想问一下这种求sensitive，只用比较最终变量range的大小，不需要除以变化变量的变化值，再比较大小吗

问题如下：

Singh and Ho next analyze Colanari. Last year, Colanari had FCFF of €140 million. Singh instructs Ho to perform a FCFF sensitivity analysis of Colanari’s firm value using the three sets of estimates presented in Exhibit 3. In her analysis, Ho assumes a tax rate of 35% and a stable capital structure of 30% debt and 70% equity.

Exhibit 3:. Sensitivity Analysis for Colanari Valuation

Based on Exhibit 3, Ho’s FCFF sensitivity analysis should conclude that Colanari’s value is most sensitive to the:

选项：

A.

FCFF growth rate

B.

before-tax cost of debt

C.

required rate of return for equity

解释：

Colanari’s valuation is most sensitive to the cost of equity (re) because the range of estimated values is larger than the valuation ranges estimated from the sensitivity analysis of both the FCFF growth rate (GFCFF) and the before-tax cost of debt (rd).

WACC = [wd × rd(1 – Tax rate)] + (we × re).

Firm value = FCFF0(1 + g)/(WACC – g).

Cost of equity sensitivity

Using the base case estimates for the FCFF growth rate and the before-tax cost of debt and using the low estimate for the cost of equity (re) of 10.0%, the valuation estimate is

WACC = [(0.30)(0.049)(1 – 0.35)] + (0.70)(0.10) = 7.96%.

Firm value = 140 million(1 + 0.046)/(0.0796 – 0.046) = €4,364.18 million.

Using the base case estimates for the FCFF growth rate and the before-tax cost of debt and using the high estimate for the cost of equity (re) of 12.0%, the valuation estimate is

WACC = [(0.30)(0.049)(1 – 0.35)] + (0.70)(0.120) = 9.36%.

Firm value = 140 million(1 + 0.046)/(0.0936 – 0.046) = €3,079.38 million.

Therefore, the range in valuation estimates from using the highest and lowest estimates of the cost of equity is €1,284.80 million.

FCFF growth rate sensitivity

Using the base case estimates for the cost of equity and the before-tax cost of debt and using the low estimate for the FCFF growth rate (GFCFF) of 4.2%, the valuation estimate is

WACC = [(0.30)(0.049)(1 – 0.35)] + (0.70)(0.11) = 8.66%.

Firm value = 140 million(1 + 0.042)/(0.0866 – 0.042) = €3,274.16 million.

Using the base case estimates for the cost of equity and the before-tax cost of debt and using the high estimate for the FCFF growth rate (GFCFF) of 5.0%, the valuation estimate is

WACC = [(0.30)(0.049)(1 – 0.35)] + (0.70)(0.11) = 8.66%.

Firm value = 140 million(1 + 0.05)/(0.0866 – 0.05) = €4,021.34 million.

Therefore, the range in valuation estimates from using the highest and lowest estimates of the FCFF growth rate is €747.18 million.

Before-tax cost of debt sensitivity

Using the base case estimates for the FCFF growth rate and the cost of equity and using the low estimate for the beforetax cost of debt (rd) of 3.9%, the valuation estimate is

WACC = [(0.30)(0.039)(1 – 0.35)] + (0.70)(0.11) = 8.46%.

Firm value = 140 million(1 + 0.046)/(0.0846 – 0.046) = €3,793.29 million.

Using the base case estimates for the FCFF growth rate and the cost of equity and using the high estimate for the before-tax cost of debt (rd) of 5.9%, the valuation estimate is

WACC = [(0.30)(0.059)(1 – 0.35)] + (0.70)(0.11) = 8.85%.

Firm value = 140 million(1 + 0.046)/(0.0885 – 0.046) = €3,445.24 million.

Therefore, the range in valuation estimates from using the highest and lowest estimates of the before-tax cost of debt is €348.05 million.