Chapter 14, Problem 30QP

Project Evaluation [LO3, 4] This is a comprehensive project evaluation problem bringing together much of what you have learned in this and previous chapters. Suppose you have been hired as a financial consultant to Defense Electronics, Inc. (DEI), a large, publicly traded firm that is the market share leader in radar detection systems (RDSs). The company is looking at setting up a manufacturing plant overseas to produce a new line of RDSs. This will be a five-year project. The company bought some land three years ago for $3.9 million in anticipation of using it as a toxic dump site for waste chemicals, but it built a piping system to safely discard the chemicals instead. The land was appraised last week for $4.4 million on an aftertax basis. In five years, the aftertax value of the land will be $4.8 million, but the company expects to keep the land for a future project. The company wants to build its new manufacturing plant on this land; the plant and equipment will cost $37 million to build. The following market data on DEI’s securities are current:

Debt:	210,000 6.4 percent coupon bonds outstanding, 25 years to maturity, selling for 108 percent of par; the bonds have a $1,000 par value each and make semiannual payments.
Common stock:	8,300,000 shares outstanding, selling for $68 per share; the beta is 1.1.
Preferred stock:	450,000 shares of 4.5 percent preferred stock outstanding, selling for $81 per share.
Market:	7 percent expected market risk premium; 3.5 percent risk-free rate.

DEI uses G.M. Wharton as its lead underwriter. Wharton charges DEI spreads of 8 percent on new common stock issues, 6 percent on new preferred stock issues, and 4 percent on new debt issues. Wharton has included all direct and indirect issuance costs (along with its profit) in setting these spreads. Wharton has recommended to DEI that it raise the funds needed to build the plant by issuing new shares of common stock. DEI’s tax rate is 35 percent. The project requires $1,300,000 in initial net working capital investment to get operational. Assume Wharton raises all equity for new projects externally.

a. Calculate the project’s initial Time 0 cash flow, taking into account all side effects.

b. The new RDS project is somewhat riskier than a typical project for DEI, primarily because the plant is being located overseas. Management has told you to use an adjustment factor of +2 percent to account for this increased riskiness. Calculate the appropriate discount rate to use when evaluating DEI’s project.

c. The manufacturing plant has an eight-year tax life, and DEI uses straight-line depreciation. At the end of the project (that is, the end of Year 5), the plant and equipment can be scrapped for $5.1 million. What is the aftertax salvage value of this plant and equipment?

d. The company will incur $6,700,000 in annual fixed costs. The plan is to manufacture 15,300 RDSs per year and sell them at $11,450 per machine; the variable production costs are $9,500 per RDS. What is the annual operating cash flow (OCF) from this project?

e. DEI’s comptroller is primarily interested in the impact of DEI’s investments on the bottom line of reported accounting statements. What will you tell her is the accounting break-even quantity of RDSs sold for this project?

f. Finally, DEI’s president wants you to throw all your calculations, assumptions, and everything else into the report for the chief financial officer; all he wants to know is what the RDS project’s internal rate of return (IRR) and net present value (NPV) are. What will you report?

Summary Introduction

To determine: The initial cash flow of the project at Time 0.

Introduction:

Project evaluation refers to the process of evaluating the project for its feasibility and economic viability.

Answer to Problem 30QP

The initial cash flow at Time 0 is $45,408,091.87.

Explanation of Solution

Given information:

Company D manufactures radar detection systems. It is planning to open a new manufacturing plant overseas. The project will take five years. It had purchased a land overseas at $3,900,000 for dumping chemical waste. However, the company found an alternative to dispose of waste and the land remained unused.

The current after-tax valuation of the land is $4,400,000. It would be worth $4,800,000 in five years. The company wants to implement the project on this unused land. The cost of plant and equipment would be $37,000,000. The current market data for Company D is as follows:

• Debt: Company D has bonds with a face value of $1,000 and a coupon rate of 6.4 percent. There are 210,000 outstanding bonds. The bonds will mature in 25 years, and they make semiannual coupon payments. The bond currently sells at 108 percent of the face value.
• Common equity: The common equity of Company D has 8,300,000 shares outstanding. The current selling price of the share is $68. The stock has a beta of 1.1. The risk-free rate is 3.5 percent, and the market risk premium is 7 percent.
• Preferred stock: Company D has 450,000 outstanding preferred shares. The dividend is 4.5 percent, and the current market value is $81 per share. Assume that the face value of the share is $100.

