Question

1. A capital investment of$10,000 can be made in a project that will produce uniform revenue of $5320 for five years and then have an estimated salvage value of $2,000. Annual expenses will be $3,000. The company is willing to accept any project that will earn at least 10% per year (including inflation), before income tax. Determine whether it is acceptable?

a. What is the IRR for this investment?

b. What is the benefit-cost ratio for this investment?

c. What is the Pay-Back Period for this investment?

2. A piece of equipment has been proposed to increase the productivity of a certain manual welding operation. The investment costs $25,000, and the equipment will have a salvage value of $5,000 at the end of its expected life of years. Increase productivity attribute to the equipment will amount to $8,000 per year increased gross income. Evaluate the IRR of the proposed equipment. If the MARR is 17, is the investment a good one?

Answer 1

1.

Investment = $10,000

Annual Revenue = $5320

Life = 5 years

Salvage Value = $2000

Annual Expenses = $3000

Interest rate = 10%

First calculate the net cash flow

Net Cash flow = Annual revenue – Annual expenses

NCF = $5320 – $3000 = $2320

a. What is the IRR for this investment?

Calculating IRR by using trial and error method

Calculating NPW at 10% = -10,000 + 2320 (P/A, 10%, 5) + 2000 (P/F, 10%, 5)

NPW at 10% = -10,000 + 2320 (3.7908) + 2000 (0.6209) = 36.45

As the NPW is positive, increase the rate of return to 11% to get negative NPW

NPW at 11% = -10,000 + 2320 (P/A, 11%, 5) + 2000 (P/F, 11%, 5)

NPW at 11% = -10,000 + 2320 (3.6959) + 2000 (0.5935) = -238.5

Using interpolation

IRR = 10% + [36.45 – 0 ÷ 36.45 – (-238.5)]*1% = 10.14%

Project can be acceptable.

b. What is the benefit-cost ratio for this investment?

Present Worth of Benefits at 10% = 2320 (P/A, 10%, 5) + 2000 (P/F, 10%, 5)

Present Worth of Benefits at 10% = 2320 (3.7908) + 2000 (0.6209) = 10036.45

Benefit cost ratio = Present Worth of benefits / PW of cost

Benefit cost ratio = 10036.45/10000 = 1.0036

c. What is the Pay-Back Period for this investment?

Discounted Payback period

Year	CF	PV Factor	DCF	CCF
0	($10,000)	1	($10,000)	($10,000)
1	$2,320	0.91	$2,109.09	($7,890.91)
2	$2,320	0.83	$1,917.36	($5,973.55)
3	$2,320	0.75	$1,743.05	($4,230.50)
4	$2,320	0.68	$1,584.59	($2,645.91)
5	$4,320	0.62	$2,682.38	$36.47

Payback period = 4+ [-2,645.91 – 0 ÷ -2,645.91 – (36.47)]*1 = 4.99 years

In all the above three methods the project can be acceptable.

2. In the question number two, the life of the investment is missing.