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Cost of Capital Question (EOC Reading 35, Q12)

This is the answer given in the solutions for EOC Reading 35, Q12:

B is correct.

  • Capital structure:

    Market value of debt: FV = $10,000,000, PMT = $400,000, N = 10,

    I/YR = 13.65%. Solving for PV gives the answer $7,999,688  (I can’t seem to get PV equal to this)

    Market value of equity: 1.2 million shares outstanding at $10 = $12,000,000

    Market value of debt
    $7,999,688
     
    40%

    Market value of equity
    12,000,000
     
    60%

    Total capital
    $19,999,688
     
    100%

     

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%

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Basically I input all the following into my calculator as shown above:

FV = $10,000,000, PMT = $400,000, N = 10,

I/YR = 13.65%, yet I get a PV value of 4,896,931.51 as opposed to 7,999,688.

Any help is much appreticated, thanks!

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Coupon is payable semi annually so I/Y = 13.65 / 2 = 6.825 should be used.

P/Y=C/Y=1 gets you $4,896,931.51.Setting P/Y=C/Y=2 gets you $7,999,687.64.yes

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