The flotation costs of raising common stock, preferred stock, and debt is 8 percent, 6 percent, and 4 percent respectively. The underwriter recommends Company D to raise all the funds through common stock. The tax rate applicable to Company D is 35 percent. The project needs an initial net working capital of $1,300,000 to begin the operations. The company raises all the common stock externally.

The calculations necessary for parts (a) and (b) of the solution:

• The market value of debt
• The market value of equity
• The market value of preferred stock
• The cost of equity
• The cost of preferred stock
• The after-tax cost of debt

The formula to calculate the market value of debt:

$\text{Market value of debt}=\text{Face value of the debt}\times \text{Price quote}$

The formula to calculate the market value of equity:

$\text{Market value of equity }(E)=\text{Outstanding equity shares}\times \text{Market value per share}$

The formula to calculate the market value of preferred stock:

$\begin{array}{l}\text{Market value of}\\ \text{preferred shares }(P)\end{array}\}=\text{Outstanding preferred shares}\times \text{Market value per share}$

The formula to calculate the total market value of the capital structure:

$\text{Total market value }(V)=\left(\begin{array}{l}\text{Market value}\\ \text{of equity }(E)\end{array}\right)+\left(\begin{array}{l}\text{Market value of}\\ \text{preferred stock }(P)\end{array}\right)+\left(\begin{array}{l}\text{Market value}\\ \text{of debt }(D)\end{array}\right)$

The formula to calculate the cost of equity using the Security market line (SML) approach:

$R_E=R_f+\left[R_M-R_f\right]\times {\beta }_E$

Where,

“R_E” refers to the expected return on equity or the cost of equity

“R_f” refers to the risk-free rate

“R_M” refers to the expected return on the market portfolio

“β_E” refers to the beta or risk of the equity

The formula to calculate the cost of preferred stock:

$R_P=\frac{D}{P_0}$

Where,

“R_P” refers to the return on preferred stock or cost of preferred stock

“D” refers to the dividend earned on the preferred stock

“P₀” refers to the current price of preference stock

The formula to calculate annual coupon payment:

$\text{Annual coupon payment}=\text{Face value of the bond}\times \text{Coupon rate}$

The formula to calculate the current price or the market value of the debt:

$\text{Current price}=\text{Face value of the debt}\times \text{Last price percentage}$

The formula to calculate the yield to maturity:

$\text{Bond value}=C\times \frac{\left[1-\frac{1}{{\left(1+r\right)}^t}\right]}{r}+\frac{F}{{\left(1+r\right)}^t}$

Where,

“C” refers to the coupon paid per period

“F” refers to the face value paid at maturity

“r” refers to the yield to maturity

“t” refers to the periods to maturity

The formula to calculate the after-tax cost of debt:

$\text{After-tax}\text{}{R}_D=R_D\times (1-T_C)$

Where,

“R_D” refers to the cost of debt

“T_C” refers to the corporate tax rate

Compute the market value of debt:

$\begin{array}{c}\text{Market value of debt}=\left(\begin{array}{l}\text{Face value}\\ \text{of one bond}\end{array}\right)\times \left(\begin{array}{l}\text{Number of}\\ \text{bonds}\end{array}\right)\times \text{Price quote}\\ =\$1,000\times 210,000\times \frac{108}{100}\\ =\$226,800,000\end{array}$

Hence, the market value of debt is $226,800,000.

Compute the market value of equity:

$\begin{array}{c}\text{Market value of equity }(E)=\text{Outstanding equity shares}\times \text{Market value per share}\\ =8,300,000\times \$68\\ =\$564,400,000\end{array}$

Hence, the market value of common equity is $564,400,000.

