Chapter 13, Problem 12P

COST-BENEFIT ANALYSIS

Listed in the diagram for Problem 7 are some probability estimates of the costs and benefits associated with two competing projects.

1. a. Compute the net present value of each alternative. Round the cost projections to the nearest month.
2. b. Repeat step (a) for the payback method.
3. c. Which method do you think provides the best source of information? Why?

To determine

Calculate the net present value of each alternative.

Explanation of Solution

Net Present Value:

Net present value (NPV) is defined as a method which is used in capital budgeting to compute the profitability of an investment. It can be calculated by subtracting the cash inflow of present value from cash outflow of a period of time.

Given information:

Average time period is 5 year.

Discount rate is 0.14.

Present value of annuity at discount rate of 0.14 and time 5 year is 3.433.

Calculation of Net present value of project A:

The formula to calculate net present value of project A is,

$\text{NPV}=\text{Cashflow}{\left(1+\text{discount}\right)}^{\text{Time}}$ (1)

The table given below represents the annual cash flow of project A:

Probability (A)	Recurring cost (B)	Cash inflow $\left(A\times B\right)$	Probability (C)	Weighted average benefits (D)	Cash outflow $\left(C\times D\right)$	Cash Flow $\left(\begin{array}{l}Cashoutflow\\ -Cashinflow\end{array}\right)$
0.1	$75,000	$7,500	0.3	$220,000	$66,000	$9,000
0.55	$95,000	$52,250	0.5	$233,000	$116,500	$64,250
0.35	105,000	$36,750	0.2	$240,000	$48,000	$11,250
Total		$96,500	Total		$230,500	$84,500

Table (1)

From Table (1), total cash inflow of project A is $84,500.

Substitute $84,500 for Cash flow and ${\left(1+\text{discount}\right)}^{\text{Time}}$ for 3.433 in the above formula.

$\begin{array}{c}\text{NPV}=\text{\$845,00}\times 3.433\\ =\$290,088.50\text{per year}\end{array}$

Hence, net present value of project A is $290,088.50 per year.

Calculation of Net present value of project B:

The formula to calculate net present value of project B is given in equation (1)

The table given below represents the annual cash flow of project B:

Probability (A)	Recurring cost (B)	Cash inflow $\left(A\times B\right)$	Probability (C)	Weighted average benefits (D)	Cash outflow $\left(C\times D\right)$	Cash Flow $\left(\begin{array}{l}Cashoutflow\\ -Cashinflow\end{array}\right)$
0.4	$85,000	$34,000	0.25	$215,000	$53,750	$1,750
0.4	$100,000	$40,000	0.5	$225,000	$112,500	$72,500
0.2	$110,000	$22,000	0.25	$235,000	$58,750	$36,750
Total		$96,000	Total		$225,000	$111,000

Table (2)

From Table (2), total cash inflow of project B is $111,000.

Substitute $111,000 for Cash flow and ${\left(1+\text{discount}\right)}^{\text{Time}}$ for 3.433 in the formula given in equation (1).

$\begin{array}{c}\text{NPV}=\text{\$111,000}\times 3.433\\ =\$381,063\end{array}$

Hence, net present value of project B is $381,063.

To determine

Compute payback method of each alternative.

Explanation of Solution

Payback Method:

Payback method is defined as the method of capital budgeting which is used to measure the length of time required to recover the cost of investment in a project.

Calculation of period using payback method of project A:

The formula to calculate payback period of project A is,

$\text{Payback period}=\frac{\text{Initial investement}}{\text{Annual cashflow}}$ (2)

The table given below represents total initial investment of project A:

Probability factor	One-time cost	Initial investment
0.35	$200,000	$70,000
0.4	$250,000	$100,000
0.25	$300,000	$75,000
Total		$245,000

Table (3)

From Table (3), total initial investment of project A is $245,000.

Substitute $245,000 for initial investment and $84,500 Cash flow in the above formula.

$\begin{array}{c}\text{Payback period}=\frac{\$245,000}{\$84,500}\\ =2.89\approx 3\text{year}\end{array}$

Hence, the payback period of project A is 3 year.

Calculation of period using payback method of project B:

The formula to calculate payback period of project B is given in equation (2).

The table given below represents total initial investment of project B:

Probability factor	One-time cost	Initial investment
0.2	$210,000	$42,000
0.55	$250,000	$137,500
0.25	$260,000	$65,000
Total		$244,500

Table (4)

From Table (4), total initial investment of project B is $244,500.

Substitute $244,500 for initial investment and $111,000 Cash flow in the above formula.

$\begin{array}{c}\text{Payback period}=\frac{\$244,500}{\$111,000}\\ =2.20\approx 2\text{year}\end{array}$

Hence, the payback period of project B is 2 year.

To determine

Explain which method net present value method or payback period method provides better information of investment.

Explanation of Solution

Net Present Value:

Net present value (NPV) is defined as a method which is used in capital budgeting to compute the profitability of an investment. It can be calculated by subtracting the cash inflow of present value from cash outflow of a period of time.

Net present value provides the information about the profitability of investment. On the other hand, payback period method gives the information about time required to recover the cost of investment.

Therefore, to analyse the budgeting of an investment both the methods are equally important.