Example 1:
A firm has the following cash flows for the next 5 years:
Year Cash flow
1 1,000,000
2 1,200,000
3 1,200,000
4 1,400,000
5 1,400,000
After these 5 years the cash flow will grow with 2% a year forever. Furthermore, the risk-free rate is
1%, the beta of the company is 2 and the return on a broad market portfolio is 7%. Finally, the cost of
debt for the company is 3% and the firm’s capital structure consists out of 50% debt and 50% equity.
Finally, the tax rate is 40%.
Required:
What is the firm’s enterprise value?
Solution
In order the calculate the value of a firm we first need to realize that the value equals the present
value of all future cash flows. Secondly, we know that we can calculate the present value of a cash
flow by dividing that cash flow by (1+the discount rate)^t, where t stands for the amount of years the
cash flow takes place into the future. So here it makes sense to first calculate the discount rate.
Step 1: Calculating the discount rate.
The discount rate we need to use in this case is the weighted average cost of capital, the WACC. The
reason for using the WACC is because we need to know the enterprise value, which is the total value
of the firm (both debt and equity). And when we need to know the enterprise value, we discount all
cash flows at the WACC (see valuation lecture 2). Remember that the WACC is the weighted average
of both the cost of debt and the cost of capital:
WACC = [E/(D+E)]*Ke + [(D/D+E)]*Kd * (1-T).
E = Total amount of equity in the company
D = Total amount of debt in the company
Ke= cost of equity
Kd = cost of debt
T = the tax rate
Since we know that the firm consists for 50% out of debt and 50% out of equity, we know that both
[E/(D+E)] and [D/(D+E)] are both equal to 0.5. Furthermore, we are given the cost of debt (3%) and
the tax rate (40%), so all we need to calculate the WACC is the cost of equity. The cost of equity we
calculate using the CAPM formula (see valuation lecture 2). The CAPM formula is:
, CAPM formula: Ke = rf + beta*(rm-rf)
Ke = cost of equity
Rf = risk free rate
Rm= return on a broad market portfolio (such as for instance the AEX).
We know all of the above variables from the CAMP model, se we can simply fill in the CAPM formula
to obtain the cost of equity:
Ke = 1% + 2*(7%-1%) = 13%.
So, the cost of equity is 13%. Now we have all the ingredients to calculate the WACC, so let’s fill in
the formula for the WACC:
WACC = 0.5* 13% + 0.5*3%*(1-0.4) = 7.4%
Alright, so now we know the discount rate, the WACC in this case, equals 7.4%. So now it is time to
use this discount rate to start discounting the actual cash flows.
Step 2: Discounting the cash flows.
In this case the cash flows in the first five years do not really follow any model; the do not grow or
decrease by an equal percentage every year nor do they stay equal. This means that we cannot apply
the constant growth or the zero growth model (see valuation lecture 2). However, we can apply the
variable growth model as there are two stages of growth. We first see a fast growth period during
the first 5 years where the cash flows grow rather quickly followed by the stable period in which the
cash flows grow at a constant (stable) but lower percentage forever. In this case we need to discount
the cash flows from the high growth period separately (the cash flows from the first 5 years in this
case) and then we can apply the constant growth model to the cash flows from the stable growth
period. So, let’s first discount the first 5 cash flows separately:
Year 1: 1,000,000/(1.074)^1 = 931,099
Year 2: 1,200,000/(1.074)^2 = 1,040,334
Year 3: 1,200,000/(1.074)^3 = 968,653
Year 4: 1,400,000/(1.074)^4 = 1,052,231
Year 5: 1,400,000/(1.074)^5 = 979,731
When we add these discounted values up we have that the total discounted value of the cash flows
during the high growth period equals: 4,972,047.
