Chapter 7, Problem 7.23P

1

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

To compute: The payback period for both the projects.

Answer to Problem 7.23P

Payback periods for A is 6.53 years and B is 7.03 years

Explanation of Solution

Annual net cash inflow

Particular	Product A	Product B
Sales Revenue	250000	350000
Less: Variable Cost	(120000)	(170000)
Fixed out of pocket and operating cost	(70000)	(50,000)
Annual net cash inflows		130

2

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

To compute: The net present value of each project.

Answer to Problem 7.23P

The net present value for A is ($88,750) and B

Explanation of Solution

Net present value for A:

Years	Net cash inflows (a) $	PV of $1 factor (i=16%) (b)	Present value of net cash inflow a×b=c $
1	26000	0.847	22022
2	26000	0.718	18668
3	26000	0.608	15808
4	26000	0.515	13390
5	26000	0.437	11362
Present value of net cash inflows			81250
Less: initial cost of investment			170000
Net present value			88750

The net present value for the project is ($88,750) and B is ($211,260).

Net present value for B:

Years	Net cash inflows (a) $	PV of $1 factor (i=16%) (b)	Present value of net cash inflow a×b=c $
1	54,000	0.847	45,728
2	54,000	0.718	38,772
3	54,000	0.608	32,832
4	54,000	0.515	27,810
5	54,000	0.437	23,598
Present value of net cash inflows			168,740
Less: initial cost of investment			380,000
Net present value			211,260

The net present value for the project is ($211,260)

3

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

Theinternal rate of return of each project.

Answer to Problem 7.23P

The internal rate of return for A is 11% and B is 13%

Explanation of Solution

Factor of the internet rate of return for A:

  $\begin{array}{l}Factorof\mathrm{int}ernalrateofreturn=\frac{Investmentrequied}{Annualnetcash\inf low}\\ =\frac{\$170,000}{\$26,000}\\ =6.53\end{array}$

According to exhibit 7B-2, the rate of return closest to the factor 6.53 is 11%

Factor of the internet rate of return for B:

  $\begin{array}{l}Factorof\mathrm{int}ernalrateofreturn=\frac{Investmentrequied}{Annualnetcash\inf low}\\ =\frac{\$380,000}{\$54,000}\\ =7.03\end{array}$

According to exhibit 7B-2, the rate of return closest to the factor 7.03 is 13%

4.

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

To compute: The profitability index for both the projects.

Answer to Problem 7.23P

The profitability index for project A is 0.522 and B is 0.55

Explanation of Solution

Net present value for A:

Years	Net cash inflows (a) $	PV of $1 factor (i=16%) (b)	Present value of net cash inflow a×b=c $
1	26000	0.847	22022
2	26000	0.718	18668
3	26000	0.608	15808
4	26000	0.515	13390
5	26000	0.437	11362
Present value of net cash inflows			81250
Less: initial cost of investment			170000
Net present value			88750

Profitability index:

  $\begin{array}{l}\mathrm{Pr}ofitabilityindex=\frac{Netpresentvalueoftheproject}{Investementrequired}\\ =\frac{88750}{170000}\\ =0.522\end{array}$

Net present value for B:

Years	Net cash inflows (a) $	PV of $1 factor (i=16%) (b)	Present value of net cash inflow a×b=c $
1	54,000	0.847	45,728
2	54,000	0.718	38,772
3	54,000	0.608	32,832
4	54,000	0.515	27,810
5	54,000	0.437	23,598
Present value of net cash inflows			168,740
Less: initial cost of investment			380,000
Net present value			211,260

Profitability index:

  $\begin{array}{l}\mathrm{Pr}ofitabilityindex=\frac{Netpresentvalueoftheproject}{Investementrequired}\\ =\frac{211,260}{380,000}\\ =0.55\end{array}$

5

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

Themost preferably ranking methods.

Answer to Problem 7.23P

Net present value is focused only the amount of investment

Explanation of Solution

Net operating income is $400000 and initial investment is $3500000

Simple rate of return A:

  $\begin{array}{l}simplerateofreturn=\frac{Netprofit}{investmentinvestment}\\ =\frac{\$26,000}{\$170,000}\\ =15.29\%\end{array}$

Simple rate of return is 15.29%

Simple rate of return B:

  $\begin{array}{l}simplerateofreturn=\frac{Netprofit}{investmentinvestment}\\ =\frac{\$54,000}{\$380,000}\\ =14.21\%\end{array}$

Simple rate of return for B is 14.21%

6

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

Theproject which L should pursue.

Answer to Problem 7.23P

Both the project should be rejected

Explanation of Solution

The net present value of both the investment is positive and its internal rate of return is 17%. However the calculated simple rate of return of A is $15.29% and B is 14.21% which is less than the expected return on investment of 18%. Therefore both the project will be rejected.