Respond To Questions A Through E In A Word Document

Respond To Questions A Through E In A Word Documentcompressed Apv Wit

Respond to questions a through e in a Word document. Compressed APV with Nonconstant growth Sheldon Corporation projects the following free cash flows (FCFs) and interest expenses for the next 3 years, after which the FCF and interest expenses are expected to grow at a constant 7% rate. Sheldon’s unlevered cost of equity is 13%; its tax rate is 25%:

YEAR 1: FCF = $20.0 million, Interest expense = $12.8 million

YEAR 2: FCF = $30.0 million, Interest expense = $14.4 million

YEAR 3: FCF = $40.0 million, Interest expense = $16.0 million

a. What is Sheldon’s unlevered horizon value of operations at Year 3?

b. What is the current unlevered value of operations?

c. What is the horizon value of the tax shield at Year 3?

d. What is the current value of the tax shield?

e. What is the current total value of the company?

Paper For Above instruction

To evaluate Sheldon Corporation's value using the Adjusted Present Value (APV) approach with a nonconstant growth period, we begin by calculating the unlevered horizon value at Year 3, then proceed to determine the current value of operations, the tax shield, and ultimately the total value of the firm. This comprehensive analysis provides insights into the company's valuation by separating the operations' value from the effects of leverage and tax shields.

a. Unlevered Horizon Value of Operations at Year 3

The horizon value at Year 3 represents the present value of all future free cash flows beyond Year 3, assuming a perpetual growth rate of 7%. To calculate this, we need the unlevered free cash flow at Year 3 and then apply the Gordon Growth Model (or perpetuity growth model). Since the cash flows are provided for the initial three years, we first estimate the Year 4 unlevered free cash flow:\n

\[ FCF_{Year 4} = FCF_{Year 3} \times (1 + g) = 40 \times (1 + 0.07) = 42.8 \text{ million} \]\n

Next, the horizon value at Year 3 (HV) is calculated as:\n

\[ HV = \frac{FCF_{Year 4}}{WACC_{unlevered} - g} = \frac{42.8}{0.13 - 0.07} = \frac{42.8}{0.06} = 713.33 \text{ million} \]\n

This calculation assumes the unlevered cost of equity (13%) as the discount rate for all unlevered cash flows, which is standard as the WACC for unlevered firms equals the unlevered cost of equity.

b. Current Unlevered Value of Operations

The current unlevered value is the present value of the forecasted free cash flows during the explicit forecast period (Years 1-3), plus the present value of the horizon value (from Year 3). The discount rate used is the unlevered cost of equity (13%).

The present value of each year's FCF is calculated as: \(\frac{FCF_t}{(1+WACC)^t}\).

• PV of Year 1 FCF: \(\frac{20}{(1+0.13)^1} = \frac{20}{1.13} \approx 17.70\) million
• PV of Year 2 FCF: \(\frac{30}{(1+0.13)^2} = \frac{30}{1.2769} \approx 23.50\) million
• PV of Year 3 FCF: \(\frac{40}{(1+0.13)^3} = \frac{40}{1.4429} \approx 27.74\) million

Next, discount the horizon value at Year 3 back to Year 0:

\(PV_{horizon} = \frac{HV}{(1 + WACC)^3} = \frac{713.33}{1.4429} \approx 494.66\) million

Adding all components gives the current unlevered value of operations:

Unlevered firm value = 17.70 + 23.50 + 27.74 + 494.66 ≈ 563.60 million

c. Horizon Value of the Tax Shield at Year 3

The tax shield benefit from debt is equal to the present value of the tax savings attributable to interest payments, which are expected to grow at the same rate as the debt's interest payments and tax rate. The interest expense at Year 3 is $16 million, and in Year 4, it will grow to:\n

\[ Interest_{Year 4} = 16 \times (1 + 0.07) = 17.12 \text{ million} \]\n

The tax shield for Year 4 is:\n

\[ Tax\ shield_{Year 4} = Interest_{Year 4} \times Tax\ rate = 17.12 \times 0.25 = 4.28 \text{ million} \]\n

The horizon value of the tax shield at Year 3 is calculated as the perpetuity of these interest tax shields beyond Year 3:\n

\[ HV_{tax\ shield} = \frac{Interest_{Year 4} \times Tax\ rate}{WACC_{debt} - g_{debt}} \]

Assuming the debt's cost of capital (WACC_debt) is close to interest rate (for simplicity, assume 7%), the calculation simplifies to:\n

\[ HV_{tax\ shield} = \frac{4.28}{0.07 - 0.07} \]

which indicates an infinite perpetuity without a differing growth rate. Given constant growth at 7% in interest, the tax shield’s horizon value is calculated as:

\( HV_{tax\ shield} = \frac{Interest_{Year 4} \times Tax\ rate}{WACC_{debt} - g} \approx \frac{4.28}{0.07 - 0.07} \)

which is undefined due to zero denominator. Usually, the tax shield is discounted at the cost of debt. Alternatively, a more precise approach involves estimating the perpetuity based on the debt's incremental interest payments and discounting at debt's cost of capital.\n

Thus, assuming debt's cost is approximately 7%, the horizon value simplifies to:\n

\[ HV_{tax\ shield} = \frac{Interest_{Year 4} \times Tax\ rate}{r_{debt} - g} = \frac{4.28}{0.07 - 0.07} \]

The value converges if growth rate and debt rate are equal; in practice, the horizon value of the tax shield is often approximated as the present value of future tax shields assuming a stable debt level and interest rate. Using a simplified approach, the Year 3 tax shield value (implying no growth in debt) is:\n

\[ HV_{tax\ shield} = \frac{Interest_{Year 3} \times Tax\ rate}{r_{debt}} = \frac{16 \times 0.25}{0.07} \approx 57.14 \text{ million} \]

which is a practical estimate for the horizon value at Year 3.

d. Current Value of the Tax Shield

The present value of future tax shields is found by discounting the Year 3 horizon value back to Year 0 at the cost of debt (assuming 7%). This gives:

\( PV_{tax\ shield} = \frac{57.14}{(1 + 0.07)^3} = \frac{57.14}{1.225} \approx 46.60 \text{ million} \)

e. Current Total Value of the Company

The total value of the firm is the sum of the unlevered value of operations and the present value of the tax shield:

\( Total\ Value = Unlevered\ Operations + PV_{tax\ shield} \approx 563.60 + 46.60 = 610.20 \text{ million} \)

This valuation reflects the firm's operational value and the benefits derived from its debt financing, appropriately discounted to present value.

References

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