Consider the following three stocks. (a) Stock A is expected to provide a divide
ID: 2659790 • Letter: C
Question
Consider the following three stocks.
(a) Stock A is expected to provide a dividend of $10 a share forever.
(b) Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is
expected to be 4 % a year forever.
(c) Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is
expected to be 20 % a year for 5 years (i.e., until year 6) and zero thereafter.
If the discount rate for each stock is 10 %, which stock is the most valuable? What if the
discount rate is 7 %?
Hint: Recall that the price of a stock is the PV of
the dividends.
I have come up with values for each stock at both discount rates, but I want to be sure that I did the calculations correctly.
For Stock A:
NPV = C/r = $10/.1 = $100 and NPV = C/r = $10/.07 = $142.86
For Stock B:
NPV = (C/1+r) + (C/r-g)*(1/(1+r)) = 5/1.1 +( 5/.06)/1.1 = $80.30 and NPV = (C/1+r) + (C/r-g)*(1/(1+r)) = 5/1.07 +( 5/.06)/1.07 = $160.44
For Stock C:
NPV = (C/1+r) + C(1+g)/(1+r)^2 + C(1+g)^2/(1+r)^3 + C(1+g)^3/(1+r)^4 + C(1+g)^4/(1+r)^5 + C(1+g)^5/(1+r)^6 + (C(1+g)^5/r)*(1/(1+r)^6) = (5/1.1) + C(1.04)/(1.1)^2 + C(1.04)^2/(1.1)^3 + C(1.04)^3/(1.1)^4 + C(1.04)^4/(1.1)^5 + C(1.04)^5/(1.1)^6 + (C(1.04)^5/.1)*(1/(1.1)^6) = $58.15
and
NPV = (C/1+r) + C(1+g)/(1+r)^2 + C(1+g)^2/(1+r)^3 + C(1+g)^3/(1+r)^4 + C(1+g)^4/(1+r)^5 + C(1+g)^5/(1+r)^6 + (C(1+g)^5/r)*(1/(1+r)^6) = (5/1.07) + C(1.04)/(1.07)^2 + C(1.04)^2/(1.07)^3 + C(1.04)^3/(1.07)^4 + C(1.04)^4/(1.07)^5 + C(1.04)^5/(1.07)^6 + (C(1.04)^5/.07)*(1/(1.07)^6) = $84.05
So, for a discount rate of 10%, Stock A is worth the most at $100, and for a discount rate of 7%, Stock B is worth the most at $160.44.
If someone could check my work/suggest another way to go about solving this problem, that would be great!
Explanation / Answer
For stock A -
Intrinsic value of stock A = $10/.10
=$100
For stock B -
Intrinsic value of stock B = $5/[.10-.04]
= $83.33
For stock C -
Intrinsic value of stock C = 5/1.10 + 5*1.20/1.10^2 + 5*1.20^2/1.10^3 + 5*1.20^3/1.10^4 + 5*1.20^4/1.10^5 + 5*1.20^5/1.10^6 + (5*1.20^6/.10)/1.10^7
= 110.89
if discount rate is 7%
For stock A -
Intrinsic value of stock A = $10/.07
=$143
For stock B -
Intrinsic value of stock B = $5/[.10-.04]
= $166.66
For stock C -
Intrinsic value of stock C = 5/1.10 + 5*1.20/1.10^2 + 5*1.20^2/1.10^3 + 5*1.20^3/1.10^4 + 5*1.20^4/1.10^5 + 5*1.20^5/1.10^6 + (5*1.20^6/.10)/1.10^7
= 131.04