Weighted average cost of capital question – Section C- which DF to use

Hi there,

I am working on Section C questions for weighted average cost of capital/ CAPM (FM exam BPP question kit). I am trying to understand what discount factors we need to use in order to work out the PV. I can’t seem to understand the answer of 4% and 5%. The risk free rate is 4% but where did 5% come from?

Question 217:
The equity beta of Fence Co is 0•9 and the company has issued 10 million ordinary shares. The market value of each ordinary share is $7•50. The company is also financed by 7% bonds with a nominal value of $100 per bond, which will be redeemed in seven years’ time at nominal value. The bonds have a total nominal value of $14 million. Interest on the bonds has just been paid and the current market value of each bond is $107•14.

Fence Co plans to invest in a project which is different to its existing business operations and has identified a company in the same business area as the project, Hex Co. The equity beta of Hex Co is 1•2 and the company has an equity market value of $54 million. The market value of the debt of Hex Co is $12 million.

The risk-free rate of return is 4% per year and the average return on the stock market is 11% per year. Both companies pay corporation tax at a rate of 20% per year.

Required: Calculate the current weighted average cost of capital of Fence Co.

Answer:

Cost of equity

The current cost of equity can be calculated using the capital asset pricing model.
Equity or market risk premium = 11 – 4 = 7%
Cost of equity = 4 + (0•9 x 7) = 4 + 6•3 = 10•3%

After-tax cost of debt

After-tax interest payment = 100 x 0•07 x (1 – 0•2) = $5•60 per bond

Year Cash flow DF @ 4% PV $ Df @ 5% PV $
0 Market value (107.14) 1 -107.14 1 -107.14
1-7 Interest 5.6 6.002 33.61 5.786 32.40
7 Redeem 100 0.76 76 0.71 71.10
2.47 -3.64

After-tax cost of debt = IRR = 4 + ((5 – 4) x 2·47)/(2·47 + 3·64) = 4 + 0·4 = 4·4%

Thanks
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