Chapter 11, Problem 3E

To determine

(a)

Introduction:

Net present value is calculated as the difference between present cash inflows and present cash outflows. Apositive value of NPV states that the investment is profitable and negative value of NPV states that the investment will result in a loss.

To calculate:

The net present value.

Answer to Problem 3E

Net present value is $730,578.13.

Explanation of Solution

Initial investment = $1,600,000

$\begin{array}{l}\text{Depreciation=}\frac{\text{Initial}\text{investment-salvage}\text{value}}{\text{Expected}\text{life}}\\ \text{=}\frac{\text{\$1,600,000-\$350,000}}{\text{8}}\\ \text{=\$156,250}\end{array}$

Annual net cash flow = net income + depreciation

= $250,000 + $156,250

= $406,250

Present value of cash flows:

$\begin{array}{l}= \left[Annual\text{ cash flows }\times {\text{ PVIFA}}_{10\%,}8periods\right] +\left[Salvage\text{ value of equipment }\times {\text{PVIFA}}_{10\%,}*periods\right]\\ =\left[\left[406,250\times 5.3349\right] +\left[350,000\times 0.4665\right]\right]\\ =\left[\$2,167,303.13\right] +\left[\$163,275\right]\\ =\text{ \$2,330,578}\text{.13}\\ \end{array}$

Net present value = Present value of inflow of cash − Present value of outflow of cash

= $2,330,578.13 - $1,600,000

= $730,578.13

To determine

(b)

Introduction:

Internal rate of return is the interest rate at which NPV of cash flows from an investment is zero. It helps in judging if the investment is profitable or not.

To state:

If the rate of IRR is more or less than 10%.

Explanation of Solution

Net present value is $730,578.13.

Since the Net present value is positive, IRR should be greater than the cost of capital of 10%.

To determine

(c)

Introduction:

Net present value is calculated as the difference between present cash inflows and present cash outflows. A positive value of NPV states that the investment is profitable and negative value of NPV states that the investment will result in a loss.

To calculate:

The net present value using 20% discount rate.

Answer to Problem 3E

Net present value is $40,272.5.

Explanation of Solution

Initial investment = $1,600,000

$\begin{array}{l}\text{Depreciation=}\frac{\text{Initial}\text{investment-salvage}\text{value}}{\text{Expected}\text{life}}\\ \text{=}\frac{\text{\$1,600,000-\$350,000}}{\text{8}}\\ \text{=\$156,250}\end{array}$

Annual net cash flow = net income + depreciation

= $250,000 + $156,250

= $406,250

Present value of cash flows:

$\begin{array}{l}= \left[Annual\text{ cash flows }\times {\text{ PVIFA}}_{20\%,}8periods\right] +\left[Salvage\text{ value of equipment }\times {\text{PVIFA}}_{20\%,}*periods\right]\\ =\left[\left[406,250\times 3.8372\right] +\left[350,000\times 0.2326\right]\right]\\ =\left[\$1,558,862.5\right] +\left[\$81,410\right]\\ =\text{ \$1,640,272}\text{.5}\\ \end{array}$

Net present value = Present value of inflow of cash − Present value of outflow of cash

= $1,640,272.5 - $1,600,000

= $40,272.5

To determine

(d)

Introduction:

Internal rate of return is the interest rate at which NPV of cash flows from an investment is zero. It helps in judging if the investment is profitable or not.

To estimate:

The IRR of the project.

Answer to Problem 3E

IRR is 19.13%.

Explanation of Solution

Year	Annual cash flow
0	($1,600,000)
1	$406,250
2	$406,250
3	$406,250
4	$406,250
5	$406,250
6	$406,250
7	$406,250
8	$406,250
IRR	19.13%

Formula used (in excel) = IRR [All the values of annual cash flow]