Equity Valuation

[reddyna]

Can someone please explain why the growth rate is becoming constant at D2, instead of D3? To me, the growth rate doesn’t become constant until D3…but I’m obviously missing something here….
Day and Associates is experiencing a period of abnormal growth. The last dividend paid by Day was $0.75. Next year, they anticipate growth in dividends and earnings of 25% followed by negative 5% growth in the second year. The company will level off to a normal growth rate of 8% in year three and is expected to maintain an 8% growth rate for the foreseeable future. Investors require a 12% rate of return on Day. The value of Day stock today is closest to:

A)
$20.70.

B)
$24.05.

C)
$18.65.
First find the abnormal dividends:
D1 = $0.75 × 1.25 = $0.9375
D2 = $0.9375 × 0.95 = $0.89
D2 is the first dividend that will grow at a constant rate. We can use this dividend in the constant growth DDM to get a value for the stock in period 1:
$0.89 / (0.12 - 0.08) = $22.25
Value of the stock today = ($22.25 + $0.9375) / 1.12 = $20.70.

 

[tickersu]

reddyna wrote:
Can someone please explain why the growth rate is becoming constant at D2, instead of D3? To me, the growth rate doesn’t become constant until D3…but I’m obviously missing something here….
Day and Associates is experiencing a period of abnormal growth. The last dividend paid by Day was $0.75. Next year, they anticipate growth in dividends and earnings of 25% followed by negative 5% growth in the second year. The company will level off to a normal growth rate of 8% in year three and is expected to maintain an 8% growth rate for the foreseeable future. Investors require a 12% rate of return on Day. The value of Day stock today is closest to:

A)
$20.70.

B)
$24.05.

C)
$18.65.
First find the abnormal dividends:
D1 = $0.75 × 1.25 = $0.9375
D2 = $0.9375 × 0.95 = $0.89
D2 is the first dividend that will grow at a constant rate. We can use this dividend in the constant growth DDM to get a value for the stock in period 1:
$0.89 / (0.12 - 0.08) = $22.25
Value of the stock today = ($22.25 + $0.9375) / 1.12 = $20.70.

The key sentence is bolded (you can take the terminal value [P1, in this example] as the first, constant-growth dividend, capitalized by r-g, and g is the constant growth rate). However, you could send D2 forward one year at 8% to get D3, then capitalize it at 0.12-0.08 to find P2. Add P2 to D2 then discount back and add to the PV of D1. You should get the same answer (it might be more intuitive for you do choose this method).
P2= D3/(r-g) = [D2*(1+g)]/(r-g) = ($0.89*1.08)/(.12-.08)
D2 + P2 = $0.89 + $24.03 = $24.92
D1 = $0.9375
Sum the PVs to get $20.703

 

[reddyna]

Thanks! Yeah, the intuition here is throwing me off. I guess the breakdown for me is why is D2 the first dividend that will grow at a constant rate at 8%?? Looks to me like D3 is the first dividend that will grow at the constant rate of 8%…
Is the logic here that D2 will grow at a rate of 8 percent to get us to D3? If that’s the case, why isn’t the 8 percent being included in the numerator of D2? Instead, it was multiplied by .95 (negative growth rate of 5 percent)