Think & Done

please send the following question:

suggest suitable project using
a)pay back period
b)NPV of 12%

Hi Nirad

Your question is bit incomplete. You asked me to suggest a suitable project using the payback period and npv of 12%

Payback Period and NPV (Net Present Value) are amongst six Discounted Cash Flow Techniques (DCF) that are used to evaluate capital budgeting proposals.

So if someone asked to you whether a project was suitable by using Payback Period and NPV at the discount rate of 12%, you would need to provide some more information such as the cash flow streams.

For example if the project at hand required an initial investment of Rs. 10,00,000 and we expected cash inflows (or benefits) at the end of next four years in the amount of Rs 5,00,000 Rs 4,00,000 Rs 3,00,000 and Rs 1,00,000. Given that our cost of capital (the discount rate ) is 12%.

With this information at hand you would need to find whether this project will provide us with monetary benefits ( profits) if we invested money in it. To find that we will use Payback Period , NPV, IRR, MIRR, Discounted Payback Period and Profitability Index to judge the benefits or losses.

You can use MS Excel to find these metrics, let me know if you want me to provide you a MS Excel Worksheet

I used WallStreet ROI calculators to find the metrics and they are as follows:

NPV = Rs 42,392
Discounted Payback Period = 3 yrs. 4 mon.
Payback Period = 2 yrs. 5 mon.
Profitability Index = 1.04
IRR = 14.4888%
MIRR = 13.1686%

As we have NPV of Rs 42,392 thus we will make money if we invested in this project.
It will take us 3 years and 4 months to regain the initial investment of Rs 10,00,000
The profitability index of 1.04 suggest that project is a good one ( a profitability index of less than 1 is usually rejected)
The IRR is the investor's required rate of return, since it is (14.4888%) which is greater than our cost of capital or discount rate of 12%, the project should be accepted. A note about IRR vs NPV. At IRR, the NPV is zero, when IRR is less than discount rate NPV is negative and when IRR is greater than discount rate NPV is positive

Conclusion

We should invest money in this project but if we were comparing this project along with others and one of those projects had higher NPV and lower Discounted Payback Period then we should select that project

What is the net present value of an investment that costs $75,000 and has a salvage value of $45,000? The annual profit from the investment is $15,000 each year for 5 years. The cost of capital at the risk level is 12%.

Hi Tamara L

Your solution to NPV problem is provided below

The present value outflow is $75,000 which represents the cost of the investment, which if purchased would be paid today. In terms of cash inflows we have the following:

1. increase in cash flow per year from annual profits = $15,000
less: tax liability from increased net income (calculated below)= (2,700)
increase in cash flow per year from machinery, years 1 to 5= 12,300
2. Salvage value of investment, end of year 5 is 45,000

Calculation of tax liability.

Additional tax payments come from increased profit.
Increased income by annual profits $15,000
Less depreciation expense (calculated below) (6,000)
Additional income before taxes 9,000
Tax payment (30%) (2,700)
Net income 6300
Tax payment = 2,700

Depreciation is calculated using the straight line method which equals (cost - salvage value)/useful life of the asset. Arithmetically, it would equal (75,000 - 45,000)/5 years or $6,000 per year. Depreciation is not a cash flow expense but reduces taxable income. In terms of cash inflows, we have additional cash flows from years 1 to 5 from operations (net of taxes) of 12,300, and 45,000 from the salvage value of the machine at the end of year 5. Our cash outflow is 75,000 (present value) representing the cost of the investment today. The interest rate is 12%.

Taking the Present Value of our cash inflow we have an annuity of 12,300 for 5 years (at the end of each period), and a lump sum payment of 45,000 at the end of year 5.

NPV = 12300 x PVIFA(12%,4 yrs) + (12,300+45,000) x PVIF(12%,5)

PVIFA(i%, n) = [1 - { 1 / (1+i)^n }] / i

PVIF(i%, n) = 1 / (1+i)^n

NPV = 12,300 x 3.037349347 + 57,300 x 0.567426856 - 75,000
NPV = 37,359.40 + 32,513.56 - 75,000
NPV = $69,872.96 - 75,000
NPV = -$5,127.04

Two independent projects, company uses a 13.8% discount rate for such projects. What are the NPV's of the two projects?

Year    Project 1      Project 2
0      -8425,375      -11,368,000
1      3,225,997      2,112,589
2      1,775,882      3,787,552
3      1,375,112      3,125,650
4      1,176,558      4,115,899
5      1,212,645      4,556,424
6      1,582,156
7      1,365,882

Hi Nino

First project has a negative NPV of ($668,283.21)

Second project has a positive NPV of $375,375.16

See the attached MS Excel Workbook for NPV calculations using MS Excel NPV function and a numerical or a manual method.

The JWD consulting company assumed that the project would produce a system in six months that would be used for three years. The company determined the estimated costs and benefits for the life of a project as shown in the Figure - 1. Estimated costs are Rs. 100,000 in Year 1 and Rs. 25,000 each year in Years 2, 3, and 4. Estimated benefits are Rs. 0 in Year 1 and Rs. 80,000 each year in Years 2, 3, and 4. And the company determined an 8 percent discount rate.

Perform a financial analysis for this project and calculate the:

NPV ( Net present value )
ROI (Return on investment)
Year in which payback occurs

Hi N. kajan

NPV = $41,740.33

Discounted Payback Period is 2 Years and 1 months

I have created a solution in MS Excel WrokSheet that I am attaching here. The spreadsheet contains solution for NPV and Discounted Payback Period using MS Excel and using Numerical or Manual calculations

A five year project has a projected net cash flow of $15,000; $25,000; $30,000; $20,000; and $15,000 in the next five years. It will cost $50,000 to implement the project. If the required rate of return is 20%, conduct a discounted cash flow calcution to determine the NPV.

