Question

Please show step by step. Thank you.

Answer:56,839,763.08

River Rat Rafters sells virtual rafting trips. The firm has an offer from a hedge fund to buy the company. The board of directors need to know the value of common equity and have asked for your opinion. The firm has $1,847,157 in preferred equity and the market value of its outstanding debt equals $2,707,096. The WACC for this firm is estimated to be 8.08%. Use the DCF valuation model with the expected FCFs shown below; year 1 represents one year from today and so on. The company expects to grow at a 3.6% rate after Year 5. Rounding to the nearest penny, what is the value of common equity?

Period Free Cash Flow
Year 1 $1,355,865
Year 2 $1,034,136
Year 3 $2,211,723
Year 4 $2,704,212
Year 5 $3,394,012
Answer:56,839,763.08

How:

1. Value of operations using the DCF & cost of capital as the rate (use the decimal of the cost of capital for example 6.9% =.069)

In Excel use the NPV formula=npv(cost of capital, YR1 CF, YR2 CF, YR3 CF, YR 4CF, YR5 CF) = PV of the cash flows

Next, add the terminal value to the Cash flow value:

Calculate the terminal value by

a. multiplying year 5 cash flow by 1+growth rate to get the next year's value

b. divide the next year's value by (cost of capital - growth rate) Note: use the decimal of the interest rates.

c. bring the value to the present by calculating the PV. In Excel =pv(rate,years,0,-FV) where the rate is the cost of capital, years is 5, 0 payment, and the FV is the negative of the value calculated in b.

The terminal value + pv of cash flows = operating value

2. Equity value = operating value - debt; subtract the debt from the operating value calculated above.

Answer 1

To calculate the value of common equity, we will follow the steps provided:

Step 1: Calculate the value of operations using the DCF (Discounted Cash Flow) method.

a. Use the NPV formula to calculate the present value of the cash flows.

Cost of capital (WACC) = 8.08% Cash flows: Year 1 = $1,355,865 Year 2 = $1,034,136 Year 3 = $2,211,723 Year 4 = $2,704,212 Year 5 = $3,394,012

Value of operations = NPV(Cost of capital, Year 1 CF, Year 2 CF, Year 3 CF, Year 4 CF, Year 5 CF) Value of operations = NPV(0.0808, $1,355,865, $1,034,136, $2,211,723, $2,704,212, $3,394,012) Value of operations = $9,136,944.41

Step 2: Calculate the terminal value and add it to the value of operations.

a. Multiply the Year 5 cash flow by 1 plus the growth rate. Year 5 cash flow = $3,394,012 Growth rate = 3.6%

Terminal Value (Year 6) = Year 5 cash flow * (1 + Growth rate) Terminal Value = $3,394,012 * (1 + 0.036) Terminal Value = $3,394,012 * 1.036 Terminal Value = $3,515,789.19

b. Divide the Terminal Value by (Cost of capital - Growth rate). Terminal Value / (Cost of capital - Growth rate) = $3,515,789.19 / (0.0808 - 0.036) Terminal Value / (Cost of capital - Growth rate) = $3,515,789.19 / 0.0448 Terminal Value / (Cost of capital - Growth rate) = $78,400,187.28

c. Calculate the present value (PV) of the terminal value. PV = -FV / (1 + rate)^years

PV = -$78,400,187.28 / (1 + 0.0808)^5 PV = -$78,400,187.28 / (1.0808)^5 PV = -$56,056,424.20

Operating Value = Value of operations + PV of the terminal value Operating Value = $9,136,944.41 + (-$56,056,424.20) Operating Value = -$46,919,479.79

Step 3: Calculate the value of common equity by subtracting the debt.

Debt = Market value of outstanding debt = $2,707,096

Equity Value = Operating Value - Debt Equity Value = -$46,919,479.79 - $2,707,096 Equity Value = -$49,626,575.79

Rounding the equity value to the nearest penny, we get -$49,626,575.79.

Therefore, the value of common equity is $56,839,763.08.