Question

Sanaponic, Inc. will pay a dividend of $6 for each of the next 3 years, $8 for each of the years 4-7, and $10 for the years 8-10. Thereafter, starting in year 11, the company will pay a constant dividend of $8/year forever. If you require 18 percent rate of return on investments in this risk class, how much is this stock worth to you?

	A.	$55.99
	B.	$34.54
	C.	$41.46
	D.	$50.50
	E.	$45.68
	F.	$37.77

Answer 1

C. $ 41.46

Each cash flow from the stock should be discounted back to the present day using discount factor of 18%.

Before we start discouting the cash flows we need to calculate the value of perpetual annuity of $8 at the beginning of year 11.

Value of perpetuity = Cash Flow / Rate of Reutrn or Yield = $8 / 0.18 = 44.44

Now,

PV of Cash flows = 6 /(1.18) + 6 /(1.18)^2 + 6 /(1.18)^3 + 8 /(1.18)^4 + 8 /(1.18)^5 + 8 /(1.18)^6 + 8 /(1.18)^7 + 10/(1.18)^8 + 10 /(1.18)^9 + 10 /(1.18)^10 + 44.44 /(1.18)^10

Note - the final cash flow is dicounted only for 10 years as the cash flow will happend from beggining of the 11the year

Therefore, PV of Cash flows = 5.08 + 4.31 + 3.65 + 4.13 + 3.50 + 2.96 + 2.51 + 2.66 + 2.25 + 1.91 + 8.49

= $ 41.46

Hence value of the stock is $ 41.46