Question

Briarcliff Stove Company is considering a new product line to supplement its range line. It is anticipated that the new product line will involve cash investment of $700,000 at time 0 and $1.0 million in year 1. After tax cash inflows of $250,000 are expected in year 2, $300,000 in year 3, $350,000 in year 4, and $400,000 each year thereafter through year 6. Though the product line might be viable after year 6, the company prefers to be conservative and end all calculations at that time.

a) If the required rate of return is 15 percent, what is the net present value of the project? Is it acceptable?

b) Calculate Accounting Rate of Return

c) What is the project’s payback period?

d) What is the project’s profitability index?

e) What would be the case if the required rate of return was 10 percent?

 

Answer 1

Qa)

An excel sheet is used here to calculate the PV.

Steps:

1. All the investments are entered in in first row.

2. All the cash flows are entered in the in the next row for all the years. Since the values given in the question are after tax cash inflows, it is assumed that the depreciation is already deducted while calculating these cash inflows.

3. The net cash inflow in all the years is calculated in the next row. It is the value obtained by subtracting the investment in each year from the after tax cash inflows.

4. The assumed Resale value / Scrap value of the investments made, at the end of year 6 is nil.

5.   The NPV formula available in excel is used to calculate NPV by using 15% RR. .Here it goes.

Year	0	1	2	3	4	5	6
investment	700000	1000000	0	0	0	0	0
After tax cash inflow			250000	300000	350000	400000	400000
NET CASH INFLOW	-700000	-1000000	250000	300000	350000	400000	400000
NPV	($531,616.58)
Since the NPV of the investment is negative, it is not acceptable.

Q b)

Accounting rate of return (also known as simple rate of return) is the ratio of estimated accounting profit of a project to the average investment made in the project. ARR is used in investment appraisal.

Formula

Accounting Rate of Return is calculated using the following formula:

ARR =	Average Accounting Profit
	Average Investment

Average accounting profit is the arithmetic mean of accounting income expected to be earned during each year of the project's life time. Average investment may be calculated as the sum of the beginning and ending book value of the project divided by 2. Another variation of ARR formula uses initial investment instead of average investment.

Solution
Initial investment                     = (70000+1000000) = 1700000

Total Accounting Income              = 250000 + 300000 +350000 + 400000 + 400000

                                                       = 1700000

Average Accounting Income = 1700000 = 242857

                                                       7

                                                      
Accounting Rate of Return = 242857 ÷ $1700000 ≈ 14.28 %

Decision Rule

Accept the project only if its ARR is equal to or greater than the required accounting rate of return. Since the ARR of 14.28% is less than the required RR of 15%, this investment is not acceptable.

Q c)

Payback Period

Payback period is the time in which the initial cash outflow of an investment is expected to be recovered from the cash inflows generated by the investment.

Formula

The formula to calculate payback period of a project depends on whether the cash flow per period from the project is even or uneven. In case they are even, the formula to calculate payback period is:

Payback Period =	Initial Investment
	Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:

Payback Period = A +	B
	C

                             
In the above formula,
A is the last period with a negative cumulative cash flow;
B is the absolute value of cumulative cash flow at the end of the period A;
C is the total cash flow during the period after A

     The problem here is a case of uneven cash flows. So the cumulative cashflow is calculated as given below:

    

Payback Period
= 4 + (|-170000| ÷ 400000)
= 4 + (170000 ÷ 400000)
≈ 4 + 0.425
≈ 4.425 years

Q d)

Profitability index is an investment appraisal technique calculated by dividing the present value of future cash flows of a project by the initial investment required for the project.

Formula:

Profitability Index
=	Present Value of Future Cash Flows
	Initial Investment Required
=	1 +	Net Present Value
		Initial Investment Required

Explanation:                                     

Profitability index is actually a modification of the net present value method. While present value is an absolute measure (i.e. it gives as the total dollar figure for a project), the profibality index is a relative measure (i.e. it gives as the figure as a ratio).

Decision Rule

Accept a project if the profitability index is greater than 1, stay indifferent if the profitability index is zero and don't accept a project if the profitability index is below 1.

In this given problem,

Profitability Index = PV of Future Net Cash Flows / Initial Investment Required
Profitability Index = 531617 / 1700000 = 0.31

Since Profitability index is less than 1, this project cannot be accepted.

Q e)

The same method shown in Q a) above is used, except that RR is taken as 10%.

Year	0	1	2	3	4	5	6
investment	700000	1000000	0	0	0	0	0
After tax cash inflows			250000	300000	350000	400000	400000
NET CASH INFLOW	-700000	-1000000	250000	300000	350000	400000	400000
NPV	($421,701.90)
Since the NPV of the investment is negative, it is not acceptable.