Compute the market value of preferred stock:

$\begin{array}{c}\begin{array}{l}\text{Market value of}\\ \text{preferred shares }(P)\end{array}\}=\text{Outstanding preferred shares}\times \text{Market value per share}\\ =450,000\times \$81\\ =\$36,450,000\end{array}$

Hence, the market value of preferred stock is $36,450,000.

Compute the total market value of the capital structure:

$\begin{array}{c}\text{Total market value }(V)=\left(\begin{array}{l}\text{Market value}\\ \text{of equity }(E)\end{array}\right)+\left(\begin{array}{l}\text{Market value of}\\ \text{preferred stock }(P)\end{array}\right)+\left(\begin{array}{l}\text{Market value}\\ \text{of debt }(D)\end{array}\right)\\ =\$564,400,000+\$36,450,000+\$226,800,000\\ =\$827,650,000\end{array}$

Hence, the total market value of the capital structure is $827,650,000.

Compute the cost of equity:

$\begin{array}{c}{R}_E=R_f+\left[R_M-R_f\right]\times {\beta }_E\\ =0.035+\left[0.07\right]\times 1.1\\ =0.035+0.077\\ =0.112\text{ or }11.20\%\end{array}$

Hence, the cost of equity is 11.20 percent.

Compute the cost of preferred stock:

The face value of the preferred stock is $100. The dividend percent is 4.5. Hence, the dividend is $4.5 $\left(\$100\times 4.5\%\right)$.

$\begin{array}{c}{R}_P=\frac{D}{P_0}\\ =\frac{\$4.5}{\$81}\\ =0.0556\text{ or }5.56\%\end{array}$

Hence, the cost of preferred stock is 5.56 percent.

Compute the annual coupon payment:

$\begin{array}{c}\text{Annual coupon payment}=\text{Face value of the bond}\times \text{Coupon rate}\\ =\$1,000\times 6.4\%\\ =\$64\end{array}$

Hence, the annual coupon payment is $64.

Compute the current price of the bond:

The face value of the bond is $1,000. The bond value is 108% of the face value of the bond.

$\begin{array}{c}\text{Current price}=\text{Face value of the bond}\times \text{Last price percentage}\\ =\$1,000\times \frac{108}{100}\\ =\$1,080\end{array}$

Hence, the current price of the bond is $1,080.

Compute the semiannual yield to maturity of the bond as follows:

The bond pays the coupons semiannually. The annual coupon payment is $64. However, the bondholder will receive the same is two equal installments. Hence, semiannual coupon payment or the 6-month coupon payment is $32 $\left(\$64÷2\right)$.

The remaining time to maturity is 25 years. As the coupon payment is semiannual, the semiannual periods to maturity are 50 $\left(25\text{ years}\times \text{2}\right)$. In other words, “t” equals to 50 6-month periods.

$\begin{array}{c}\text{Bond value}=C\times \frac{\left[1-\frac{1}{{\left(1+r\right)}^t}\right]}{r}+\frac{F}{{\left(1+r\right)}^t}\\ \$1,080=\$34\times \frac{\left[1-\frac{1}{{\left(1+r\right)}^{50}}\right]}{r}+\frac{\$1,000}{{\left(1+r\right)}^{50}}\end{array}$ Equation (1)

Finding “r” in Equation (1) would give the semiannual yield to maturity. However, it is difficult to simplify the above the equation. Hence, the only method to solve for “r” is the trial and error method.

The first step in trial and error method is to identify the discount rate that needs to be used. The bond sells at a premium in the market if the market rates (Yield to maturity) are lower than the coupon rate. Similarly, the bond sells at a discount if the market rate (Yield to maturity) is greater than the coupon rate.

In the given information, the bond sells at a premium because the market value of the bond is higher than its face value. Hence, substitute “r” with a rate that is lower than the coupon rate until one obtains the bond value close to $1,080.

The coupon rate of 6.4 percent is an annual rate. The semiannual coupon rate is 3.2 percent $\left(\text{6}\text{.4 percent}÷2\right)$. The trial rate should be below 3.2 percent.

