Suppose that you just received the dividend of $2, which is expected to grow by 1% forever. What is the firm's WACC?

Hint: Use dividend growth model in slide 4 of Week10 to calculate Re.

Question

Suppose that you just received the dividend of $2, which is expected to grow by 1% forever. What is the firm's WACC?

Hint: Use dividend growth model in slide 4 of Week10 to calculate Re.

BlackTom AI · Accepted Answer

To tackle the question, I’ll first restate what’s being asked and identify the variables involved.
The question says: you just received a dividend of $2, which is expected to grow by 1% forever. What is the firm’s WACC? Hint: use the dividend growth model to calculate Re.
Key quantities we need for the dividend growth model (Gordon growth formula) are:
- D1: the next expected dividend
- g: the growth rate of dividends
- P0: the current price of the equity (or the value used in the model)
- Re: cost of equity, which under the Gordon model is Re = (D1 / P0) + g

Step 1: compute D1 from the given D0. If the current dividend just received is D0 = 2 and the dividend grows at g = 1% forever, then the next dividend is D1 = D0 × (1 + g) = 2 × 1.01 = 2.02.

Step 2: express Re in terms of P0 using the Gordon growth formula: Re = (D1 / P0) + g = (2.02 / P0) + 0.01.

Step 3: relate WACC to Re. In many problems, if the firm is financed entirely with equity or if we are only asked for the cost of equity in a simplified context, WACC is taken as Re. However, in a normal WACC calculation you’d also need the cost of debt and the capital structure ( weights of debt and equity ). The question as stated does not provide debt levels or any information about taxes or debt costs, so we cannot compute a full WACC value without additional data.

Step 4: assess the given answer. The single numeric option provided is 19% (0.19). If we plug Re = 0.19 into the formula from Step 2, we would have 0.19 = (2.02 / P0) + 0.01, which rearranges to (2.02 / P0) = 0.18, so P0 ≈ 2.02 / 0.18 ≈ 11.22. This would imply a current equity price around $11.22. Whether that price is reasonable depends on market data not supplied in the problem. Because P0 is not given, the 19% figure cannot be confirmed purely from the information provided.

Step 5: explain why the other possibilities (if any were present) would be incorrect. Since no alternative options are listed in the prompt besides the single answer "19%", we can’t critique specific other choices. But generally, common mistakes would be:
- Confusing D0 with D1: using 2 instead of 2.02 would understate Re by 1 percentage point (assuming P0 is fixed).
- Forgetting the growth term g in Re: omitting the + g would understate Re.
- Misapplying WACC as something other than Re when debt and tax shields are not specified: WACC cannot be determined without debt cost and weights.

Step 6: summarize what would be required to definitively compute the answer. We would need either:
- the current price P0 to plug into Re = (D1 / P0) + g, or
- additional context (e.g., the firm is all-equity financed and WACC equals Re, plus P0 is known). Without P0, Re (and thus WACC) cannot be uniquely determined from the information given.

If you assume P0 ≈ 11.22, then Re ≈ (2.02 / 11.22) + 0.01 ≈ 0.18 + 0.01 = 0.19, i.e., 19%. This shows how the 19% figure arises under that price assumption, but that price is not specified in the problem statement.

Suppose that you just received the dividend of $2, which is expected to grow by 1% forever. What is the firm's WACC? Hint: Use dividend growth model in slide 4 of Week10 to calculate Re. 单项选择题

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