Question 9.EX.4.4: The CAPM in the investment appraisal process Arclight plc, ...
The CAPM in the investment appraisal process
Arclight plc, a company producing high-quality household lighting products, is considering diversifying into the furniture business. The new venture has an expected return of 15 per cent. Arclight plc will use the CAPM to establish an appropriate discount rate to apply to the new venture and has the following information about three suitable proxy companies.
Furnisure plc
This company has an equity beta of 1.23 and is wholly involved in furniture making. It is financed 35 per cent by debt and 65 per cent by equity.
Home Furnish plc
This company has an equity beta of 1.27 and is also wholly involved in furniture making. It is financed 40 per cent by debt and 60 per cent by equity.
Lux Interior plc
This company has an equity beta of 1.46 and is financed 30 per cent by debt and 70 per cent by equity. It is split into two divisions of equal size: one division produces furniture and the other produces luxury wallpaper. The wallpaper division is seen as 50 per cent more risky than the furniture division.
Other information
■ Arclight plc has traditionally adopted a financing mix of 33 per cent debt and 67 per cent equity, although the project, if accepted, will be financed entirely by equity.
■ The current yield on Treasury bills is 4 per cent and the current return on the stock market is 10 per cent.
■ The corporation tax rate is 30 per cent.
■ Corporate debt can be assumed to be risk-free.
Using the above information, calculate an appropriate discount rate to apply to the new venture and decide whether it should be accepted.
1 Ungearing the proxy companies’ equity betas to give asset betas using the equation:
\beta_{ a }=\beta_{ e } \times\left[\cfrac{E}{E+D\left(1-C_{ T }\right)}\right]Furnisure plc
\beta_{ a }=1.23 \times 65 /(65+35 \times(1-0.30))=0.89Home Furnish plc
\beta_a=1.27 \times 60 /(60+40 \times(1-0.30))=0.87Lux Interior plc
\beta_{ a }=1.46 \times 70 /(70+30 \times(1-0.30))=1.12We have to make a further calculation as Lux Interior’s asset beta partly reflects the business risk of its wallpaper division, which is of no relevance to the project under consideration. As the wallpaper division is 50 per cent more risky than the furniture division, its asset beta is 1.5 times the asset beta of the furniture division. We can find the asset beta of its furniture division \left(\beta_{ af }\right) as follows:
\begin{aligned}& \text { Lux Interior asset beta }=(0.5 \times \text { Wallpaper asset beta })+(0.5 \times \text { Furnisure asset beta }) \\& 1.12=\left(0.5 \times 1.5 \times \beta_{\text {af }}\right)+\left(0.5 \times \beta_{\text {af }}\right)\end{aligned}Hence:
\beta_{ af }=1.12 / 1.25=0.902 Taking an average of the three asset betas:
\text { Proxy asset beta }=(0.89+0.87+0.90) / 3=0.893 Regearing the proxy asset beta to reflect Arclight’s financial risk using the equation:
\beta_{ e }=\beta_{ a } \times\left[\frac{E+D\left(1-C_{ T }\right)}{E}\right]\text { Proxy equity beta }=0.89 \times(67+33 \times(1-0.30)) / 67=1.20
4 Insert the proxy equity beta into the CAPM to calculate the discount rate:
R_j=0.04+1.20 \times(0.10-0.04)=0.112 \text {, i.e. } 11.2 \%The expected rate of return of the project (15 per cent) is greater than the discountrate (11.2 per cent) and so Arclight plc should accept the project.