06-26-2010, 07:21 AM
ABC Co. just paid a dividend of Rs.7.50 per share. The company will increase its dividend by 15% next year, and then will reduce this dividend growth rate by 5% annually until it reaches the industry average of 5 percent, after which the company will keep a constant growth rate forever. If the required return on ABC stock is 14.50 percent, what will be a share of stock sell for today?
Here we have D0= 7.5. Supernatural growth rate Gn = 15%. Ks=14.5%
Then in Y1 & Y2, G= 15%-5% = 10% & in Y3 it is 10%- 5%.= 5%
Step 1. Calculate the dividends expected at the end of each year during the supernormal growth period.
Step 2. The price of the stock is the PV of dividends from Time 1 to infinity, so in theory we could project each future dividend, with the normal growth rate, gn = 5%, used to calculate D2 and subsequent dividends. However, we know that after D2 has been paid, which is at Time 2, the stock becomes a constant growth stock. Therefore, we can use the constant growth formula to find P2, which is the PV of the dividends from Time 2 to infinity as evaluated at Time 2.
First, we determine D3 for use in the formula, and then we calculate P2 as follows: P2=D3/(Ks-g).
Step 3. Now that the cash flows have been placed on the time line, we can discount each cash flow at the required rate of return, ks=14.5%. We could discount each cash flow by dividing by (1.145)t, where t=1 for Time 1, t=2 for Time 2. This produces the PVs shown to the left below the time line, and the sum of the PVs is the value of the supernormal growth stock.
0 Gs=15% 1 Gs=10% 2 g=5% 3
|------------------------|---------------------------|-----------------------------|
D0=7.5 D1=8.625 D2=9.4875 D3=9.04
P2=95.11
a. Terminal or Horizon date is at end of 3 Yrs when Non-constant growth stops.
b. Do=7.5, Gs
= 15% = 0.15, N=2 yrs, g=5%, Ks=14.5%
So D1 = Do(1+Gs) = 7.5*(1+15%) = 7.5*1.15 = $8.625
AT Y2, Gs = 15%-5% = 10%
D2 = D1(1+Gs) = 8.625*1.10 = $9.4875
After 2 yrs, supernatural growth is over & normal growth of 5% starts till infinity
So D3 = D2(1+g) = 9.4875*(1+5%) = 9.4875*1.05 = $9.04
So P2 = D3/(Ks-g) = 9.04/(14.5%-5%) = 9.04/9.5% = $95.11
So Horizon value = D1/(1+Ks)^1 + D2/(1+Ks)^2 + (P2+D3)/(1+Ks)^3
ie HV = 8.625/1.145 + 9.4875/(1.145)^2 + (95.11+9.04)/(1.145)^3
ie HV = 7.53 + 7.24 + 69.38
ie HV = 84.15
So Horizon value of Stock is $84.15
So Share of Stock will sell today for $84.15
Here we have D0= 7.5. Supernatural growth rate Gn = 15%. Ks=14.5%
Then in Y1 & Y2, G= 15%-5% = 10% & in Y3 it is 10%- 5%.= 5%
Step 1. Calculate the dividends expected at the end of each year during the supernormal growth period.
Step 2. The price of the stock is the PV of dividends from Time 1 to infinity, so in theory we could project each future dividend, with the normal growth rate, gn = 5%, used to calculate D2 and subsequent dividends. However, we know that after D2 has been paid, which is at Time 2, the stock becomes a constant growth stock. Therefore, we can use the constant growth formula to find P2, which is the PV of the dividends from Time 2 to infinity as evaluated at Time 2.
First, we determine D3 for use in the formula, and then we calculate P2 as follows: P2=D3/(Ks-g).
Step 3. Now that the cash flows have been placed on the time line, we can discount each cash flow at the required rate of return, ks=14.5%. We could discount each cash flow by dividing by (1.145)t, where t=1 for Time 1, t=2 for Time 2. This produces the PVs shown to the left below the time line, and the sum of the PVs is the value of the supernormal growth stock.
0 Gs=15% 1 Gs=10% 2 g=5% 3
|------------------------|---------------------------|-----------------------------|
D0=7.5 D1=8.625 D2=9.4875 D3=9.04
P2=95.11
a. Terminal or Horizon date is at end of 3 Yrs when Non-constant growth stops.
b. Do=7.5, Gs
= 15% = 0.15, N=2 yrs, g=5%, Ks=14.5%
So D1 = Do(1+Gs) = 7.5*(1+15%) = 7.5*1.15 = $8.625
AT Y2, Gs = 15%-5% = 10%
D2 = D1(1+Gs) = 8.625*1.10 = $9.4875
After 2 yrs, supernatural growth is over & normal growth of 5% starts till infinity
So D3 = D2(1+g) = 9.4875*(1+5%) = 9.4875*1.05 = $9.04
So P2 = D3/(Ks-g) = 9.04/(14.5%-5%) = 9.04/9.5% = $95.11
So Horizon value = D1/(1+Ks)^1 + D2/(1+Ks)^2 + (P2+D3)/(1+Ks)^3
ie HV = 8.625/1.145 + 9.4875/(1.145)^2 + (95.11+9.04)/(1.145)^3
ie HV = 7.53 + 7.24 + 69.38
ie HV = 84.15
So Horizon value of Stock is $84.15
So Share of Stock will sell today for $84.15