% and there is no payment of dividend, then the share value for today is

= 100/( 1+10/100)

= 100/( 1+ 0.1)

= 100/1.1

= $90.909

= $90.91 ( to 2 decimal places)

iii) If the safe interest is 5% and the risk premium is 3% with no payment of dividend, the share value for today is calculated as

= 100/(1+8/100)

= 100/(1+0.08)

= 100/1.08

= $92.592

= $92.59 ( to 2 decimal places)

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