Topic 2 - Cost of Capital Flashcards
Problem 1 - Calculating WACC - Top Down - Part 1 - Calculating Weightings of Equity
Risk Free Rate (10yr Tstrip yield) + Beta * Default Premium (expected market return – risk free rate)
Rf Rate = 4.20%
Beta is Covariance (CFK, Market) = 0.00224 / Variance (Market) = (0.04)^2 or (Market std dev)^2
This is 1.4
Default Premium is mentioned in Historical Risk Premiums (use 10y) this gives us 4.60%
Problem 1 - Calculating WACC - Top Down - Part 2 - Calculating Weightings of Debt
Find the appropriate T-strip yield (short-term = 1, mid-term = 3 or 5, long-term = 10) We want 10 as the question asks us for a long-term valuation. We find the yield to be 4.20%
Add the default premium for the right debt rating (this one is A- as mentioned) So we use the A- 10y, which is 1.40%
The answer for this is 5.60%. We will later multiply this by the market value of the debt, as mentioned in the information.
D = $2,000,000 as mentioned in the information
We can find E by doing $20,00 (common stock price) * 300,000 (common shares outstanding) = $6,000,000
(10.64% * [6/(2+6)] + 5.6% * [2/(2+6)] * (1-25%)) = 9.03%
10.64% * 3/4 + 5.6% * 1/4 * (75%) = 9.03%
Problem 2 - Calculating WACC - Bottom-Up Beta and Public Debt - Part 1 (Context)
Constant Current Debt Ratio – 600mm/40b = 0.15 D/E ratio
Debt = $600mm, Equity = $4b, Tax = 40%
Debt = Zero-coupon bonds – 20y priced at $252.5725 each, Par value = $1,000 and Semi-Annual compounding.
RfR = 3% and Market Return = 7%
Problem 2 - Calculating WACC - Bottom-Up Beta and Public Debt - Part 2
1) Calculate Unlev Beta of all, and then average.
Do Lev Beta / [ 1 + (1 – t)* (D/E)]
GI = 1.6 / [1 + (1 – 40%) * (0.5)] = 1.2308
LI = 1.9 / [1 + (1 – 35%) * 1)] = 1.1515
FC =
1.5 / [1 + (1 – 38%) * (0.4) = 1.2019
ULI
= 1.3 / [1 + (1 – 40%) * (0.2) = 1.1607
RC
= 1.5 / [1 + (1 – 35%) * (0.3) = 1.2552
Average = Add all (6.0001) / Number of firms (5) = 1.2000
Problem 2 - Calculating WACC - Bottom-Up Beta and Public Debt - Part 3 (Steps 2 and 3)
2) Find Beta of RWP = 1.3080
Avg Unlev Beta * [1 + (1 – t) * (D/E) = (1.2) * [1 + (1 – 40%) * (0.15) = 1.3080
3) Find Cost of Equity = 8.2320%
Risk-Free Rate + Beta * (Rm – Rf) which we have to calculate instead of finding in the information
RfR is given, it is 3%, Beta is 1.3080, We find Rm – Rf by doing 7% (market return) - 3% (RfR)
3 + 1.3080*(7-3) = 8.2320%
Problem 2 - Calculating WACC - Bottom-Up Beta and Public Debt - Part 4
4) Find Cost of Debt = 7%
252.5725 = 1000 / (1 + YTM)^40 (this is 40 because of semi-annual compounding)
REARRANGE to 1000 / 252.5725 = (1 + YTM)^40
3.95925922 = (1 + YTM) ^ 40
SQRT40 both sides = 1.035 = 1 + YTM
0.035 = YTM or 3.5%
Cost of Debt is YTM * 2 = 7%
Problem 2 - Calculating WACC - Bottom-Up Beta and Public Debt - Part 5
5) Bring all together to find WACC
Cost of Equity * Weighting of Equity + Cost of taxed Debt * Weighting of Debt
8.2320% * (4000 / 4600) + [7% * (1-40%)] * (600 / 4600) = 7.7061%
Problem 3 - Calculating Merger Beta - Part 1 (Context)
Firm A, Novell, has market value of $2 billion and beta of 1.5.
Is Acquiring Firm B, WordPerfect, which had a market value of equity of $1 billion and a beta of 1.3.
Neither has debt at the time of transaction
The tax rate is 40%
Remember that the combined firm is basically a two-asset portfolio.
1st Asset = Acquirer
2nd Asset = Target
Beta = weighted average of the individual asset’s beta.
