Calculating Present Value and Sustainable Growth Rates

Investment Project Cash Flow Analysis

Southgate Inc. has identified an investment project with the following cash flows:

Present Value Calculations

a) If the discount rate is 8 percent, what is the total present value?
PV at 8% = $2,500/1.08 + $1,000/1.08² + $2,000/1.08³ + $3,000/1.08⁴ = $6,964.91

b) If the discount rate is 10 percent, what is the total present value?
PV at 10% = $2,500/1.10 + $1,000/1.10² + $2,000/1.10³ + $3,000/1.10⁴ = $6,650.84

c) If the discount rate is 9 percent, what is the total present value?
PV at 9% = $2,500/1.09 + $1,000/1.09² + $2,000/1.09³ + $3,000/1.09⁴ = $6,804.90

Financial Statements and Long-Term Planning

Given: Profit margin = 8.2%; Capital intensity ratio = 0.65; Debt-equity ratio = 0.40; Net income = $24,900; Dividends = $9,400.

a) What is the return on equity (ROE)?

ROE = Profit margin × Total asset turnover × Equity multiplier
ROE = 0.0820 × (1 / 0.65) × (1 + 0.40) = 0.1766 = 17.66%

b) What is the sustainable growth rate?

• Retention ratio (R): R = 1 - (Dividends / Net income) = 1 - ($9,400 / $24,900) = 0.6225
• Sustainable growth rate (g): g = (ROE × R) / (1 - ROE × R) = (0.1766 × 0.6225) / (1 - 0.1766 × 0.6225) = 12.35%