However, we also need to add the discounted value of all cash flows during the stable growth period,
and for this we can use the formula of the constant growth model. This is because the cash flows
during the stable growth period grow be a constant growth percentage of 2% per year forever. The
formula for the constant growth model is:
PV of cash flows 1 year before the first stable cash flow = First stable cash flow / (WACC-g)
A firm has the following cash flows for the next 5 years:
Year Cash flow
1 1,000,000
2 1,200,000
3 1,200,000
4 1,400,000
5 1,400,000
After these 5 years the cash flow will grow with 2% a year forever. Furthermore, the risk-free rate is
1%, the beta of the company is 2 and the return on a broad market portfolio is 7%. Finally, the cost of
debt for the company is 3% and the firm’s capital structure consists out of 50% debt and 50% equity.
Finally, the tax rate is 40%.
Required:
What is the firm’s enterprise value?
Solution
In order the calculate the value of a firm we first need to realize that the value equals the present
value of all future cash flows. Secondly, we know that we can calculate the present value of a cash
flow by dividing that cash flow by (1+the discount rate)^t, where t stands for the amount of years the
cash flow takes place into the future. So here it makes sense to first calculate the discount rate.
Step 1: Calculating the discount rate.
The discount rate we need to use in this case is the weighted average cost of capital, the WACC. The
reason for using the WACC is because we need to know the enterprise value, which is the total value
of the firm (both debt and equity). And when we need to know the enterprise value, we discount all
cash flows at the WACC (see valuation lecture 2). Remember that the WACC is the weighted average
of both the cost of debt and the cost of capital:
WACC = [E/(D+E)]*Ke + [(D/D+E)]*Kd * (1-T).
E = Total amount of equity in the company
D = Total amount of debt in the company
Ke= cost of equity
Kd = cost of debt
T = the tax rate
Since we know that the firm consists for 50% out of debt and 50% out of equity, we know that both
[E/(D+E)] and [D/(D+E)] are both equal to 0.5. Furthermore, we are given the cost of debt (3%) and
the tax rate (40%), so all we need to calculate the WACC is the cost of equity. The cost of equity we
calculate using the CAPM formula (see valuation lecture 2). The CAPM formula is:
, CAPM formula: Ke = rf + beta*(rm-rf)
Ke = cost of equity
Rf = risk free rate
Rm= return on a broad market portfolio (such as for instance the AEX).
We know all of the above variables from the CAMP model, se we can simply fill in the CAPM formula
to obtain the cost of equity:
Ke = 1% + 2*(7%-1%) = 13%.
So, the cost of equity is 13%. Now we have all the ingredients to calculate the WACC, so let’s fill in
the formula for the WACC:
WACC = 0.5* 13% + 0.5*3%*(1-0.4) = 7.4%
Alright, so now we know the discount rate, the WACC in this case, equals 7.4%. So now it is time to
use this discount rate to start discounting the actual cash flows.
Step 2: Discounting the cash flows.
In this case the cash flows in the first five years do not really follow any model; the do not grow or
decrease by an equal percentage every year nor do they stay equal. This means that we cannot apply
the constant growth or the zero growth model (see valuation lecture 2). However, we can apply the
variable growth model as there are two stages of growth. We first see a fast growth period during
the first 5 years where the cash flows grow rather quickly followed by the stable period in which the
cash flows grow at a constant (stable) but lower percentage forever. In this case we need to discount
the cash flows from the high growth period separately (the cash flows from the first 5 years in this
case) and then we can apply the constant growth model to the cash flows from the stable growth
period. So, let’s first discount the first 5 cash flows separately:
Year 1: 1,000,000/(1.074)^1 = 931,099
Year 2: 1,200,000/(1.074)^2 = 1,040,334
Year 3: 1,200,000/(1.074)^3 = 968,653
Year 4: 1,400,000/(1.074)^4 = 1,052,231
Year 5: 1,400,000/(1.074)^5 = 979,731
When we add these discounted values up we have that the total discounted value of the cash flows
during the high growth period equals: 4,972,047.
However, we also need to add the discounted value of all cash flows during the stable growth period,
and for this we can use the formula of the constant growth model. This is because the cash flows
during the stable growth period grow be a constant growth percentage of 2% per year forever. The
formula for the constant growth model is:
PV of cash flows 1 year before the first stable cash flow = First stable cash flow / (WACC-g)