The attempt under the trial and error method using 2.895 percent as “r”:

$\begin{array}{c}\text{Bond value}=C\times \frac{\left[1-\frac{1}{{\left(1+r\right)}^t}\right]}{r}+\frac{F}{{\left(1+r\right)}^t}\\ =\$32\times \frac{\left[1-\frac{1}{{\left(1+0.02895\right)}^{50}}\right]}{0.02895}+\frac{\$1,000}{{\left(1+0.02895\right)}^{50}}\\ =\$840.02+\$240.04\\ =\$1,080.06\end{array}$

The current price of the bond is $1,080.60 when “r” is 2.895 percent. Hence, 2.895 percent is the semiannual yield to maturity.

Compute the annual yield to maturity:

$\begin{array}{c}\text{Yield to maturity}=\text{Semiannual yield to maturity}\times \text{2}\\ =2.895\%\times 2\\ =5.79\%\end{array}$

Hence, the yield to maturity is 5.79 percent.

Compute the after-tax cost of debt:

The pre-tax cost of debt is equal to the yield to maturity of the bond. The yield to maturity of the bond is 5.79 percent. The corporate tax rate is 35 percent.

$\begin{array}{c}\text{After-tax}\text{}{R}_D=R_D\times (1-T_C)\\ =0.0579\times (1-0.35)\\ =0.0579\times 0.65\\ =0.0376\text{ or }3.76\%\end{array}$

Hence, the after-tax cost of debt is 3.76 percent.

The formula to calculate the weighted average flotation cost:

$f_A=\left(\frac{E}{V}\right)\times f_E+\left(\frac{P}{V}\right)\times f_P+\left(\frac{D}{V}\right)\times f_D$

Where,

“f_A” refers to the weighted average flotation cost

“f_E” refers to the flotation cost of equity

“f_P” refers to the flotation cost of preferred stock

“f_D” refers to the flotation cost of debt

“E” refers to the amount of common equity capital

“D” refers to the amount of debt

“P” refers to the amount of preferred stock

“V” refers to the total amount of capital

The formula to calculate the total amount of capital that the firm should raise after taking into account the flotation costs:

$\text{Total capital to be raised}=\frac{\text{Project cost}}{\left(1-f_A\right)}$

Here, “f_A” refers to the weighted average flotation cost

Compute the weighted average flotation cost:

The market value of equity (E) is $564,400,000, the market value of preferred stock (P) is $36,450,000, and the market value of debt (D) is $226,800,000. The total market value (V) is $827,650,000. The flotation cost of equity “f_E” is 8 percent, the flotation cost of preferred stock “f_E” is 6 percent, and the flotation cost of debt “f_D” is 3.5 percent.

$\begin{array}{c}{f}_A=\left(\frac{E}{V}\right)\times f_E+\left(\frac{P}{V}\right)\times f_P+\left(\frac{D}{V}\right)\times f_D\\ =\left(\frac{\$564,400,000}{\$827,650,000}\times 0.08\right)+\left(\frac{\$36,450,000}{\$827,650,000}\times 0.06\right)+\left(\frac{\$226,800,000}{\$827,650,000}\times 0.04\right)\\ =0.0546+0.0026+0.011\\ =0.0682\text{ or }6.82\%\end{array}$

Hence, the weighted average flotation cost is 6.82percent.

Compute the total capital to be raised:

The project cost includes the cost plant and equipment. Hence, the amount to be raised before the flotation costs is $37,000,000. The company has already purchased the land. Assume that the company will fund the initial net working capital from internal sources. The weighted average flotation cost is 6.82 percent.

$\begin{array}{c}\text{Total capital to be raised}=\frac{\text{Project cost}}{\left(1-f_{Average}\right)}\\ =\frac{\$37,000,000}{\left(1-0.0682\right)}\\ =\$39,708,091.87\end{array}$

Hence, the total capital to be raised is $39,708,091.87.

Compute the initial cash outflow:

The initial cash flow includes the cost of the land, plant and equipment, and the initial net working capital. The land currently values at $4,400,000. The cost of buying plant and equipment including the flotation costs is $39,708,091.87. The initial working capital required is $1,300,000. Hence, the initial cash outflow at Time 0 is $45,408,091.87 $\left(\$4,400,000+\$39,708,091.87+\$1,300,000\right)$.