Problem 3 - Calculating Merger Beta - Part 2 (Step 1 - Calculate post-merger, all-equity-financed Beta for Firm A)
Firm A Equity Value / Combined Equity Value post-Merger * Firm A Beta = [2 / (1+2)] * 1.5 = 1
Firm B Equity Value / Combined Equity Value post-Merger * Firm B Beta = [1 / (1+2) * 1.3 = 0.4333
Add them together, we get Combined Asset Unlevered Beta = 1.4333
Because there’s no debt in either of the firm’s capital structures, this is also the firm’s levered beta.
This is further proved by the leveraged equation.
UnLevBeta * [1 + (1-t) * D/E] = LevBeta
1.4333 * [1 + (1-40%) * 0/3] = 1.4333
0 debt, 3 equity (2 firm A, 1 firm B)
Problem 3 - Calculating Merger Beta - Part 3 (Step 2 - Calculate post-merger, 1b of debt used to acquire, Beta for Firm A)
The leveraged equation actually has some leverage.
1.43 * (1 + (1-40%) * 1/2 = 1.85900
1 debt, 2 equity (both Firm A)
Combined unlevered beta = Weighted average of unlevered betas of target and acquirer
Post-acquisition debt = Acquirer old debt + Target old debt + New debt issued
Post-acquisition equity = Acquirer old equity + New equity used for acquisition
= Acquirer old equity + (Total cost of acquisition – New debt issued)
New beta = Combined unlevered beta (1+(1-t) New debt/equity ratio)
Problem 4 - Calculating Divestiture Beta (Context)
HP Beta, is split into 4 business groups, each with individual market values and unlev. betas.
HP had $1b in debt, and this is allocated to divisions in proportion to the equity market value.
T-bond rate is 7.5% and Market Risk Premium is 5.5% (expected market return – risk-free rate) so E(Mr) = 13%
Tax Rate = 36%
Problem 4 - Calculating Divestiture Beta - Part 1 (Step 1 - Estimate Beta for HP as a company. Is it equal to the Beta estimated by regressing part returns on the stock against a market index?)
Firm has $1b debt and $8b equity (sum of all business market value of equity)
Debt is allocated to divisions proportionally to the market value of equity.
MF: 2/8 * 1 = 0.250
PC: 2/8 * 1 = 0.250
SW: 1/8 * 1 = 0.125
PR: 3/8 * 1 = 0.375
Problem 4 - Calculating Divestiture Beta - Part 1 (Step 1 CONTINUED - Estimate Beta for HP as a company. Is it equal to the Beta estimated by regressing part returns on the stock against a market index?)
UnLevBeta for HP as a firm =
Beta for Division * (division market value of equity + debt / total firm market value of equity + debt)
1.1 * (2.25/9) + 1.5 * (2.25/9) + 2.0 * (1.125/9) + 1.0 * (3.375/9) = 1.275
Debt/Equity Ratio = 1/8
We can re-lever HP’s beta by:
1.275 * (1 + (1-36%) * 1/8 = 1.377
Regression part of the question:
Since the divisional structure, leverage, and market position of HP have changed over the years, this beta will likely differ from the beta obtained by regressing past returns of HP against a market index.
Problem 4 - Calculating Divestiture Beta - Part 2 (Estimate cost of equity for HP (and individual divs). Which cost of equity do we use to value the printer division?
Div Unlev Beta * (1 + (1 – tax) * (Div D/Eq) = x.xx
Risk Free Rate + Beta (Market Risk Premium) = CAPM
Mainframes
1.1 * (1 + (1-0.36) * (0.25/2) = 1.19
0.075 + 1.19 * (0.055) = 0.1405
Personal Comps
1.5 * (1 + (1-0.36) * (0.25/2) = 1.62
0.075 + 1.62 * (0.055) = 0.1641
Software
2 * (1 + (1-0.36) * (0.125/1) = 2.16
0.075 + 2.16 * (0.055) = 0.1938
Printers
1 * (1 + (1-0.36) * (0.375/3) = 1.08
0.075 + 1.08 * (0.055) = 0.1344 – For the second part of the question.
Problem 4 - Calculating Divestiture Beta - Part 3 (1) (Estimate beta for HP after the divestiture of mainframes group for 2.25 billion (use money to buy back stock)
Assume Mainframe is sold for 2.25$ Billion.
The asset value of the remaining divisions, and HP, is now $6.75 billion.
After divestiture, we have beta:
Divisional Beta * (Divisional Market Value of Equity and Debt / Total Firm Asset Value, which is now 6.75)
PC: 1.5 * (2.25/6.75) = 0.5
Software: 2.0 * (1.125/6.75) = 0.333333333
Printers 1.0 * (3.375/6.75) = 0.5
Total Unlev Beta: 1.3333
