Question

Stock X is expected to pay $2 dividend per year for ten

years and then a $20 liquidating dividend in the tenth year.
The appropriate discount rate is 12%.
What is X’s intrinsic value?

Answer 1

Answer:To calculate the intrinsic value of stock X, we need to find the present value of all the expected future cash flows using the given discount rate of 12%.

The annual dividends for the first nine years are $2, so the total present value of these dividends can be calculated using the perpetuity formula:

PV of perpetuity = Annual dividend / Discount rate

PV of perpetuity = $2 / 0.12 = $16.67

For the final year, the liquidating dividend is $20, which needs to be discounted back to the present value using the formula:

PV of lump sum = Future value / (1 + Discount rate) ^ Number of periods

PV of lump sum = $20 / (1 + 0.12) ^ 10 = $4.33

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

Intrinsic value = PV of perpetuity + PV of lump sum

Intrinsic value = $16.67 + $4.33 = $21

Therefore, the intrinsic value of stock X is $21.

Step-by-step explanation:

Answer 2

To calculate the intrinsic value of stock X, we need to find the present value of all the expected future cash flows using the given discount rate of 12%.

The annual dividends for the first nine years are $2, so the total present value of these dividends can be calculated using the perpetuity formula:

PV of perpetuity = Annual dividend / Discount rate
PV of perpetuity = $2 / 0.12 = $16.67

For the final year, the liquidating dividend is $20, which needs to be discounted back to the present value using the formula:

PV of lump sum = Future value / (1 + Discount rate) ^ Number of periods
PV of lump sum = $20 / (1 + 0.12) ^ 10 = $4.33

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

Intrinsic value = PV of perpetuity + PV of lump sum
Intrinsic value = $16.67 + $4.33 = $21

Therefore, the intrinsic value of stock X is $21.