Chapter 12, Problem 37E

1.

To determine

Find out the payback period for the new equipment for each of KD’s projects. Recommend the project to be chosen if rapid payback is important. Also, recommend the project should be chosen.

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Calculate payback period for Project A:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,0001	10,000	0.60
	0		2.60

Table (1)

Therefore, payback period is 2.60 years.

Calculate payback period for Project B:

Year	Unrecovered investment($) (Beginning of year)	Annual cash Flow($)	Time needed for payback (Years)
1	20,000	6,000	1.0
2	14,000	8,000	1.0
3	6,0001	10,000	0.60
	0		2.60

Table (2)

Therefore, payback period is 2.60 years.

As both the projects have same payback period, the profitable project must be chosen. The cash flow from project B beyond the payback period is lesser than that of project A. Therefore, project A should be chosen because it is more profitable.

Working Note:

1. Calculation of payback period for third year:

$\begin{array}{c}Paybackperiod=\frac{Unrecovered\mathrm{investment}}{Annualcashflow}\\ =\frac{\$6,000}{\$10,000}\\ =0.60\end{array}$

2.

To determine

Find out the project to be chosen on the basis of accounting rate of return (ARR). Also, explain the reason for better performance of ARR in this setting than payback period.

Explanation of Solution

Accounting Rate of Return:

A method that measures returns from an investment in terms of income instead of cash flow is known as accounting rate of return. It is a non-discounting model of capital investment decision.

Use the following formula to calculate accounting rate of return (ARR) for project A:

$ARR=\frac{Averageincome}{Initialinvestment}$

Substitute $4,800¹ for average income and $20,000 for initial investment in the above formula.

$\begin{array}{c}ARR=\frac{\$4,800}{\$20,000}\\ =24\%\end{array}$

Therefore, accounting rate of return is 24%.

Use the following formula to calculate accounting rate of return (ARR) for project A:

$ARR=\frac{Averageincome}{Initialinvestment}$

Substitute $2,000² for average income and $20,000 for initial investment in the above formula.

$\begin{array}{c}ARR=\frac{\$2,000}{\$20,000}\\ =10\%\end{array}$

Therefore, accounting rate of return is 10%.

ARR considers the cash inflow from a project beyond its payback period which is not the case in the payback period. Therefore, ARR performs better than the payback period in this case.

Working Note:

1. Calculation of average cash inflow:

$\begin{array}{c}Averagecashinflow=\frac{Totalcashinflow}{Numberofyears}\\ =\frac{\left(\begin{array}{l}\$6,000+\$8,000+\$10,000\\ +\$10,000+\$10,000\end{array}\right)}{5}\\ =\frac{\$44,000}{5}\\ =\$8,800\end{array}$

Calculation of depreciation:

$\begin{array}{c}Depreciation=\frac{Cost-Salvagevalue}{Usefullife}\\ =\frac{\$20,000-0}{5}\\ =\$4,000\end{array}$

Calculation of average income:

$\begin{array}{c}Averageincome=Average\text{}cashinflow-Depreciation\\ =\$8,800-\$4,000\\ =\$4,800\end{array}$

2. Calculation of average cash inflow:

$\begin{array}{c}Averagecashinflow=\frac{Totalcashinflow}{Numberofyears}\\ =\frac{\left(\$6,000+\$8,000+\$10,000+\$3,000+\$3,000\right)}{5}\\ =\frac{\$30,000}{5}\\ =\$6,000\end{array}$

Calculation of depreciation:

$\begin{array}{c}Depreciation=\frac{Cost-Salvagevalue}{Usefullife}\\ =\frac{\$20,000-0}{5}\\ =\$4,000\end{array}$

Calculation of average income:

$\begin{array}{c}Averageincome=Average\text{}cashinflow-Depreciation\\ =\$6,000-\$4,000\\ =\$2,000\end{array}$

3.

To determine

Calculate present value of the annuity to recommend that Person WG should accept the lump sum amount or annuity.

Explanation of Solution

Calculate present value of a future annuity:

Use the following formula to calculate present value of a future annuity;

$\mathrm{Present}value=Annuityvalue\times Discountfactor$

Substitute $30,000 for annuity value and 11.46992 for discount factor in the above formula.

$\begin{array}{c}\mathrm{Present}value=\$30,000\times 11.46992\\ =\$344,098\end{array}$

Therefore, the present value of the annuity is $344,098.

The present value of the future annuity is lesser than the lump sum amount. Therefore, Person WG should accept the lump sum amount.

4.

To determine

Find out the NPV of the investment if the RRR is 8%. Also, recommend that Person D should invest or not.

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Use the following formula to calculate NPV of the investment:

$NPV=Presentvalueofcashinflow\left(P\right)-Presentvalueofcashoutflow\left(I\right)$

Substitute $41,606³ for P and $30,000 for I in the above formula.

$\begin{array}{c}NPV=\$41,606-\$30,000\\ =\$11,606\end{array}$

Therefore, net present value of the investment is $11,606.

Person D should make the investment because NPV of the investment is positive.

Working Note:

3. Calculation of present value of future cash flow:

$\begin{array}{c}Presentvalue\text{}offuturecashflow=Futurevalue\times Discountfactor\\ =\$9,000\times 4.62288\\ =\$41,606\end{array}$

5.

To determine

Find out the IRR for Person PF’s project. Also recommend that Person PF should acquire the equipment or not.

Explanation of Solution

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is zero in case of an internal rate of return.

Use the following formula to calculate discount factor:

$Discountfactor=\frac{Investment}{Annualcashflow}$

Substitute $400,000 for investment and $75,000 for annual cash flow in the above formula.

$\begin{array}{c}Discountfactor=\frac{\$40,000}{\$75,000}\\ =5.33333\end{array}$

Therefore, discount factor for Model CX is 5.33333.

The IRR is approximately 13% which is more than Person PF’s cost of capital. Therefore, Person PF should acquire the equipment.