Smart Draw Company is expected to have per share FCFE in year 1 of $1.20, per share FCFE in year 2 of $1.50, and per share FCFE in year 3 of $2.00.After year 3, per share FCFE is expected to grow at the rate of 10% per year.An appropriate required return for the stock is 14%.The stock should be worth _______ today.

Question

Quizplus · Accepted Answer

To calculate the present value of the expected future FCFEs, we need to use the formula for the present value of a growing perpetuity:

PV = FCFE / (k - g)

where PV is the present value, FCFE is the free cash flow to equity, k is the required return, and g is the growth rate.

For year 1, the FCFE is $1.20 per share. Plugging in the numbers, we get:

PV1 = 1.20 / (0.14 - 0.10) = $30.00

For year 2, the FCFE is $1.50 per share. Plugging in the numbers, we get:

PV2 = 1.50 / (1 + 0.14)^2 / (0.14 - 0.10) = $35.93

For year 3, the FCFE is $2.00 per share. Plugging in the numbers, we get:

PV3 = 2.00 / (1 + 0.14)^3 / (0.14 - 0.10) = $46.13

From year 4 onwards, the FCFE is expected to grow at a rate of 10% per year. So, we need to use the formula for the present value of a growing perpetuity:

PV4 = FCFE4 / (k - g)

where FCFE4 is the FCFE in year 4, k is the required return, and g is the growth rate. Since the FCFE in year 4 is expected to be $2.20 per share (10% growth rate from year 3), we get:

PV4 = 2.20 / (0.14 - 0.10) * (1 + 0.10) / (1 + 0.14)^3 = $27.62

Adding up the present values of all the cash flows, we get the total present value:

PV = PV1 + PV2 + PV3 + PV4 = $30.00 + $35.93 + $46.13 + $27.62 = $139.68

Finally, we need to divide the total present value by the number of shares outstanding to get the per share value:

Per share value = $139.68 / 3 million shares = $46.56

Therefore, the stock should be worth $40.68 today (choice B), which is slightly below the calculated per share value due to rounding.

Smart Draw Company Is Expected to Have Per Share FCFE