Chapter 8, Problem 10QP

a)

Summary Introduction

To calculate: The IRR (Internal Rate of Return) for the proposed projects of Company R, the project that the company must accept and discuss whether the decision taken is appropriate.

Introduction:

The IRR (Internal Rate of Return) is a rate of discount which makes the predictable investment’s NPV equal to zero.

The NPV (Net Present Value) is a capital budgeting technique which is used to assess the investment that, in turn, is utilized to identify the profitability in a proposed investment.

Answer to Problem 10QP

As IRR is higher in Project A when compared to that of Project B, Project A can be accepted. However, it is not the appropriate decision because the criterion of IRR has a problem in ranking mutually exclusive projects.

Explanation of Solution

Given information:

Company R has identified two mutually exclusive projects where the cash flows of Project A are$34,000, $27,000, $21,000, and $17,000 for years 1, 2, 3, and 4 respectively. The cash flows of Project B are $19,000, $25,000, $29,000, and $34,000 for years1, 2, 3, and 4 respectively. The initial costs of both the projects are -$65,000 respectively.

Note:

• NPV is the difference between the present values of the cash inflows and the present value of cash outflows.
• The IRR is the rate of interest which makes the project’s NPV equal to zero. Hence, using the available information, assume that NPV is equal to zero and form an equation to compute the IRR.

Equation of NPV to compute IRR assuming that NPV is equal to zero:

$\begin{array}{l}\text{NPV}=0=-\$65000+\frac{\$34,000}{\left(1+\text{IRR}\right)}+\frac{\$27,000}{{\left(1+\text{IRR}\right)}^2}+\frac{\$21,000}{{\left(1+\text{IRR}\right)}^3}+\frac{\$17,000}{{\left(1+\text{IRR}\right)}^4}\\ 0=-\$65,000+\frac{\$34,000}{\left(1+\text{IRR}\right)}+\frac{\$27,000}{{\left(1+\text{IRR}\right)}^2}+\frac{\$21,000}{{\left(1+\text{IRR}\right)}^3}+\frac{\$17,000}{{\left(1+\text{IRR}\right)}^4}\end{array}$

Compute IRR for Project A using a spreadsheet:

Step 1:

• Type the equation of NPV in H6 in the spreadsheet and consider the IRR value as H7

Step 2:

• Assume the IRR value as 10%

Step 3:

• In the spreadsheet, go to data and select What-If-Analysis.
• In What-If-Analysis, select goal seek.
• In set cell, select H6 (the formula).
• The “To value” is considered as 0 (the assumption value for NPV).
• The H7 cell is selected for "by changing cell".

Step 4:

• Following the previous step, click OK in the goal seek. The goal seek status appears with the IRR value.

Step 5:

• The value appears to be 22.2341361533847%.

Hence, the IRR value is 22.23%.

Compute IRR for Project B using a spreadsheet:

Step 1:

• Type the equation of NPV in H6 in the spreadsheet and consider the IRR value as H7.

Step 2:

• Assume the IRR value as 10%.

Step 3:

• In the spreadsheet, go to data and select What-If-Analysis.
• In What-If-Analysis, select goal seek.
• In set cell, select H6 (the formula).
• The “To value” is considered as 0 (the assumption value for NPV).
• The H7 cell is selected for "by changing cell".

Step 4:

• Following the previous step click OK in the goal seek. The goal seek status appears with the IRR value,

Step 5:

• The value appears to be 21.0065648408326%.

Hence, the IRR value is 21%.

b)

Summary Introduction

To calculate: The NPV to choose the best project for the company.

Introduction:

The IRR (Internal Rate of Return) is a rate of discount which makes the predictable investment’s NPV equal to zero.

The NPV (Net Present Value) is a capital budgeting technique which is used to assess the investment that, in turn, is utilized to identify the profitability in a proposed investment.

Answer to Problem 10QP

As NPV is greater in Project B, the company must accept Project B.

Explanation of Solution

Given information:

Company R has identified two mutually exclusive projects where the cash flows of Project A are$34,000, $27,000, $21,000, and $17,000 for years 1, 2, 3, and 4 respectively. The cash flows of Project B are $19,000, $25,000, $29,000, and $34,000 for years1, 2, 3, and 4 respectively. The initial costs of both the projects are -$65,000 respectively.

