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吴超 Cassie · 2022年03月23日

No.PZ2016021705000030 (选择题)

NO.PZ2016021705000030

问题如下:

Happy Resorts Company currently has 1.2 million common shares of stock outstanding and the stock has a beta of 2.2. It also has $10 million face value of bonds that have five years remaining to maturity and 8 percent coupon with semi-annual payments, and are priced to yield 13.65 percent. If Happy issues up to $2.5 million of new bonds, the bonds will be priced at par and have a yield of 13.65 percent; if it issues bonds beyond $2.5 million, the expected yield on the entire issuance will be 16 percent. Happy has learned that it can issue new common stock at $10 a share. The current risk-free rate of interest is 3 percent and the expected market return is 10 percent. Happy's marginal tax rate is 30 percent. If Happy raises $7.5 million of new capital while maintaining the same debt-to-equity ratio, its weighted average cost of capital is closest to:

选项:

A.

14.5 percent.

B.

15.5 percent.

C.

16.5 percent.

解释:

B is correct.

Capital structure:Market value of debt: FV = $10,000,000, PMT = $400,000, N = 10,I/YR = 13.65%/2. Solving for PV gives the answer $7,999,688.Market value of equity: 1.2 million shares outstanding at $10 = $12,000,000

To raise $7.5 million of new capital while maintaining the same capital structure, the company would issue $7.5 million × 40% = $3.0 million in bonds, which results in a before-tax rate of 16 percent.

rd(1 t) = 0.16(1 0.3) = 0.112 or 11.2%

re = 0.03 + 2.2 (0.10 0.03) = 0.184 or 18.4%

WACC = [0.40(0.112)] + [0.6(0.184)] = 0.0448 + 0.1104 = 0.1552 or 15.52%


我记得李老师在讲WACC的时候特地讲了一下成本的概念是机会成本、要求回报率或者是风险补偿,并不是预期expected return/yield 的概念,所以这里bond的成本Rd为什么是用16%,而不是原来的13.65%。主要Bond的market value是用13.65%折现求出来的,如果要求回报率是16%,不应该用16%来折吗?

1 个答案

王琛_品职助教 · 2022年03月24日

嗨,爱思考的PZer你好:


1)所以这里bond的成本Rd为什么是用16%,而不是原来的13.65%。

因为债券融资规模不同,适用的融资成本不同

如果融资规模小于 2.5 m,融资成本是 13.65%

如果融资规模大于 2.5 m,融资成本是 16%

现在计算出的债务融资规模为 3 m,大于 2.5 m,所以适用的融资成本是 16%

2)主要Bond的market value是用13.65%折现求出来的,如果要求回报率是16%,不应该用16%来折吗?

题干中涉及的债务有两部分,一个是现有的债务,一个是计划发的新债

我们先使用 13.65% 计算现有债务的市值,然后计算资本结构

因为发新债使用的是同样的资本结构,所以再算如果要融资 7.5 m,需要发多少债,结果算出来为 3 m

再根据题干涉及的,不同规模的融资成本,适用 16%

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