Chapter 5, Problem 17QP

Comparing Investment Criteria The treasurer of Amaro Canned Fruits, Inc., has projected the cash flows of Projects A, B, and C as follows:

Suppose the relevant discount rate is 12 percent per year.

1. a. Compute the profitability index for each of the three projects.
2. b. Compute the NPV for each of the three projects.
3. c. Suppose these three projects are independent. Which project(s) should Amaro accept based on the profitability index rule?
4. d. Suppose these three projects are mutually exclusive. Which project(s) should Amaro accept based on the profitability index rule?
5. e. Suppose Amaro’s budget for these projects is $450,000. The projects are not divisible. Which project(s) should Amaro accept?

Summary Introduction

To determine: The profitability index.

Profitability Index:

Profitability index shows whether a project is worth following or not by dividing net present value cash inflow from initial investment.

Explanation of Solution

Project A

Given,

PV of the entire cash inflow is $278,858.41.

Initial investment is $225,000.

Formula to calculate profitability index:

$\text{Profitability index}=\frac{\text{PV of the entire cash inflow}}{\text{Initial investment}}$

Substitute $278,858.41 for PV of the entire cash inflow and $225,000 for initial investment.

$\begin{array}{c}\text{Profitability index}=\frac{\$278,858.41}{\$225,000}\\ =1.23\end{array}$

The profitability index is 1.23.

For Project B

Given,

PV of the entire cash inflow is $507,015.30.

Initial investment is $450,000.

Formula to calculate profitability index:

$\text{Profitability index}=\frac{\text{PV of the entire cash inflow}}{\text{Initial investment}}$

Substitute $507,015.30for PV of the entire cash inflow and $450,000 for initial investment.

$\begin{array}{c}\text{Profitability index}=\frac{\$507,015.30}{\$450,000}\\ =1.12\end{array}$

The profitability index is 1.12.

For Project C

Given,

PV of the entire cash inflow is $275,206.61.

Initial investment is $225,000.

Formula to calculate profitability index:

$\text{Profitability index}=\frac{\text{PV of the entire cash inflow}}{\text{Initial investment}}$

Substitute $275,206.61 for PV of the entire cash inflow and $225,000 for initial investment.

$\begin{array}{c}\text{Profitability index}=\frac{\$275,206.61}{\$225,000}\\ =1.22\end{array}$

The profitability index is 1.22.

Working notes:

Calculation for present value of Project A,

$\begin{array}{c}PV=PMT\times \left(\frac{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}{\frac{i}{m}}\right)\\ =\$165,000\times \left(\frac{1-{\left(1+\frac{0.12}{1}\right)}^{-2\times 1}}{\frac{0.12}{1}}\right)\\ =\$165,000\times \frac{1-0.7971}{0.12}\\ =\$278,858.41\end{array}$

Calculation for present value of Project B,

$\begin{array}{c}PV=PMT\times \left(\frac{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}{\frac{i}{m}}\right)\\ =\$300,000\times \left(\frac{1-{\left(1+\frac{0.12}{1}\right)}^{-2\times 1}}{\frac{0.12}{1}}\right)\\ =\$300,000\times \frac{1-0.7971}{0.12}\\ =\$507,015.30\end{array}$

Calculation for present value of Project C,

Conclusion

Hence, the profitability index of project A, B and C is 1.23, 1.12 and 1.22 respectively.

Summary Introduction

To determine: The Net present value.

Net Present Value (NPV):

Net present value refers to the present value of all the future cash flow that is adjusted according to the time value of money.

Explanation of Solution

For Project A

Given,

PV of the entire cash inflow is $278,858.41.

Initial investment is $225,000.

Formula to calculate NPV:

$\text{NPV}=\text{PV}\text{of the entire cash flow}-\text{Initial investment}$

Substitute $278,858.41for PV of the entire cash flow and $225,000 for initial investment.

$\begin{array}{c}\text{NPV}=\$278,858.41-\$225,000\\ =\$53,858.41\end{array}$

The NPV of this project is $53,858.41.

For Project B

Given,

PV of the entire cash inflow is $507,015.30.

Initial investment is $450,000.

Formula to calculate NPV:

$\text{NPV}=\text{PV}\text{of the entire cash flow}-\text{Initial investment}$

Substitute $507,015.30 for PV of the entire cash flow and $450,000 for initial investment.

$\begin{array}{c}\text{NPV}=\$507,015.30-\$450,000\\ =\$57,015.3\end{array}$

The NPV of this project is $57,015.3.

For Project C

Given,

PV of the entire cash inflow is $275,206.61.

Initial investment is $225,000.

Formula to calculate NPV:

$\text{NPV}=\text{PV}\text{of the entire cash flow}-\text{Initial investment}$

Substitute$275,206.61 for PV of the entire cash flow and $225,000 for initial investment.

$\begin{array}{c}\text{NPV}=\$275,206.61-\$225,000\\ =\$50,206.61\end{array}$

The NPV of this project is $50,206.61.

Conclusion

Hence, the NPV of project A, B and C is$53,858.41, $57,015.3 and $275,206.61 respectively.

Summary Introduction

To determine: Whether to choose project A or B or C on the basis of profitability index, if these projects are independent.

Answer to Problem 17QP

Solution:

Company AC should choose Project A first then Project C and at last Project B.

Explanation of Solution

Profitability index shows the dollar earned for the par dollar invested and higher the profitability index means higher the money he is earning on his investment. On the basis of this, Company AC should choose Project A first then Project C and at last Project B because the profitability index is highest for Project A and at second for Project C and at last for Project B.

Conclusion

Hence, Company AC should choose Project A first then Project C and at  lastProject B.

Summary Introduction

To determine: Whether to choose project A or B or C on the basis of profitability index, if the projects are mutually exclusive.

Answer to Problem 17QP

Solution:

A should choose Project A.

Explanation of Solution

Profitability index shows the dollar earned for the par dollar invested and higher the profitability index means higher the money he is earning on his investment. On the basis of this, A should choose Project A because project A has the highest profitability index of 1.23.

Conclusion

Hence, Company AC  should choose Project A.

Summary Introduction

To determine: Whether to choose project A or B or C, if total budget is $450,000.

Answer to Problem 17QP

Solution:

Company AC should choose Project A and Project C.

Explanation of Solution

Company AC should choose Project A and C because the total; NPV of Project A and C is $104,065.02 which is far above than the NPV of Project B which is $57,015.3.

Conclusion

Hence, Company AC should choose Project A and Project C.