Summary Introduction

To determine: The discount rate

Answer to Problem 30QP

The discount rate is 10.91 percent.

Explanation of Solution

The company can use the weighted average cost of capital as its discount rate if the new project’s risk is similar to the company’s risk. It is given that the project is riskier than the firm is. The company adds 2 percent to its weighted average cost of capital to match the riskiness of the project. Therefore, the discount rate for the project would we equal to the sum of the weighted average cost of capital and the adjustment factor of 2 percent.

The formula to calculate the weighted average cost of capital:

$WACC=\left(\frac{E}{V}\right)\times R_E+\left(\frac{P}{V}\right)\times R_P+\left[\left(\frac{D}{V}\right)\times R_D\times \left(1-T_C\right)\right]$

Where,

“WACC” refers to the weighted average cost of capital

“R_E” refers to the return on equity or cost of equity

“R_D” refers to the return on debt or cost of debt

“R_P” refers to the return on debt or cost of preferred stock

“E” refers to the amount of common equity capital

“D” refers to the amount of debt

“P” refers to the amount of preferred stock

“V” refers to the total amount of capital

“T_C” refers to the corporate tax rate

Compute the weighted average cost of capital:

The market value of equity (E) is $564,400,000, the market value of preferred stock (P) is $36,450,000, and the market value of debt (D) is $226,800,000. The total market value (V) is $827,650,000. The cost of equity “R_E” is 11.20 percent, the cost of preferred stock “R_P” is 5.56 percent, and the after-tax cost of debt “R_D” is 3.76 percent. As the after-tax cost of debt is available, omit “1‑T_C” from the formula.

$\begin{array}{c}WACC=\left(\frac{E}{V}\right)\times R_E+\left(\frac{P}{V}\right)\times R_P+\left(\frac{D}{V}\right)\times R_D\\ =\left[\begin{array}{l}\left(\frac{\$564,400,000}{\$827,650,000}\times 0.1120\right)+\left(\frac{\$36,450,000}{\$827,650,000}\times 0.0556\right)+\\ \left(\frac{\$226,800,000}{\$827,650,000}\times 0.376\right)\end{array}\right]\\ =0.0764+0.0024+0.0103\\ =0.0891\text{ or }8.91\%\end{array}$

Hence, the weighted average cost of capital is 8.91 percent.

Compute the discount rate:

The company adds 2 percent to its weighted average cost of capital to match the riskiness of the project. The weighted average cost of capital is 8.91 percent. Hence, the discount rate is 10.91 percent $(8.91\%+2\%)$.

Summary Introduction

To determine: The after-tax salvage value after 5 years

Answer to Problem 30QP

The after-tax salvage value after 5 years is $8,171,250.

Explanation of Solution

The formula to calculate the depreciation per year:

$\text{Depreciation}=\frac{\text{Cost of the equipment}}{\text{Number of years of tax life}}$

The formula to calculate the book value after 5 years:

$\text{Book value after 5 years}=\text{Cost of the equipment}-\left(\begin{array}{l}\text{Depreciation per year}\times \\ 5\text{ years}\end{array}\right)$

The formula to calculate the after-tax salvage value:

$\text{After-tax salvage value}=\text{Salvage value}+\left(\text{Book value}-\text{Market value}\right)\times \text{Tax rate}$

Compute the depreciation per year:

The cost of the equipment is $37,000,000, and its tax life is 8 years (Given).

$\begin{array}{c}\text{Depreciation}=\frac{\text{Cost of the equipment}}{\text{Number of years of tax life}}\\ =\frac{\$37,000,000}{8\text{ years}}\\ =\$4,625,000\end{array}$

Hence, the depreciation per year is $4,625,000.

Compute the book value after 5 years:

$\begin{array}{c}\text{Book value after 5 years}=\text{Cost of the equipment}-\left(\begin{array}{l}\text{Depreciation per year}\times \\ 5\text{ years}\end{array}\right)\\ =\$37,000,000-\left(\$4,625,000\times 5\text{ years}\right)\\ =\$37,000,000-\$23,125,000\\ =\$13,875,000\end{array}$

Hence, the book value after five years is $13,875,000.

