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问一道题：NO.PZ2016021706000030

问题如下：

HTA Company has financed an asset of $100 million with 60% equity and 40% debt. The company is expected to raise additional capital, and the following is the information of the costs of debt and equity.

If the firm wants to finance total assets of $200 million, the marginal cost of capital will be?

选项：

6.28%.

5.28%.

C.5.68%

解释：

C is correct.

The firm will need to raise $100 million in additional capital. Recall that the target capital structure of 60% equity, 40% debt, so the firm will need to raise $60 million in new equity and $40 in new debt. According to the capital schedule, the marginal cost of capital at that point will be (0.4 x 3.7%) + (0.6 x 7.0%) = 5.68%.

请问为什么不是0.6*8%+0.4*4%=6.4呢？MCC不是多融的那100万的成本吗？

嗨，爱思考的PZer你好：

# 回答问题

同学你好, 这道题有两个关键点

计算正确 additional capital
代入对应的融资成本

你第一步没问题: MCC 就是多融的那 100 百万;

但是第二步算错了: 确认对应的融资成本时, 「不用」考虑已融资金额

题目中的表格 Marginal Cost of Capital Schedule, 就是「基于当前」的资本结构

已融资 100 百万 (has financed an asset of $100 million)
资本结构 (with 60% equity and 40% debt)

要新融资时, New Equity 和 New Debt 的融资金额和对应成本.

所以, Equity 和 Debt (after tax) 的融资成本分别为 7.00% 和 3.70%

# 破题思路

## 计算 additional capital

已融资 100 百万 (has financed an asset of $100 million)
总共要融资 200 百万 (wants to finance total assets of $200 million)

所以, additional capital = 200 - 100 = 100 百万

## 计算 New Equity 和 New Debt

根据目标资本结构 (with 60% equity and 40% debt)

New Equity = 100 * 60% = 60 百万
New Debt = 100 * 40% = 40 百万

## 确认股债融资成本 Re 和 Rd * (1-T)

Cost of Equity: 60 ~ [51, 100] --> Re = 7.00%
Cost of Debt (after-tax): 40 ~ [0, 50] --> Rd * (1-T) = 3.70%

## 计算 MCC

MCC = We * Re + Wd * Rd * (1-T) = 0.6 * 7.00% + 0.4 * 3.70% = 5.68%

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问一道题：NO.PZ2016021706000030

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