If the current risk free-rate is 6%, what should the current price of a stock be if its price and dividend next year are forecast to be $122 and $7, respectively, and its risk premium is 4%.

Question

BlackTom AI · Accepted Answer

The question asks for the present price of a stock given the next-year price, the dividend next year, and the total required return. Keep in mind that the stock’s current price today should be the present value of the next-year cash flow (price plus dividend) discounted at the required return.

Option 1: $70.00
This value would imply a very large discount or a much higher discount rate than the given 10% (6% risk-free plus 4% risk premium). If we discount 129 by 10%, we get 117.27, not 70.00. In other words, this price would underprice the stock relative to the provided forecast cash flows and required return.

Option 2: $110.91
At first glance, this looks like a plausible discounted value, but it corresponds to a discount factor slightly different from 10%. If we solve 129 ÷ (1 + r) = 110.91, we'd get (1 + r) ≈ 1.162, i.e., r ≈ 16.2%, which is not the stated 10% (6% + 4%). Therefore this option mismatches the given risk premium.

Option 3: $117.27
This is the value you get when you apply the correct discounting: price today equals (P1 + D1) divided by (1 + required return). Here, P1 = 122 and D1 = 7, so (122 + 7) = 129. With a required return of 6% + 4% = 10%, the present value is 129 / 1.10 = 117.27. This aligns with the provided inputs.

Option 4: $129.00
This would correspond to not discounting at all, i.e., treating the next-year cash flow as if it were received today. That ignores the time value of money and the required return, so it is inconsistent with the given risk premium and risk-free rate.

2025Fall-ECN3615-01 Final Exam Practice Quiz

If the current risk free-rate is 6%, what should the current price of a stock be if its price and dividend next year are forecast to be $122 and $7, respectively, and its risk premium is 4%.

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