Chapter 13, Problem 22QP

Flotation Costs and NPV Photochronograph Corporation (PC) manufactures lime series photographic equipment. It is currently at its target debt-equity ratio of .55. It’s considering building a new $50 million manufacturing facility. This new plant is expected to generate aftertax cash flows of $6.7 million a year in perpetuity. The company raises all equity from outside financing. There are three financing options:

1. 1. A new issue of common stock: The flotation costs of the new common stock would be 8 percent of the amount raised. The required return on the company's new equity is 14 percent.
2. 2. A new issue of 20-yec.r bonds: The flotation costs of the new bonds would be 4 percent of the proceeds. If the company issues these new bonds at an annual coupon rate of 8 percent, they will sell at par.
3. 3. Increased use of accounts payable financing: Because this financing is part of the company’s ongoing daily business, it has no flotation costs, and the company assigns it a cost that is the same as the overall firm WACC. Management has a target ratio of accounts payable to long-term debt of .20. (Assume there is no difference between the pretax and aftertax accounts payable cost.)

What is the NPV of the new plant? Assume that PC has a 35 percent tax rate.

Summary Introduction

To determine: The NPV of the New Plant.

Introduction:   Flotation Costs is an assortment of costs that are related with issuing new securities. Ordinarily these expenses will be greater with bigger offering extents or because of expanded risk with the offering.

Answer to Problem 22QP

The NPV of the New Plant is $6,251,949

Explanation of Solution

Determine the Weight of Accounts Payable

$\begin{array}{c}Weigh{t}_{AccountsPayable}=\left[\frac{0.20}{1+0.20}\right]\\ =\left[\frac{0.20}{1.20}\right]\\ =0.166667or16.67\%\end{array}$

Therefore the Weight of Accounts Payable is 16.67%

Determine the Weight of Long-Term Debt

$\begin{array}{c}Weigh{t}_{LongTermDebt}=\left[\frac{1}{1+0.20}\right]\\ =\left[\frac{1}{1.20}\right]\\ =0.833333or83.33\%\end{array}$

Therefore the Weight of Long-Term Debt is 83.33%

Determine the WACC

$\begin{array}{c}WACC=\left[\begin{array}{l}\left(\left(\frac{1}{1+DERatio}\right)\times Rat{e}_{Equity}\right)+\left(\frac{DERatio}{1+DERatio}\right)\times \\ \left(\left(\frac{CurrentDERatio}{1+DERatio}\right)\times WACC\right)+\left(\left(\frac{1}{1+DERatio}\right)\times Rat{e}_{Equity}\times \left(1-Tax\right)\right)\end{array}\right]\\ WACC=\left[\begin{array}{l}\left(\left(\frac{1}{1+0.55}\right)\times 14\%\right)+\left(\frac{0.55}{1+0.55}\right)\times \left(\left(\frac{0.20}{1+0.20}\right)\times WACC\right)\\ +\left(\left(\frac{1}{1+0.20}\right)\times 8\%\times \left(1-35\%\right)\right)\end{array}\right]\\ WACC=\left[\begin{array}{l}\left(0.645161\times 0.14\right)+\left(0.354839\right)\times \left(0.166667\times WACC\right)\\ +\left(0.833333\times 0.08\times 0.65\right)\end{array}\right]\\ WACC=\left[0.090323+\left(0.354839\right)\times \left(0.166667\times WACC\right)+0.043333\right]\\ WACC=0.090323+0.059140WACC+0.015376\\ WACC=\left[\frac{0.105699}{0.940860}\right]\\ =0.112343or11.23\%\end{array}$

Therefore the WACC is 11.23%

Determine the Weighted Average Floatation Costs

$\begin{array}{c}FloatationCosts=\left[\begin{array}{l}\left(\left(\frac{1}{1+CurrentDERatio}\right)\times CouponRate\right)+\left(\frac{CurrentDERatio}{1+CurrentDERatio}\right)\times \\ \left(\left(\left(\frac{DERatio}{1+DERatio}\right)\times Rate\right)+\left(\left(\frac{1}{1+DERatio}\right)\times FloatationRate\right)\right)\end{array}\right]\\ =\left[\left(\left(\frac{1}{1+0.55}\right)\times 8\%\right)+\left(\frac{0.55}{1+0.55}\right)\times \left(\left(\frac{0.20}{1+0.20}\right)+\left(\left(\frac{1}{1+0.20}\right)\times 4\%\right)\right)\right]\\ =\left[0.645161\times 0.08+\left(\frac{0.55}{1+0.55}\right)\times 0.16667\times 0+\left(\left(\frac{1}{1+0.2}\right)\times 4\%\right)\right]\\ =\left[0.645161\times 0.08+\left(\frac{0.55}{1+0.55}\right)\times \left(0+0.83333\times 0.04\right)\right]\\ =\left[0.051613+\left(\frac{0.55}{1+0.55}\right)\times 0.03333\right]\\ =\left[0.051613+0.011828\right]\\ =0.06344or6.34\%\end{array}$

Therefore the Weighted Average Floatation Costs is 6.34%

Determine the Amount Raised

$\begin{array}{c}AmountRaised=\left[\frac{BuildingCost}{\left(1+FloatationCosts\right)}\right]\\ =\left[\frac{\$50,000,000}{\left(1-6.34\%\right)}\right]\\ =\$53,384,582.53\end{array}$

Therefore the Amount Raised is $53,384,582.53

Determine the NPV of the New Plant

  $\begin{array}{c}NPVofNewPlant=\left[-AmountRaised+\left(\frac{AftertaxCashFlows}{WACC}\right)\right]\\ =\left[-\$53,384,582.53+\left(\frac{\$6,700,000}{11.23\%}\right)\right]\\ =\left[-\$53,384,582.53+\$59,661,620.66\right]\\ =\$6,277,038.13\end{array}$

Therefore the NPV of the New Plant is $6,277,038.13.