Below is the question with the answer. I am having a hard time understanding whe

Question

Below is the question with the answer. I am having a hard time understanding where some of the numbers are coming from (specifiaclly Rd). Any help is much appreciated!   

Cowbell Corp. is a manufacturer of musical instruments. There are 52 million shares, each selling at $80 / share with an equity beta of 0.99. The risk-free rate is 5% and the market risk premium is 9%. There is $1.18 billion in outstanding debt (face value), paying a 9% s/a coupon for 15 years, which is currently quoted at 110% of par. Assuming a 40% tax rate, what is Cowbell Corp.’s WACC?

E=52m x80=4.16 billion

D=1.18 x1.1=1.298 billion

V=5.458

wE = E/V = 4.16 / 5.458 = .7622

RE = Rf + bE x (RM – Rf) = 5 + 0.99 x (9) = 13.91%

wD = D/V = 1.298/ 5.458 = .2378

N = 30, PV = -1,000, PMT = 45, FV = 1,000; RD = 3.9268%*2=7.8536%

RD(1-TC) = 7.8536 (1-.40) = 4.7122%

WACC = wERE + wDRD(1-TC) = .7622 (13.91%) + .2378 (4.7122%) = 11.72%

Explanation / Answer

Face value (FV) $                                  1,000.00 Coupon rate 9.00% Number of compounding periods per year 2 Interest per period (PMT)                                            45.00 Bond price (PV) $                               (1,100.00) Number of years to maturity 15 Number of compounding periods till maturity (N) 30 Bond Yield to maturity (Rd) RATE(NPER,PMT,PV,FV)*2 Bond Yield to maturity (Rd) 7.8537% (Pre-tax cost of debt) Bond Yield to maturity 4.7122% (After-tax cost of debt) 7.8537%*(1-40%)

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