Compute the after-tax salvage value:

It is given that the market value of the equipment after 5 years is $5,100,000. The book value after 5 years is $13,875,000. The tax rate is 35 percent.

$\begin{array}{c}\text{After-tax salvage value}=\text{Market value}+\left(\text{Book value}-\text{Market value}\right)\times \text{Tax rate}\\ =\$5,100,000+\left(\$13,875,000-\$5,100,000\right)\times 0.35\\ =\$5,100,000+\$3,071,250\\ =\$8,171,250\end{array}$

Hence, the after-tax salvage value is $8,171,250.

Summary Introduction

To determine: The operating cash flow of the project

Answer to Problem 30QP

The operating cash flow of the project every year is $16,656,500.

Explanation of Solution

Given information:

The new project has annual fixed costs worth $6,700,000. The new plant will manufacture 15,300 products. The selling price of each product is $11,450, and the cost of production is $9,500.

The formula to calculate the operating cash flow:

$\text{Operating cash flow}=\left(\begin{array}{l}\left[\begin{array}{l}\left(\text{Selling price}–\text{Cost price}\right)\times \\ \text{Number of units produced}–\text{ Fixed costs}\end{array}\right]\times \\ \left(1–\text{Tax rate}\right)\end{array}\right)+\left(\begin{array}{l}\text{Tax rate}\times \\ \text{Depreciation}\end{array}\right)$

Compute the operating cash flow:

The selling price of each product is $11,450, and the cost of production is $9,500. The depreciation per year is $4,625,000. The fixed costs are $6,700,000. The tax rate is 35 percent.

$\begin{array}{c}\text{Operating cash flow}=\left(\begin{array}{l}\left[\begin{array}{l}\left(\text{Selling price}–\text{Cost price}\right)\times \\ \text{Number of units produced}–\text{ Fixed costs}\end{array}\right]\times \\ \left(1–\text{Tax rate}\right)\end{array}\right)+\left(\begin{array}{l}\text{Tax rate}\times \\ \text{Depreciation}\end{array}\right)\\ =\left(\begin{array}{c}\left(\left[\left(\$11,450–\$9,500\right)\times 15,300–\$6,700,000\right]\times \left(1–0.35\right)\right)+\\ \left(0.35\times \$4,625,000\right)\end{array}\right)\\ =\$15,037,750+\$1,618,750\\ =\$16,656,500\end{array}$

Hence, the operating cash flow is $16,656,500.

Summary Introduction

To determine: The accounting break-even quantity

Answer to Problem 30QP

The break-even quantity is 5,808 units.

Explanation of Solution

The break-even point is a point where the total cost of the manufacturing is equal to the total revenue. The fixed costs of the project divided by the contribution per product give the break-even units.

The formula to calculate the break-even quantity:

$\text{Break-even point}=\frac{\text{Fixed costs}+\text{Depreciation}}{\text{Selling price per unit}-\text{Cost price per unit}}$

Compute the break-even quantity:

The selling price of each product is $11,450, and the cost of production is $9,500. The depreciation per year is $4,625,000. The fixed costs are $6,700,000.

$\begin{array}{c}\text{Break-even point}=\frac{\text{Fixed costs}+\text{Depreciation}}{\text{Selling price per unit}-\text{Cost price per unit}}\\ =\frac{\$6,700,000+\$4,625,000}{\$11,450-\$9,500}\\ =\frac{\$11,325,000}{\$1,950}\\ =5,808\text{ units}\end{array}$

Hence, the break-even quantity is 5,808 units.

Summary Introduction

To determine: The net present value and the internal rate of return

Answer to Problem 30QP

The net present value is $24,795,955.34, and the internal rate of return is 28.94 percent.

Explanation of Solution

Net present value is a tool that helps in evaluating a new project. It determines whether the present value of cash flows from the project exceed the initial cost of investment. The internal rate of return in a return where the net present value of the project is zero.

