Chapter 12, Problem 23P

Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows:

a. Determine the net present value of the projects based on a zero percent discount rate.

b. Determine the net present value of the projects based on a 9 percent discount rate.

c. The internal rate of return on Project E is 13.25 percent, and the internal rate of return on Project H is 16.30 percent. Graph a net present value profile for the two investments similar to Figure 12-3. (Use a scale up to $\$$ 8,000 on the vertical axis, with $\$$ 2,000 increments. Use a scale up to 20 percent on the horizontal axis, with 5 percent increments.)

d. If the two projects are not mutually exclusive, what would your acceptance or rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net present value profile for your decision; no actual numbers are necessary.)

e. If the two projects are mutually exclusive (the selection of one precludes the selection of the other), what would be your decision if the cost of capital is (1) 6 percent, (2) 13 percent, (3) 18 percent? Once again, use the net present value profile for your answer.

Summary Introduction

To calculate: The NPV of the projects by using zero discount rate for Keller Construction Company.

Introduction:

Net present value (NPV):

It is the difference between the PV (present value) of cash inflows and the PV of cash outflows. It is used in capital budgeting and planning of investment to assess the benefits and losses of any project or investment.

Answer to Problem 23P

The NPV of the project E is $8,000 and project H is $5,000 based on zero discount rate for Keller Construction Company.

Explanation of Solution

The calculation of NPV of project E:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$28,000-\$20,000\\ =\$8,000\end{array}$

The calculation of NPV of project H:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$25,000-\$20,000\\ =\$5,000\end{array}$

Working Notes:

The calculation of inflows for project E:

$\begin{array}{c}\text{Cash Inflows}=\text{Cash Inflow of 1st Year}+{\text{Cash Inflow of 2}}^{\text{nd}}\text{ year}+{\text{Cash Inflow of 3}}^{\text{rd}}\text{year}\\ +{\text{Cash flow of 4}}^{\text{th}}\text{year}\\ =\$5,000+\$6,000+\$7,000+\$10,000\\ =\$28,000\end{array}$

The calculation of inflows for project H:

$\begin{array}{c}\text{Cash Inflows}=\text{Cash Inflow of 1st Year}+{\text{Cash Inflow of 2}}^{\text{nd}}\text{ year}+{\text{Cash Inflow of 3}}^{\text{rd}}\text{year}\\ =\$16,000+\$5,000+\$4,000\\ =\$25,000\end{array}$

Summary Introduction

To calculate: The NPV of the projects by using 9% discount rate for Keller Construction Company.

Introduction:

Net present value (NPV):

It is the difference between the PV (present value) of cash inflows and the PV of cash outflows. It is used in capital budgeting and planning of investment to assess the benefits and losses of any project or investment.

Present value (PV):

The current value of an investment or an asset is termed as its present value. It is calculated by discounting the future value of the investment or asset.

Answer to Problem 23P

The calculation of PV of inflows for Project E at 9%:

The calculation of PV of inflows for Project H at 9%:

Thus, the NPV of project E is $2,127 and project H is $1,976.

Explanation of Solution

The calculation of NPV of project E:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$22,127-\$20,000\\ =\$2,127\end{array}$

The calculation of NPV of project H:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$21,976-\$20,000\\ =\$1,976\end{array}$

The formulae used for the calculation of PV of inflows for Project E:

The formulae used for the calculation of PV of inflows for Project E:

Summary Introduction

To plot: The graph for the NPV of the project according to the Fig. 12-3 for the Keller Construction Company.

Introduction:

Internal rate of return (IRR):

A method of capital budgeting that is used to measure the profitability of potential projects or investments. It is a discount that makes the NPV equals to zero for a specific project.

Answer to Problem 23P

The graph for the NPV of the project according to the Fig. 12-3 for the Keller Construction Company:

Explanation of Solution

Calculation of IRR:

Working Note:

The formulae used in the calculation of IRR:

Summary Introduction

To determine: The decision regarding the acceptance or the rejection of the projects, if the projects are mutually exclusive and discount rate of the cost of capital is 8% for the Keller Construction Company.

Introduction:

Net present value (NPV):

It is the difference between the PV (present value) of cash inflows and the PV of cash outflows. It is used in capital budgeting and planning of investment to assess the benefits and losses of any project or investment.

Present value (PV):

The current value of an investment or an asset is termed as its present value. It is calculated by discounting the future value of the investment or asset.

Answer to Problem 23P

The calculation of PV of project E and project H at 8%:

The NPV of project E is $2,681 and project H is $2,277. Thus, the NPV of project E is higher than the project H. Therefore, project E must be accepted as it is more profitable than the project H.

Explanation of Solution

The calculation of NPV of project E:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$22,681-\$20,000\\ =\$2,681\end{array}$

The calculation of NPV of project H:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$22,277-\$20,000\\ =\$2,277\end{array}$

The formulae used in the calculation of PV of project E and H at 8% are shown below:

Summary Introduction

To determine: The decision regarding the acceptance or rejection of the projects, if the projects are mutually exclusive and discount rates of cost of capital are 6%, 13%, and 18% for the Keller Construction Company.

Introduction:

Net present value (NPV):

It is the difference between the PV (present value) of cash inflows and the PV of cash outflows. It is used in capital budgeting and planning of investment to assess the benefits and losses of any project or investment.

Present value (PV):

The current value of an investment or an asset is termed as its present value. It is calculated by discounting the future value of the investment or asset.

Answer to Problem 23P

The calculation of PV of project E and project H at 6%:

The NPV of project E is $3,855 and project H is $2,903. Thus, the NPV of project E is higher than the project H, So, project E must be accepted at 6% discount rate as it is superior to the project H.

The calculation of PV of project E and project H at 13%:

The NPV of project E is $108 and project H is $847. Thus, the NPV of project H is higher than the project E, So, project H must be accepted at 13% discount rate as it is superior to the project E.

The calculation of PV of project E and project H at 18%:

The NPV of project E is ($2,035) and project H is ($415). Thus, both projects must be rejected at 18% discount rate as NPV of both projects are negative.

Explanation of Solution

The calculation of NPV of project E at 6%:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$23,855-\$20,000\\ =\$3,855\end{array}$

The calculation of NPV of project H at 6%:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$22,903-\$20,000\\ =\$2,903\end{array}$

The calculation of NPV of project E at 13%:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$20,108-\$20,000\\ =\$108\end{array}$

The calculation of NPV of project H at 13%:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$20,847-\$20,000\\ =\$847\end{array}$

The calculation of NPV of project E at 18%:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$17,965-\$20,000\\ =-\left(\$2035\right)\end{array}$

The calculation of NPV of project H at 18%:

$\begin{array}{c}\text{NPV}=\text{Cash Inflows}-\text{Cash Outflows}\\ =\$19,585-\$20,000\\ =-\left(\$415\right)\end{array}$

The formulae used in the calculation of PV of project E and H at 6% are shown below:

The formulae used in the calculation of PV of project E and H at 13% are shown below:

The formulae used in the calculation of PV of project E and H at 18% are shown below: