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HL · 2022年03月02日

I/YR = 6.825%怎么来的?

NO.PZ2021091701000017

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 an 8% coupon with semiannual payments and are priced to yield 13.65%. If Happy issues up to $2.5 million of new bonds, the bonds will be priced at par and will have a yield of 13.65%; if it issues bonds beyond $2.5 million, the expected yield on the entire issuance will be 16%. Happy has learned that it can issue new common stock at $10 a share. The current risk-free rate of interest is 3%, and the expected market return is 10%. Happy’s marginal tax rate is 30%. If Happy raises $7.5 million of new capital while maintaining the same debt-to-equity ratio, its weighted average cost of capital will be closest to

选项:

A.

14.5%

B.

15.5%

C.

16.5%

解释:

B is correct. The capital structure is as follows:

Market value of debt: FV = $10,000,000, PMT = $400,000, N = 10, and I/YR = 6.825%. Solving for PV gives $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%.

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%

I/Y=6.825应该是13.65%÷2来的,但13.65%是价格收益,怎么会是年回报率呢?

1 个答案

王琛_品职助教 · 2022年03月03日

嗨,从没放弃的小努力你好:


priced to yield 13.65% 的意思是,给债券定价时,年化的折现率使用 13.65% 

因为是半年付息一次,所以按计算器时,I/Y = 13.65 / 2 = 6.825

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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