Question

Company Jedi AB has 10 million shares of equity outstanding. The current share price is 50 SEK, and the book value per share is 5 SEK.

The company also has two bond issues outstanding. The first bond issue has a face value of 100Million SEK (MSEK) and a 10 per cent annual coupon payment , sells for 90 per cent of par (face value of 1,000SEK), and matures in 1 year.

The second issue has a face value of £60 million and a 7.5 per cent annual coupon payment and sells for 96.5 per cent of par. The first issue matures in 10 years, the second in 6 years.

Note that in both bonds, there will be one coupon payment and face value.

Suppose the company’s equity has a beta of 2. The risk-free rate is 6 per cent, and the expected return on the market is 16 per cent. Assume that the overall cost of debt is the weighted average implied by the two outstanding debt issues. Both bonds make semi-annual payments. The tax rate is 35 per cent.

Calculate:

1. Return of Equity (4 points)
2. YTM of each bond (6 points)
3. The weighted average after-tax cost of debt (5 points)
4. Company’s WACC? (10 points)

Answer 1

a) For Return of Equity:

Here JEDI AB cost of equity will be return on equity:

Therfore :

We will use :

Rf=6%( risk free rate)

Rm=16%( Market expected return)

Beta=2

We will us CAPM equation:

Re=Rf+Betax(RM-Rf)

where Ke=Return on Equity

Re=6%+2x(16%-6%)

Re=26%

Therefore cost of Equity is 26%

2) YTM of Each Bond:

We will us the simplest formula for calculatin the YTM, and confirm one of the YTM with Financial calulator for any major deviations , if any:

We will Use:

YTM %=[C+(FV-PV)/t]/(FV+PV)/2 X100

Note:

FV=Face1 Value

PV=Present VAlue

t=maturity

C=coupon payments

Bond 1:

FV=100 MSEK

Coupon rate annual=10%

Coupon payments semi-annually=10/2%*100=5 MSEK

PV=0.90X100=90 MSEK

t=10x2=20 periods

Putting the value in the formula:

YTM%=5+(100-90)/2/(100+90)/20 x 100=5.7895%

Annual YTM=5.7895%x2=11.5789%

Now as we check our calculation from Financial Calc. YTM=5.862%( Here Put P/Y, C/Y both =1, N=20, PV=-90, PMT=5, FV=100; CPT+I/Y=5.862%)

Annual YTM=5.862%x2=11.724%

You can take any of the values, but I would prefer to go with YTM calculated with Financial Calc. for accuarcy.

Which is near to our approx calculation

YTM for Bond 2

Again data given for 2nd bond

FV=60 MSEK

PV=0.965*60=57.90 MSEK

Coupon rate 7.5%

Semiannula Coupon Payment C=0.075/2x60=2.25 MSEK

t=6*2=12

Putting the above values in appromixation formula:

YTM %=[2.35+(60-57.90)/12]/(60+57.2)/2 x 100=4.2378%

Annual YTM =2x4.2378=8.4755%

YTM with Financial Calc=4.2546%(Here FV=60, N=12, PMT=2.25, PV=-57.20, CPT+I/Y=4.2378%)

Annual YTM=8.50923%

Weighted average cost of Capital:

Kd=Weighted cost of debt=YTM1xMVBond1+YTM2xMVDebt2=(90X11.724%+57.20x8.50923%)/(90+57.20)=10.4748%

Total Outstanding shares 0f Jedi AB=10 Mn

Current Share Price=50 SEK

Book Value/Share= 5 SEK

Market value of equity=10*50=500 MSEK

Market value of Debt=90+57.20=147.20 MSEK

WACC=Ke*MV(E/D+E)+Kd*(1-t)*MV(D/D+E)=26%*(500/(500+147.20)+10.4748%*(147.20/500+147.20)*(1-0.35)

WACC=21.6351%

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