hart enterprises recently paid a dividend, Do, of$1.25. It expects to have nonco
ID: 2662404 • Letter: H
Question
hart enterprises recently paid a dividend, Do, of$1.25. It expects to have nonconstant growth of 20% for 2years followed by a constant rate of 5% thereafter. Thefirms required return is 10%. a) how far away is the terminal or hoizon date? b) What is the firm's horizon or terminal Value? c) What is the firm's intrinisc value today, P0? hart enterprises recently paid a dividend, Do, of$1.25. It expects to have nonconstant growth of 20% for 2years followed by a constant rate of 5% thereafter. Thefirms required return is 10%. a) how far away is the terminal or hoizon date? b) What is the firm's horizon or terminal Value? c) What is the firm's intrinisc value today, P0?Explanation / Answer
Step 1. Calculate the dividends expected at the end of eachyear during the supernormal growth period. Step 2. The price of the stock is the PV of dividends fromTime 1 to infinity, so in theory we could project each future dividend, with the normal growth rate, gn= 5%, used to calculate D3 and subsequent dividends. However, we know that after D2 has beenpaid, which is at Time 2, the stock becomes a constant growth stock. Therefore, we can usethe constant growth formula to find P2, which is the PV of the dividends from Time 3 toinfinity as evaluated at Time 2. First, we determine D3 for use in the formula, and then wecalculate P2 as follows: P2=D3/(Ks-g).Step 3. Now that the cash flows have been placed on the timeline, we can discount each cash flow at the required rate of return, ks=10%. We could discount eachcash flow by dividing by (1.10)t, where t=1 for Time 1, t=2 forTime 2. This produces the PVs shown to the left below the timeline, and the sum of the PVs is the value of the supernormal growthstock. 0 Gs=20% 1 Gs=20% 2 g=5% 3 |------------------------|---------------------------|-----------------------------| D1=1.50 D2=1.80 D3=1.89 P2=37.80
a. Terminal or Horizon date is at end of 2 Yrs whenNon-constant growth stops.
b. Do=1.25, Gs = 20% = 0.20, N=2 yrs, g=5%, Ks=10%. Weneed to find Horizon Value P2 when Supernatural growth stops.
So D1 = Do(1+Gs) = 1.25(1+20%) = 1.25*1.20 = $1.50 D2 = D1(1+Gs) = 1.50*1.20 = $1.80 After 2 yrs, supernatural growth is over & normal growthof 5% starts till 8. So D3 = D2(1+g) = 1.80*(1+5%) = 1.80*1.05 = $1.89. So P2 = D3/(Ks-g) = 1.89/(10%-5%) = 1.89/0.05 = $37.80 So Horizon Value of stock is $37.80
c. Intrinsic Value P0 = PV of Dividend during non-constantgrowth + PV of Horizon value
So P0 = D1/(1+Ks)^1 + D2/(1+Ks)^2 + (P2+D3)/(1+Ks)^3 ie P0 = 1.5/1.10 + 1.8/(1.1)^2 + (37.80+1.89)/(1.1)^3 ie P0 = 1.364 + 1.488 + 29.82 ie P0 = 32.672 So Intrinsic value of Stock P0 is$32.672
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