Note:

• NPV is the difference between the present values of the cash inflows andthe present value of cash outflows.
• The IRR is the rate of interest which makes the project’s NPV equal to zero. Hence, using the available information, assume that NPV is equal to zero and form an equation to compute the IRR.

Formula to calculate the NPV:

$\text{NPV}=\text{Present value of cash inflow}-\text{Present value of cash outflow}$

Compute NPV for Project A:

$\begin{array}{c}\text{NPV at 11\%}=\frac{\$34,000}{\left(1+0.11\right)}+\frac{\$27,000}{{\left(1+0.11\right)}^2}+\frac{\$21,000}{{\left(1+0.11\right)}^3}+\frac{\$17,000}{{\left(1+0.11\right)}^4}-\$65,000\\ =\frac{\$34,000}{1.11}+\frac{\$27,000}{1.2321}+\frac{\$21,000}{1.367631}+\frac{\$17,000}{1.51807041}-\$65,000\\ =\left(\begin{array}{l}\$30,630.63063+\$21,913.8057+\$15,355.01901+\\ \$11,198.42656-\$65,000\end{array}\right)\\ =\$14,097.88\end{array}$

Hence, the NPV for Project A is $14,097.88.

Compute NPV for Project B:

$\begin{array}{c}\text{NPV at 11\%}=\frac{\$19,000}{\left(1+0.11\right)}+\frac{\$25,000}{{\left(1+0.11\right)}^2}+\frac{\$29,000}{{\left(1+0.11\right)}^3}+\frac{\$34,000}{{\left(1+0.11\right)}^4}-\$65,000\\ =\frac{\$19,000}{1.11}+\frac{\$25,000}{1.2321}+\frac{\$29,000}{1.367631}+\frac{\$34,000}{1.51807041}-\$65,000\\ =\left(\begin{array}{l}\$17,117.11712+\$20,290.56083+\$21,204.55006+\\ \$22,396.85312-\$65,000\end{array}\right)\\ =\$16,009.08113\end{array}$

Note: The rate is given at 11%.

Hence, the NPV for project B is $16,009.08.

c)

Summary Introduction

To calculate: The rates of discount at which the company will select Project A and Project B and the discount rate in which the company will be indifferent in selecting between the two projects.

Introduction:

The IRR (Internal Rate of Return) is a rate of discount which makes the predictable investment’s NPV equal to zero.

The NPV (Net Present Value) is a capital budgeting technique which is used to assess the investment that, in turn, is utilized to identify the profitability in a proposed investment.

Answer to Problem 10QP

At the rate of discount above 16.30%, the company must choose Project A, and for the rate below 16.30%, the company should choose Project B. Hence, it is indifferent at the discount rate of 16.30%.

Explanation of Solution

Given information:

Company R has identified two mutually exclusive projects where the cash flows of Project A are$34,000, $27,000, $21,000, and $17,000 for years 1, 2, 3, and 4 respectively. The cash flows of Project B are $19,000, $25,000, $29,000, and $34,000 for years1, 2, 3, and 4 respectively. The initial costs of both the projects are -$65,000 respectively.

Note:

• NPV is the difference between the present values of the cash inflows and the present value of cash outflows.
• The IRR is the rate of interest which makes the project’s NPV equal to zero. Hence, using the available information, assume that NPV is equal to zero and form an equation to compute the IRR.

Equation to calculate the crossover rates:

$0=\frac{\$15,000}{\left(1+R\right)}+\frac{\$2,000}{{\left(1+R\right)}^2}-\frac{-\$8000}{{\left(1+R\right)}^3}-\frac{-\$17000}{{\left(1+R\right)}^4}$

Compute the discount rate using a spreadsheet:

Step 1:

• Type the equation of NPV in H6 in the spreadsheet and consider the R value as H7.

Step 2:

• Assume the R value as 10%.

Step 3:

• In the spreadsheet, go to data and select What-If-Analysis.
• In What-If-Analysis, select goal seek.
• In set cell, select H6 (the formula).
• The “To value” is considered as 0 (the assumption value for NPV).
• The H7 cell is selected for "by changing cell".

Step 4:

• Following the previous step click OK in the goal seek. The goal seek status appears with the R value.

Step 5:

• The value appears to be 16.3057295259374%.

Hence, the R value is 16.31%.