Question

I am considering buying a preferred stock for $90 per share. The stock has an annual dividend of $16 and I expect to be able to sell it for its $100 per share face value in three years. What is the required rate of return of the stock?

Answer 1

Solution

Current Market Price of Stock = $90/Share

Annual Dividend = $16/Share

Period = 3Years

Required rate of Return By IRR Method

Current market price = Dividend for 1st Year/(1+Required rate of return)¹ + Dividend for 2nd Year/(1+Required rate of return)² + Dividend for 3rd Year/(1+Required rate of return)³ + Selling Price/(1+Required rate of return)³

Now Dividend is same in all 3 years therefore we have

Current market price = Dividend * PVAF (r, nYears) + Selling Price * PVF (r, nYears)

Let Required rate of return be 20%

$90 = Dividend * PVAF (20%, 3Years) + Selling Price * PVF (20%, 3Years)

$90 = $16 * 2.106 + $100 * 0.579

NPV = $91.596 - $90

NPV = +$1.596

Let Required rate of return be 25%

$90 = Dividend * PVAF (25%, 3Years) + Selling Price * PVF (25%, 3Years)

$90 = $16 * 1.952 + $100 * 0.512

NPV = $82.432 - $90

NPV = -$7.568

Now By Internal rate of return we have

Lower rate return + Lower rate NPV/(Lower rate NPV - Higher rate NPV) * Difference of Higher rate and lower rate

20% + $1.596/$1.596 - (-$7.568) * (25% - 25%)

= 20.87%

Therefore Required rate of Return is 20.87%