The formula to calculate the net present value and the internal rate of return:

$\text{Net present value}=\left(\frac{{\text{CF}}_1}{1+r}+\frac{{\text{CF}}_2}{{\left(1+r\right)}^2}+\frac{{\text{CF}}_3}{{\left(1+r\right)}^3}+\mathrm{...}+\frac{{\text{CF}}_t}{{\left(1+r\right)}^t}\right)-\text{Initial investment}$

Where,

“CF₁ to CF_t” refer to the cash flow from period 1 to period t

“r” refers to the discount rate

Compute the net present value:

The initial investment in the project is $45,408,091.87. The operating cash flow of the project is $16,656,500. Hence, it is the cash flow from Year 1 to Year 4. For Year 5, the cash flow should include the operating cash flow plus the after-tax salvage value, after-tax land value, and the recovery of the initially invested working capital.

The after-tax salvage value is $8,171,250, the after-tax land value is $4,800,000, and the initial working capital is $1,300,000. Hence, the cash flow in Year 5 is $30,927,750 $\left(\$16,656,500+\$8,171,250+\$4,800,000+\$1,300,000\right)$. The discount rate is 10.91 percent.

$\begin{array}{c}\text{Net present value}=\left(\frac{{\text{CF}}_1}{1+r}+\frac{{\text{CF}}_2}{{\left(1+r\right)}^2}+\frac{{\text{CF}}_3}{{\left(1+r\right)}^3}+\mathrm{...}+\frac{{\text{CF}}_t}{{\left(1+r\right)}^t}\right)-\text{Initial investment}\\ =\left(\begin{array}{l}\left(\begin{array}{l}\frac{\$16,656,500}{1+0.1091}+\frac{\$16,656,500}{{\left(1+0.1091\right)}^2}+\frac{\$16,656,500}{{\left(1+0.1091\right)}^3}+\\ \frac{\$16,656,500}{{\left(1+0.1091\right)}^4}+\frac{\$30,927,750}{{\left(1+0.1091\right)}^5}\end{array}\right)\\ -\$45,408,091.87\end{array}\right)\\ =\left(\begin{array}{l}\$15,018,032.64+\$13,540,738.11+\\ \$12,208,762.16+\$11,007,810.08+\\ \$18,428,704.22\end{array}\right)-\$45,408,091.87\\ =\$24,795,955.34\end{array}$

Hence, the net present value is $24,795,955.34.

Compute the internal rate of return:

The internal rate of return in a return where the net present value of the project is zero. It is possible to determine the internal rate of return only through the trail and error method or by using a software. The net present value is positive. Hence, the trial and error rate should be higher than the discount rate. Use a trial rate of 28.94 percent to determine whether the net present value is zero.

$\begin{array}{c}\text{Net present value}=\left(\frac{{\text{CF}}_1}{1+r}+\frac{{\text{CF}}_2}{{\left(1+r\right)}^2}+\frac{{\text{CF}}_3}{{\left(1+r\right)}^3}+\mathrm{...}+\frac{{\text{CF}}_t}{{\left(1+r\right)}^t}\right)-\text{Initial investment}\\ 0=\left(\begin{array}{l}\left(\begin{array}{l}\frac{\$16,656,500}{1+r}+\frac{\$16,656,500}{{\left(1+r\right)}^2}+\frac{\$16,656,500}{{\left(1+r\right)}^3}+\\ \frac{\$16,656,500}{{\left(1+r\right)}^4}+\frac{\$30,927,750}{{\left(1+r\right)}^5}\end{array}\right)\\ -\$45,408,091.87\end{array}\right)\\ 0=\left(\begin{array}{l}\left(\begin{array}{l}\frac{\$16,656,500}{1+0.2894}+\frac{\$16,656,500}{{\left(1+0.2894\right)}^2}+\frac{\$16,656,500}{{\left(1+0.2894\right)}^3}+\\ \frac{\$16,656,500}{{\left(1+0.2894\right)}^4}+\frac{\$30,927,750}{{\left(1+0.2894\right)}^5}\end{array}\right)\\ -\$45,408,091.87\end{array}\right)\\ =\$45,408,091.87-\$45,408,091.87\\ =\$0\end{array}$

Hence, the approximate internal rate of return is 28.94 percent