Shares in Brothers Grimm Incorporated, manufacturers of gingerbread houses, are expected to pay a dividend of 8.00 in one year and to sell for 94 per share at that time. How much should you be willing to pay today per share of Grimm under the following circumstances? Instructions: Enter all responses rounded to two decimal places. a. Consider a safe rate of interest of 5.6 percent and assume that investing in Grimm carries no risk. Grimm's share value would be square b. Consider a safe rate of interest of 10.6 percent and assume that investing in Grimm carries no risk. Grimm's share value would be c. Consider a safe rate of interest of 5.6 percent, but your risk premium is 2 percent. The share value today would be 1 square Now assume that Grimm is not expected to pay a dividend, but the expected price is unchanged. Instructions: Enter all responses rounded to two decimal places. d. Consider a safe rate of interest of 5.6 percent and assume that investing in Grimm carries no risk Grimm's share value would be ( e. Consider a safe rate of interest of 10.6 percent and assume that investing in Grimm carries no risk. Grimm's share value would be f. Consider a safe rate of interest of 5.6 percent and a risk premium of 2 percent. Grimm's share value would be square

To determine the present value of Grimm's shares under different scenarios, we use the formula for the present value of a future cash flow:<br /><br />\[ \text{Present Value} = \frac{\text{Future Cash Flow}}{(1 + r)^n} \]<br /><br />where \( r \) is the discount rate and \( n \) is the number of periods (in this case, 1 year).<br /><br />### Part a:<br />- **Safe rate of interest:** 5.6%<br />- **Dividend in one year:** \$8<br />- **Expected price in one year:** \$94<br /><br />The future cash flow is the sum of the dividend and the expected price: <br />\[ \text{Future Cash Flow} = 8 + 94 = 102 \]<br /><br />The present value is calculated as follows: <br />\[ \text{Present Value} = \frac{102}{(1 + 0.056)^1} = \frac{102}{1.056} \approx 96.59 \]<br /><br />Grimm's share value would be **\$96.59**.<br /><br />### Part b:<br />- **Safe rate of interest:** 10.6%<br /><br />Using the same future cash flow of \$102: <br />\[ \text{Present Value} = \frac{102}{(1 + 0.106)^1} = \frac{102}{1.106} \approx 92.20 \]<br /><br />Grimm's share value would be **\$92.20**.<br /><br />### Part c:<br />- **Safe rate of interest:** 5.6%<br />- **Risk premium:** 2%<br />- **Total discount rate:** 5.6% + 2% = 7.6%<br /><br />Using the total discount rate: <br />\[ \text{Present Value} = \frac{102}{(1 + 0.076)^1} = \frac{102}{1.076} \approx 94.79 \]<br /><br />The share value today would be **\$94.79**.<br /><br />### Part d:<br />- **No dividend**<br />- **Safe rate of interest:** 5.6%<br />- **Expected price in one year:** \$94<br /><br />The future cash flow is just the expected price: <br />\[ \text{Present Value} = \frac{94}{(1 + 0.056)^1} = \frac{94}{1.056} \approx 89.20 \]<br /><br />Grimm's share value would be **\$89.20**.<br /><br />### Part e:<br />- **No dividend**<br />- **Safe rate of interest:** 10.6%<br /><br />Using the expected price of \$94: <br />\[ \text{Present Value} = \frac{94}{(1 + 0.106)^1} = \frac{94}{1.106} \approx 84.97 \]<br /><br />Grimm's share value would be **\$84.97**.<br /><br />### Part f:<br />- **No dividend**<br />- **Safe rate of interest:** 5.6%<br />- **Risk premium:** 2%<br />- **Total discount rate:** 7.6%<br /><br />Using the total discount rate: <br />\[ \text{Present Value} = \frac{94}{(1 + 0.076)^1} = \frac{94}{1.076} \approx 87.34 \]<br /><br />Grimm's share value would be **\$87.34**.