Hi Ikenna Ugorji

The NPV for the series of cash flows is $12,895.45

This value means that the investment will provide us returns that is worth 12,895.45 in terms of today's money. Thus we would be inclined to accept this project. But you need to keep in mind that we should use other financial metrics such as IRR, MIRR, Discounted Payback Period and Profitability Index to get a wider picture. As it may happen that a project with a higher NPV has a longer payback period thus it won't make sense to invest in it if there was an alternative project with a lower NPV and a lower payback period. A value of IRR will inform you of the required rate of return at which NPV is zero.

NPV is found by first discounting each of the cash flows in the stream starting at t=1, the sum of these discounted cash flows is then subtracted from the initial cash outlay or initial expense at t=0

I have put together two solutions in the attached MS Excel Worksheet the first solution uses NPV function found in MS Excel, but keep in view that NPV function found in MS Excel only find sum of discounted value starting at t=1, we then subtract the initial cash flow from this sum. The second solution is what you would commonly do with paper and pencil and simple calculator.

project cost 50,000k
cash flow 10,000
years=5
ror=1%

Hi Kristen

The NPV for the series of cash flows is -$1465.69

So what does a negative NPV mean?

This suggests even though the sum of cash outflows and cash inflows is in the same amounts of $50,000 yet we don't even break even with this investment. The reason is Time Value of money. The sum of discounted cash flows of $10,000 for each of the next five years at the rate of 1% yields a negative NPV.

We only accept projects that have positive NPV. If we look at the IRR for the same investment, the internal rate of return as calculated in the attached MS Excel worksheet shows a value of 0%. An IRR that is lower than the cost of capital will suggest that project has a negative NPV.

In conclusion, we shall reject this project and look at alternative projects for consideration.

i belive i can sell 10000 devices per yr @300 a piece , cost to manufactuer is 200 per device, equipment cost is 1.5M to buy , life expectant is 5 yrs, fixed production cost is 300000 per year , working capital , upfront is 400 000 and 10% thereafter, tax rate is 30%,

calculate simple payback period
Calculate NPV at 10%

Hi Hellen

The payback period for your investment is 3.103 years ( 3 years and 2 months )
The NPV is R. 389,565
You did say that the Upfront working capital is R 400 000 but you did specify 10% for the working capital for Years 1 to 5.
See the attached MS Excel Worksheet for the detailed solution to find Free cash flows , NPV and Payback Period.

Project Evaluation.
The following table presents sales forecasts for Golden Gelt Giftware. The unit price is $ 40. The unit cost of the giftware is $25.

Year    Unit Sales
1      22,000
2      30,000
3      14,000
4      5,000
Thereafter     0

It is expected that net working capital will amount to 20 percent of sales in the following year. For example, the store will need an initial (year - 0) investment in working capital of .20 x 22,000 x $ 40 = $176,000. Plant and equipment necessary to establish the Giftware business will require an additional investment of $200,000. This investment will be depreciated using MACRS and a 3-year life.
After 4 years, the equipment will have an economic and book balue of zero.
The firm\'s tax rate is 35%.
What is the net present value of the project?
The discount rate is 20 percent.

Hi Lowee Cripps

NPV = $222,281

See the attached MS Excel Worksheet for the calculations.

Dubai Inc. is considering an investment project that would last for 9 years and require an intial investment of $250,000. The annual cash receipts from the project would be $175,000 and the annual cash expesnes would be $79,000. The equipment used in the project could be sold at the end of project a salvage value of $13,000. The company\'s tax rate is 30%. For tax purposes, the entire intial investment will be depreciated over 7 years without any reduction for salvage value. The company uses a discount rate of 10%

1. When computing the net present value of the project, what are the annual after tax cash receipts?

2. The net present value of the project is clostest to?

Hi Alexandra

Solution to your NPV problem is provided below

The present value outflow is $250,000 which represents the cost of the investment, which if purchased would be paid today.

In terms of cash inflows we have the following:

1. increase in cash flow per year from annual profits = $96,000
less: tax liability from increased net income (calculated below)= ($20,467)
increase in cash flow per year from machinery, years 1 to 9= $75,533
2. Salvage value of investment, end of year 9 is $13,000

Calculation of tax liability.

Additional tax payments come from increased profit.
The annual cash receipts $175,000
The annual cash expesnes would be ($79,000)
Increased income by annual profits $96,000
Less depreciation expense (calculated below) ($27,778)
Additional income before taxes $68,222
Tax payment (30%) ($20,467)
Net income $47,755
Tax payment = $20,467

Depreciation is calculated using the straight line method which equals (cost - salvage value)/useful life of the asset. Arithmetically, it would equal (250,000 - 0)/9 years or $27,778 per year. Depreciation is not a cash flow expense but reduces taxable income. In terms of cash inflows, we have additional cash flows from years 1 to 9 from operations (net of taxes) of $75,533, and $13,000 from the salvage value of the machine at the end of year 9. Our cash outflow is $250,000 (present value) representing the cost of the investment today. The discount rate is 10%.

Taking the Present Value of our cash inflow we have an annuity of $75,533 for 8 years (at the end of each period), and a lump sum payment of $88,533 at the end of year 9.

NPV = $75,533 x PVIFA(10%,8 yrs) + ($75,533 + $13,000) x PVIF(10%,9)

PVIFA(i%, n) = [1 - { 1 / (1+i)^n }] / i

PVIF(i%, n) = 1 / (1+i)^n

NPV = 75,533 x 5.335 + 88,533 x 0.424 - 250,000

NPV = $402,968 + $37,538 - 250,000

NPV = $440,506 - 250,000

NPV = $190,506