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Fowler Corporation is considering a four year project. The project cash flows are projected to be the following:

Year 0=-$70,000.00
Year 1=$24,000.00
Year 2=$26,000.00
Year 2=$26,000.00
Year 3=$22,000.00
Year 4=$15,000.00
Fowler has a capital structure of 30.00% debt and 70.00% common equity. The cost of debt for the project is 4.00%, while the estimated cost of equity is 9.00%. The tax rate facing Fowler is 34.00%.

What is the weighted average cost of capital for the project?

3 answers

To calculate the Weighted Average Cost of Capital (WACC) for Fowler Corporation, we need to account for both the cost of debt and the cost of equity, weighted by their respective proportions in the overall capital structure.

Formula for WACC:

\[ \text{WACC} = \left( \frac{E}{V} \times r_e \right) + \left( \frac{D}{V} \times r_d \times (1 - T) \right) \] Where:

  • \( E \) = market value of equity
  • \( D \) = market value of debt
  • \( V \) = total market value of the company ( \( V = E + D \) )
  • \( r_e \) = cost of equity
  • \( r_d \) = cost of debt
  • \( T \) = tax rate

Given:

  • Proportion of debt (\( \frac{D}{V} \)): 30% or 0.30
  • Proportion of equity (\( \frac{E}{V} \)): 70% or 0.70
  • Cost of debt (\( r_d \)): 4% or 0.04
  • Cost of equity (\( r_e \)): 9% or 0.09
  • Tax rate (\( T \)): 34% or 0.34

Calculation Steps:

  1. Calculate the after-tax cost of debt: \[ r_d \times (1 - T) = 0.04 \times (1 - 0.34) = 0.04 \times 0.66 = 0.0264 \]

  2. Substitute values into the WACC formula: \[ \text{WACC} = \left( 0.70 \times 0.09 \right) + \left( 0.30 \times 0.0264 \right) \]

  3. Calculate each component: \[ 0.70 \times 0.09 = 0.063 \] \[ 0.30 \times 0.0264 = 0.00792 \]

  4. Add the two components to get the WACC: \[ \text{WACC} = 0.063 + 0.00792 = 0.07092 \]

Final WACC:

Converting to percentage: \[ \text{WACC} = 0.07092 \times 100 = 7.092% \]

Conclusion:

Thus, the weighted average cost of capital (WACC) for Fowler Corporation is approximately 7.09%.

What is the NPV for this project?

To calculate the Net Present Value (NPV) of the project, we will first need to discount the projected cash flows using the WACC we calculated earlier. The steps to calculate NPV are as follows:

Cash Flows:

  • Year 0: \(-70,000\)
  • Year 1: \(24,000\)
  • Year 2: \(26,000\)
  • Year 3: \(22,000\)
  • Year 4: \(15,000\)

WACC:

As previously calculated, the WACC is approximately \(7.09%\) or \(0.0709\).

Formula for NPV:

\[ \text{NPV} = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t} \] Where:

  • \( C_t \) = cash flow at time \( t \)
  • \( r \) = discount rate (WACC)
  • \( n \) = total number of periods

NPV Calculation Steps:

  1. Calculating Present Values of each cash flow:
    • For Year 0: \[ PV_0 = \frac{-70,000}{(1 + 0.0709)^0} = -70,000 \]
    • For Year 1: \[ PV_1 = \frac{24,000}{(1 + 0.0709)^1} = \frac{24,000}{1.0709} \approx 22,388.40 \]
    • For Year 2: \[ PV_2 = \frac{26,000}{(1 + 0.0709)^2} = \frac{26,000}{1.1449} \approx 22,703.19 \]
    • For Year 3: \[ PV_3 = \frac{22,000}{(1 + 0.0709)^3} = \frac{22,000}{1.2250} \approx 17,938.04 \]
    • For Year 4: \[ PV_4 = \frac{15,000}{(1 + 0.0709)^4} = \frac{15,000}{1.3105} \approx 11,438.14 \]

Summing Present Values:

Now we sum the present values of all cash flows: \[ \text{NPV} = PV_0 + PV_1 + PV_2 + PV_3 + PV_4 \] \[ \text{NPV} = -70,000 + 22,388.40 + 22,703.19 + 17,938.04 + 11,438.14 \]

\[ \text{NPV} \approx -70,000 + 74,467.77 \approx 4,467.77 \]

Final NPV:

Thus, the NPV for the project is approximately $4,467.77.

A positive NPV indicates that the project is expected to generate value above the cost of capital and may be considered a worthwhile investment.