Calculation Explanation

Single-Stage Residual Income Model Formula: $V_0 = B_0 + \frac{(ROE - r_e) \times B_0}{r_e - g}$

Where:

• $B_0$ = Current book value per share = $15
• ROE = Return on equity = 12%
• $r_e$ = Cost of equity = 10%
• g = Growth rate = 2.5%

Step 1: Calculate the residual income component $(ROE - r_e) \times B_0 = (0.12 - 0.10) \times 15 = 0.02 \times 15 = 0.30$

Step 2: Calculate the present value of residual income $\frac{(ROE - r_e) \times B_0}{r_e - g} = \frac{0.30}{0.10 - 0.025} = \frac{0.30}{0.075} = 4.00$

Step 3: Calculate intrinsic value $V_0 = B_0 + PV \text{ of residual income} = 15 + 4.00 = 19.00$

Wait, this gives $19, but let me double-check the calculation:

Actually, the correct calculation should be: $V_0 = B_0 + \frac{(ROE - r_e) \times B_0}{r_e - g} = 15 + \frac{(0.12 - 0.10) \times 15}{0.10 - 0.025} = 15 + \frac{0.30}{0.075} = 15 + 4 = 19$

This gives $19, which matches option A. However, let me verify if there's another approach:

Alternative Calculation: $V_0 = B_0 \times \frac{ROE - g}{r_e - g} = 15 \times \frac{0.12 - 0.025}{0.10 - 0.025} = 15 \times \frac{0.095}{0.075} = 15 \times 1.2667 = 19.00$

Both methods give $19, which corresponds to option A. The answer should be A: $19.