Chapter 11, Problem 12E

To determine

(a)

Introduction:

Payback period is the time period required to cover the cost of an investment or it is the duration of time needed to recover the initial cost of an investment.

To compute:

The payback period of the given investments and rank them in order of their payback period.

Answer to Problem 12E

Payback period (project X) = 1.6 years (Rank 1)

Payback period (Project Y) = 2 years (Rank 3)

Payback period (Project Z) = 1.9 years (Rank 2)

Explanation of Solution

To calculate the payback period:

Formula used:

$Paybackperiod=\frac{Inititalinvestment}{Annualcashflows}$

$\begin{array}{l}Paybackperiod\text{(Project}\text{X)}=\frac{\$40,000}{\$25,000}\\ =1.6years\end{array}$

$\begin{array}{l}Paybackperiod\text{(Project}Y\text{)}=\frac{\$20,000}{\$10,000}\\ =2years\end{array}$

$\begin{array}{l}Paybackperiod\text{(Project}Z\text{)}=\frac{\$50,000}{\$25,400}\\ =1.9years\end{array}$

To determine

(b)

Introduction:

Net present value is calculated as the difference between present cash inflows and present cash outflows. A positive value of NPV states that the investment is profitable and negative value of NPV states that the investment will result in a loss.

To compute:

The net present value of the given investments and rank them in order of their Net present value.

Answer to Problem 12E

Net present value (Project X) = $5,000 (Rank 3)

Net present value (Project Y) = $13,000 (Rank 2)

Net present value (Project Z) = $20,000 (Rank 1)

Explanation of Solution

To calculate NPV:

Formula used:

Net present value = PV of cash inflows − Initial investment

Net present value (Project X) = $45,000 - $40,000

= $5,000

Net present value (Project Y) = $33,000 - $20,000

= $13,000

Net present value (Project Z) = $70,000 - $50,000

= $20,000

To determine

(c)

Introduction:

Profitability index is the ratio of the benefits of a project to its costs. There is a directly proportional relationship between profitability index and the attractiveness of a project.

To compute:

The Profitability index of the given investments and rank them in order of their Net present value.

Answer to Problem 12E

Profitability Index

1. Project X = 1.12 (Rank 3)
2. Project Y = 1.65 (Rank 1)
3. Project Z = 1.40 (Rank 2)

Explanation of Solution

Formula used to calculate profitability index:

$\text{Profitability}\text{index=}\frac{\text{Present}\text{}\text{value}\text{of}\text{cash}\text{inflows}}{InitialInvestment}$

Projects	Profitability index
Project X	$=\frac{\$45,000}{\$40,000}$ = 1.12
Project Y	$=\frac{\$33,000}{\$20,000}$ = 1.65
Project Z	$=\frac{\$70,000}{\$50,000}$ = 1.40

To determine

(d)

Introduction:

Profitability index is the ratio of the benefits of a project to its costs. There is a directly proportional relationship between profitability index and the attractiveness of a project.

To state:

In case of limited availability of funds, which investment should be opted by the manager.

Answer to Problem 12E

As per the profitability index, investment in project Y should be opted by the manager.

Explanation of Solution

In case of limited availability of funds, it will be better for the company to prioritize the projects depending upon their profitability index. The profitability index will make the comparison a lot easier as it is expressed as a ratio and not as the dollar value.