In: Finance
(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 ?
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