Suppose that the effective 1-year risk-free rate is 6% per annum. The value of the stock in 1 year is random and not known today. The different possible values of the stock in 1 year are given in the table below. The corresponding risk-neutral probabilities are also shown in the table.
|
Value |
$10 |
$12 |
$14 |
$15 |
$17 |
$22 |
$26 |
|
Risk Neutral Prob. |
0.10 |
0.10 |
0.25 |
0.15 |
0.20 |
0.10 |
0.10 |
The annual cost-of-capital for the stock is 19.45%.
Find the fair value of the stock today.
Price of Bond = PV of CFs from it.
Price after 1 Year:
| Prob | Price | Expetec Price |
| 0.1 | $ 10.00 | $ 1.00 |
| 0.1 | $ 12.00 | $ 1.20 |
| 0.25 | $ 14.00 | $ 3.50 |
| 0.15 | $ 15.00 | $ 2.25 |
| 0.2 | $ 17.00 | $ 3.40 |
| 0.1 | $ 22.00 | $ 2.20 |
| 0.1 | $ 26.00 | $ 2.60 |
| Expected Price after 1 Year | $ 16.15 |
Price Today = price after 1 Year / [ 1 + ke ]
= $ 16.15 / [ 1+0.1945 ]
= $ 16.15 / 1.1945
= $ 13.52
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