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Expert-verified Found in: Page 441 ### Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

# Rio National Corp. is a U.S.-based company and the largest competitor in its industry. Tables 13.5 – 13.8 present financial statements and related information for the company.Table 13.9 presents relevant industry and market data.The portfolio manager of a large mutual fund comments to one of the fund’s analysts, Katrina Shaar: “We have been considering the purchase of Rio National Corp. equity shares, so I would like you to analyze the value of the company. To begin, based on   Rio National’s past performance, you can assume that the company will grow at the same rate as the industry.”a. Calculate the value of a share of Rio National equity on December 31, 2012, using the constant-growth model and the capital asset pricing model.b. Calculate the sustainable growth rate of Rio National on December 31, 2012. Use 2012 beginning-of-year balance sheet values.

a. 13% and $22.40 b. 9.97% See the step by step solution ### Step by Step Solution ## Step 1: Calculation of required rate of return ‘a’ The value of a share of Rio National equity =$22.40,

Formulae

k = rf + β [E(rM) – rf ] (Constant Growth model)

= 0.04 + 1.8 x (0.09 – 0.04)

= 0.13 or 13%

The share value (Gordon growth model):

P0 = D0 x (1 + g) / k – g

= $0.20 x (1 + 0.12) / 0.13 – 0.12 =$22.40

## Step 2: Calculation of sustainable growth rate ‘b’

g = ROE × b

= ROE × Retention Rate

= ROE × (1 – Payout Ratio)

= (1 – Dividend / Net income) x Net income / Beginning equity

= (1 - $3.20) /$30.16 x $30.16 /$270.35

= 0.0997

= 9.97%

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