Chapter 26, Problem 3MAD

a.

To determine

Compute the net present value of the equipment.

Explanation of Solution

Net present value method:

Net present value method is used to compare the initial cash outflow of the investment with the present value of its cash inflows. In the net present value, the interest rate is determined by the business based on the net income received from the investment. This is also called as the discounted cash flow method.

Calculate the net present value of the equipment:

Particulars	Amount ($)
Present value of annual net cash flows (1)	$4,520,000
Present value of residual value (2)	$64,400
Total present value	$4,584,400
Amount to be invested	($3,000,000)
Net present value	$1,584,400

Table (1)

Hence, the net present value of the equipment is $1,584,400.

Working Note 1:

Calculate the present value of annual net cash flows:

$\begin{array}{c}\begin{array}{l}\text{Present}\text{value}\text{of}\\ \text{annual net cash}\text{flows}\end{array}\}\text{=}\text{Annual net cash}\text{flows}\times 5.650\\ \text{=\$800,000}\times 5.650\\ \text{=\$4,520,000}\end{array}$

Working Note 2:

Calculate the present value of annual net cash flows:

$\begin{array}{c}\begin{array}{l}\text{Present}\text{value}\text{of}\\ \text{Residual value}\end{array}\}\text{=}\text{Residual value}\times \text{0}\text{.322}\\ \text{=\$200,000}\times \text{0}\text{.322}\\ \text{=\$64,400}\end{array}$

b.

To determine

Compute the net present value of the equipment, assuming 12% desired rate of return for the given annual net cash flows.

Explanation of Solution

Calculate the net present value of the equipment:

Estimated Annual Net Cash Flow
Particulars	Amount ($)	Amount ($)	Amount ($)
Estimated annual net cash flows	$400,000	$600,000	$800,000
Multiply: Present value factor from Exhibit 5	$(\times )$5.650	$(\times )$5.650	$(\times )$5.650
Present value of annual net cash flows	$2,260,000	$3,390,000	$4,520,000
Present value of residual value (2)	$64,400	$64,400	$64,400
Total present value	$2,324,400	$3,454,400	$4,584,400
Amount to be invested	($3,000,000)	($3,000,000)	($3,000,000)
Net present value	($675,600)	$454,400	$1,584,400

Table (2)

Hence, the net present value of the equipment for annual net cash flow of $400,000 is ($675,600), for annual net cash flow of $600,000 is $454,400 and for annual net cash flow of $800,000 is $1,584,400.

c.

To determine

Compute the net present value of the equipment, assuming 15% desired rate of return for the given annual net cash flows.

Explanation of Solution

Calculate the net present value of the equipment:

Estimated Annual Net Cash Flow
Particulars	Amount ($)	Amount ($)	Amount ($)
Estimated annual net cash flows	$400,000	$600,000	$800,000
Multiply: Present value factor from Exhibit 5	$(\times )$5.019	$(\times )$5.019	$(\times )$5.019
Present value of annual net cash flows	$2,007,600	$3,011,400	$4,015,200
Present value of residual value (3)	$49,400	$49,400	$49,400
Total present value	$2,057,000	$3,060,800	$4,064,600
Amount to be invested	($3,000,000)	($3,000,000)	($3,000,000)
Net present value	($943,000)	$60,800	$1,064,600

Table (3)

Hence, the net present value of the equipment for annual net cash flow of $500,000 is ($811,700), for annual net cash flow of $700,000 is $417,300 and for annual net cash flow of $900,000 is $1,646,300.

Working Note 3:

Calculate the present value of annual net cash flows:

$\begin{array}{c}\begin{array}{l}\text{Present}\text{value}\text{of}\\ \text{Residual value}\end{array}\}\text{=}\text{Residual value}\times \text{0}\text{.247}\\ \text{=\$200,000}\times \text{0}\text{.247}\\ \text{=\$49,400}\end{array}$

d.

To determine

Identify the minimum annual net cash flow required to generate a positive net present value.

Explanation of Solution

Calculate the minimum annual net cash flows:

$\begin{array}{c}\begin{array}{l}\text{Minimum annual }\\ \text{net cash flow}\end{array}\}\text{=}\frac{\text{Initial cost}-\text{ Present value of Residual value}}{\text{Present value factor at 12\%}}\\ \text{=}\frac{\text{\$3,000,000}-\text{\$64,400}}{5.650}\\ \text{=}\frac{\$2,935,600}{6.145}\\ =\$519,575\end{array}$

Hence, the minimum annual net cash flow required to generate a positive net present value is $519,575.

e.

To determine

Interpret the results in parts (a), (b) and (c).

Explanation of Solution

Every business desires to get maximum profit with minimum investment. The net cash flow of $800,000 is generated from the investment which has a present value of $1,584,400. This clearly indicates the management could invest in the equipment. However, when there is a decrease in the annual net cash flows there is also a drastic decrease in the present value of the equipment. The annual net cash flow must be above $519,575 to generate a profit by the company.