Question

(DDM-Three stage Model Question)

Cathy Evert has been given the assignment of preparing a business valuation of ABC LTD. The following information was collected:

High Growth Stage Stable Growth Stage

Return on Assets 19% 4%

Payout 35% 59%

Debt Ratio 0.20 0.65

Length 2 Years Indefinite

Beta 1.05 0.90

Evert expects the high growth period to phase into the stable growth period evenly over a 2 year period before reaching stable growth in Year 5. The 20 year government bond rate is 5% and the market risk premium is 4.5%. Dividends per share were $3.52 at the end of the last period. Estimate the intrinsic value of ABC's shares ?

Answer 1

Calculation of Intrinsic value of ABC's shares:

Given,

Year	stage
1	High growth stage
2	High growth stage
3	Both High growth stage and Stable growth stage
4	Both High growth stage and Stable growth stage
5	Stable growth stage
6 to indefinite period	Stable growth stage

For year 1 and 2 :

Given,

Particulars	At High growth stage
DPS	$3.52
20 Year government bond(Rf)	5%
Market risk premium (Rm-Rf)	4.5%
β of firm	1.05
Debt Equity Ratio	0.20
Payout Ratio	35%
Return on assets	19%

Payout Ratio = 35%

Retention ratio

= 1 - Payout ratio

Retention ratio = 1 - 0.35 = 0.65

Growth rate(g)

= Return on assets×Retention Ratio

g = 19×0.65 = 12.35%

β of firm = 1.05

β of equity

= β of firm×(1+Debt equity ratio)

β of Equity = 1.05×(1+0.20) = 1.26

Cost of Equity (Ke) = Rf+β(Rm-Rf)

Ke = 5+1.26(4.5)

Ke = 10.67%

DPS1 = DPS0×(1+g)

DPS1 = 3.52×(1+0.1235) = 3.95472

DPS2 = DPS1×(1+g)

DPS2 = 3.95472×(1+0.1235) = 4.44312

For year 3 and 4 :

Given,

Particulars	At High growth stage	At Stable growth stage	At Both stages spread evenly
β of firm	1.05	0.90	0.975
Debt Equity Ratio	0.20	0.65	0.425
Payout ratio	35%	59%	47%
Return on assets	19%	4%	11.5%

Retention ratio = 1 - 0.47 = 0.53

Growth rate (g) = 11.5×0.53 = 6.095%

β of Equity = 0.975×(1+0.425) = 1.3894

Cost of Equity (Ke) = 5+1.3894(4.5) = 11.25%

DPS3 = DPS2×(1+g)

DPS3 = 4.44312×(1+0.06095) = 4.71394

DPS4 = DPS3×(1+g)

DPS4 = 4.71394×(1+0.06095) = 5.00125

For year 5 and indefinite period :

Given,

Particulars	At Stable growth stage
β of firm	0.90
Debt Equity Ratio	0.65
Payout ratio	59%
Return on assets	4%

Retention ratio = 1-0.59 = 0.41

Growth rate (g) = 4×0.41 = 1.64%

β of Equity = 0.90×(1+0.65) = 1.485

Cost of Equity (Ke) = 5+1.485(4.5) = 11.68%

DPS5 = DPS4×(1+g)

DPS5 = 5.00125×(1+0.0164) = 5.08327

Terminal value for Indefinite period:

= [ DPS5×(1+g)]÷(Ke - g)

= [5.08327×(1+0.0164)]÷(0.1168 - 0.0164)

= 51.4601

Calculation of value of ABC's shares:

Value of ABC's shares:

DPS1÷(1+Ke) + DPS2÷(1+Ke)^2 + DPS3÷(1+Ke)^3 + DPS4÷(1+Ke)^4 + DPS5÷(1+Ke)^5 + Terminal value÷(1+Ke)^5

Calculation of present value of dividends and present value of Terminal value:

Year	Dividend per share/Terminal value	Ke	Present value of Dividend per share/Terminal value
1	DPS1 = 3.95472	10.67%	3.95572÷1.1067 = 3.5734
2	DPS2 = 4.44312	10.67%	4.44312÷(1.1067)^2 = 3.6277
3	DPS3 = 4.71394	11.25%	4.71394÷(1.1067)^2×(1.1125) = 3.4596
4	DPS4 = 5.00125	11.25%	5.00125÷(1.1067)^2×(1.1125)^2 = 3.2993
5	DPS5 = 5.08327	11.68%	5.08327÷(1.1067)^2×(1.1125)^2×(1.1168) = 3.0027
6th year to indefinite period	Terminal value = 51.4601	11.68%	51.4601÷(1.1067)^2×(1.1125)^2×(1.1168) = 30.3973

Value of ABC's shares

= 3.5734+3.6277+3.4596+3.2993+3.0027+30.3973

= $47.36