Determining PB Ratio for Companies with Different Returns Assume that the present value of expected ROPI follows a perpetuity with growth g (Value = Amount/ [r - g]). Determine the theoretically correct PB ratio for each of the following companies A and B. Company Net Operating Assets Equity RNOA ROE Weighted Avg. Cost of Capital Growth Rate in ROPI A $100 $100 21% 21% 10% 2% B $100 $100 14% 14% 10% 2% Round answers to two decimal places. PB Ratio Company A Answer 10 Company B Answer 0

Pb R atio:

For company A = 2.375

For company B = 1.5

Explanation:

As per the data given in the question,

ROPI = NDA (RNOA - WACC)

For Company A 100 × (21%-10%)

For Company B 100 × (14%-10%)

Present value of ROPI = (ROPI ÷ (1+WACC)) ÷ [1-(1+g) ÷ (1+WACC)]

For Company A = (11 ÷ (1+0.10)) ÷ [1-(1+0.02) ÷ (1+0.10)]

= $137.50

For Company B = (4 ÷ (1+0.10)) ÷ [1-(1+0.02) ÷ (1+0.10)]

= $50

Market value of equity = NOA + present value of ROPI

= $100 + 137.50 = $237.50(Company A)

= $100 + $50 = $150(Company B)

Pb Ratio = Market value of equity ÷ Book value of equity

For company A = $237.50÷100 = 2.375

For company B = $150÷100 = 1.5

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