Question

Howard Company operates a chain of sandwich shops. The company is considering two possible expansion plans. Plan A would open eight smaller shops at a cost of \(8,500,000. Expected annual net cash inflows are \)1,600,000 for 10 years, with zero residual value at the end of 10 years. Under Plan B, Howard Company would open three larger shops at a cost of \(8,100,000. This plan is expected to generate net cash inflows of \)1,000,000 per year for 10 years, which is the estimated useful life of the properties. Estimated residual value for Plan B is $990,000. Howard Company uses straight-line depreciation and requires an annual return of 6%.

Requirements

1. Compute the payback, the ARR, the NPV, and the profitability index of these two plans.

2. What are the strengths and weaknesses of these capital budgeting methods?

3. Which expansion plan should Howard Company choose? Why?

4. Estimate Plan A’s IRR. How does the IRR compare with the company’s required rate of return?

Short answer

1. Capital budgeting methods:

	Plan A	Plan B
Payback	5.31 years	8.18 years
ARR	8.82%	3.56%
NPV	$3,276,000	($187,580)
Profitability index	1.39	0.97

2. Payback period and ARR are simple and easy but they do not consider the time value of money. NPV and profitability index considers the time value of money but sometimes ARR does not reflect accurate figures and also NPV cannot be used in certain situations.

3. The business entity must select Plan A.

4. IRR of plan A is 13.53%.

Step-by-step solution

Definition of Payback Period

A capital budgeting metric that determines the time period in which the investment will give back the cash invested or the investment/cash recovery period is known as the payback period.

Calculation of payback, ARR, NPV and profitability index

Calculation of payback period:

Plan	Initial investment	/	Expected net annual cash inflows	=	Payback period
A	$8,500,000	/	$1,600,000	=	5.31 years
B	$8,100,000	/	$990,000	=	8.18 years

Calculation of ARR:

Plan A:

$\begin{array}{c}\mathrm{ARR}=\frac{\mathrm{Average}\mathrm{annual}\mathrm{revenue}}{\mathrm{Initial}\mathrm{investment}}\times 100\\ =\frac{\mathrm{\$}750,000}{\mathrm{\$}8,500,000}\times 100\\ =8.82\mathrm{\%}\end{array}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	$16,000,000
Less: Total depreciation during the life of the asset	8,500,000
Total operating income during the operating life	7,500,000
Asset operating life in years	10
Average annual operating income ($7,500,000 / 10)	$750,000

Plan B:

role="math" localid="1656755103521" $\begin{array}{c}\mathrm{ARR}=\frac{\mathrm{Average}\mathrm{annual}\mathrm{revenue}}{\mathrm{Initial}\mathrm{investment}}\times 100\\ =\frac{\mathrm{\$}289,000}{\mathrm{\$}8,100,000}\times 100\\ =3.56\mathrm{\%}\end{array}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	10,000,000
Less: Total depreciation during the life of the asset ($8,100,000-$990,000)	7,110,000
Total operating income during the operating life	2,890,000
Asset operating life in years	10
Average annual operating income ($2,890,000 /10)	$289,000

Calculation of NPV:

Plan A:

Time	Particular	Net cash inflow	Ordinary annuity PV factor	PV factor	Present value
1-10 years	PV of annuity	$1,600,000	7.36	-	$11,776,000
10 years	Residual value	$0	-		0
Total PV of net cash flow					$11,776,000
0	Initial investment				(8,500,000)
Net present value of the Plan					$3,276,000

Plan B:

Time	Particular	Net cash inflow	Ordinary annuity PV factor	PV factor	Present value
1-10 years	PV of annuity	$1,000,000	7.36	-	$7,360,000
10 years	Residual value	$990,000	0.558		552,420
Total PV of net cash flow					$7,912,420
0	Initial investment				(8,100,000)
Net present value of the Plan					($187,580)

Calculation of profitability index:

Plan A:

$\begin{array}{c}\mathrm{Profitability}\mathrm{index}=\frac{\mathrm{Total}\mathrm{present}\mathrm{value}\mathrm{of}\mathrm{net}\mathrm{cashflows}}{\mathrm{Initial}\mathrm{investment}}\\ =\frac{\mathrm{\$}11,776,000}{\mathrm{\$}8,500,000}\\ =1.39\end{array}$

Plan B:

$\begin{array}{c}\mathrm{Profitability}\mathrm{index}=\frac{\mathrm{Total}\mathrm{present}\mathrm{value}\mathrm{of}\mathrm{net}\mathrm{cashflows}}{\mathrm{Initial}\mathrm{investment}}\\ =\frac{\mathrm{\$}7,912,420}{\mathrm{\$}8,100,000}\\ =0.97\end{array}$

Strength and weakness of capital budgeting

Method	Strength	Weakness
Payback	It is a simple method and determines the risk of the investments that will require a longer time to recover the cash.	It does not consider the time value of the money and cash flows occurring after the payback period.
ARR	It uses the figures of accrual accounting and measures the Plan's profitability over its useful life.	It also does not consider the time value of money.
NPV	It considers the time value of money and cash flow from the Plan over its useful life. It also determines the return that the company requires.	It is not helpful when different initial investments are required for various assets.
Profitability index	It also considers money’s time value and net cash flows during the Plan’s life. It also calculates the unique rate of return and does not require any additional steps.	It cannot be determined accurately without using the business calculator and software.

Appropriate expansion plan

Plan A will be appropriate because the net present value of this plan is positive and the profitability index of this plan is above 1.

IRR of plan A

$\begin{array}{c}\mathrm{NPV}=\sum _{\mathrm{t}=0}^{}\frac{{\mathrm{C}}_{\mathrm{t}}}{{\left(1+\mathrm{IRR}\right)}^{\mathrm{t}}}\\ 0=\left(\begin{array}{l}\frac{-\mathrm{\$}8,500,000}{{\left(1+\mathrm{IRR}\right)}^0}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^1}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^2}+\\ \frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^3}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^4}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^5}+\\ \frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^7}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^6}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^7}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^8}+\\ \frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^9}+\frac{\mathrm{\$}1,600,000}{{\left(1+\mathrm{IRR}\right)}^{10}}\end{array}\right)\\ \mathrm{IRR}=13.53\mathrm{\%}\end{array}$

IRR is 13.53% which is more than the required rate of return i.e., 6%. Therefore, the business entity must select Plan A.