Question

Valuation Methods Exercise

Assume all years' cash flows will grow 4%

Excel 1

11.875% - cost of equity
4.000%- terminal growth rate
Forecasted years in the future 0 1 2 3 4 5 Terminal value FCFE 1050
What is the total value of equity?
What % of the total equity value is represented by the PV of the Terminal Value?
By what % does the equity value change if the terminal growth rate increases 1/2 percentage point?
By what % does the equity value change if the discount rate increases 1/10 percentage point?
By what % does the equity value change if the terminal growth rate decreases 1/2 percentage point?
By what % does the equity value change if the discount rate decreases 1/10 percentage point? Excel 2: 9.454%-WACC 4.000%-terminal growth rate $5,200-MV debt st year 0 Forcasted years in the future 0 1 2 3 4 5 FCFE 1000 What is the total value of equity? What % of the total equity value is represented by the PV of the Terminal Value? By what % does the equity value change if the terminal growth rate increases 1/2 percentage point? By what % does the equity value change if the discount rate increases 1/10 percentage point? By what % does the equity value change if the terminal growth rate decreases 1/2 percentage point? By what % does the equity value change if the discount rate decreases 1/10 percentage point? Excel 3: 10.000% - unlevered cost of capital 4.000%- terminal growth rate 40.000% - tax rate $          5,200 - MV debt at year 0 Forecasted years in the future 0 1 2 3 4 5 TV FCFF 1000 Tax saving 100 What is the total value of equity? What % of the total equity value is represented by the PV of the Terminal Value? By what % does the equity value change if the terminal growth rate increases 1/2 percentage point? By what % does the equity value change if the discount rate increases 1/10 percentage point? By what % does the equity value change if the terminal growth rate decreases 1/2 percentage point? By what % does the equity value change if the discount rate decreases 1/10 percentage point?

Answer 1

(1) Cost of Equity = 11.875 %, All cash flow will grow at a uniform rate of 4 % per annum. The terminal growth rate is also 4 %. As is observable, the terminal value of FCFE is calculated for cash flows after the end of Year 5 and the calculation is done at the end of Year 5.

FCFE0 = $ 1050

FCFE1 = 1.04 x 1050 = $ 1092

FCFE2 = 1092 x 1.04 = $ 1135.68

FCFE3 = 1135.68 x 1.04 = $ 1181.072

FCFE4 = 1181.1072 x 1.04 = $ 1228.351488

FCFE5 = 1.04 x 1228.351488 = $ 1277.485548

FCFE6 = 1.04 x 1277.485548 = $ 1328.584969

Terminal Value of Equity (at the end of Year 5) = 1328.584969 / (0.11875 - 0.04) = $ 16870.92025

Total Equity Value = FCFE1 / (Cost of Equity - Growth Rate) = 1092 / (0.11875 - 0.04) = $ 13866.67

As the FCFEs grow at the same rate of 4 % throughout any FCFE can function as the terminal FCFE and used as an input in the Gordon Growth Model to determine the firm's equity value.

(b) Terminal Value pf Equity = $ 16870.92025

PV of Terminal Value = 16870.92025 / (1.11875)^(5) = $ 9626.6134

% of Total Equity Value = (9626.6134 / 13866.67) x 100 = 69.423 % approximately.

(c) A terminal growth rate of 4.5 % entails that one cannot use any FCFE as the terminal FCFE as the growth rates becomes non-uniform. The terminal FCFE has to be the one which is the first of a series after which the terminal growth rate of 4.5 % is prevalent. In this context the terminal FCFE is FCFE5

PV of FCFE5 = 1277.485548 / (0.11875 - 0.045) x 1 / (1.11875)^(4) = $ 11057.62297

PV of FCFEs from Year 1 to Year 4 = $ 3511.089862

Total Equity Value = 11057.62297 + 3511.089862 = $ 14568.713

% Change in Equity Value = (14568.713 - 13866.67 / 13866.67) x 100 = 5.063 %

(d) A 1/10 % point change in the discount rate would mean that the new cost of equity would be 11.975 %

As all cash flows grow at the perpetual growth rate of 4 %, any FCFE can be used as the terminal FCFE.

Hence, Equity Value = FCFE1 / (0.11975 - 0.04) = 1092 / (0.11975 - 0.04) = $ 13692.79

% Change in Equity Value = (13692.79 - 13866.67/ 13866.67) x 100 = - 1.254 %

NOTE: Please raise separate queries for solutions to the remaining sub-part and the second unrelated question.