# Applying the annuity method - how?

• MHB
• indigo2
In summary, the food processing company should expand its production facilities if the desired rate of return is 13%.
indigo2
Hello,

I was given following task:

A food processing company has to make a decision whether or not to expand its production facilities. A feasibility study showed the following estimates:

Initial cost outlay €800,000
Further outlay in 4 years €600,000
Residual value after 10 years €200,000
Net returns at the end of each year for 10 years €220,000

Indicate whether the expansion should be undertaken if the desired rate of return on investment is 13%. Apply the annuity method!

I do not know how to use the annuity method to this task, I thought this would be solved with present value method, or can both be done? What is the right formula to use the annuity method here?

I am happy about any hint how to solve it! :)

indigo said:
Hello,

I was given following task:

A food processing company has to make a decision whether or not to expand its production facilities. A feasibility study showed the following estimates:

Initial cost outlay €800,000
Further outlay in 4 years €600,000
Residual value after 10 years €200,000
Net returns at the end of each year for 10 years €220,000

Indicate whether the expansion should be undertaken if the desired rate of return on investment is 13%. Apply the annuity method!

I do not know how to use the annuity method to this task, I thought this would be solved with present value method, or can both be done? What is the right formula to use the annuity method here?

I am happy about any hint how to solve it! :)
Annuity Method? Does that mean something other than the consideration of the time value of money?

If v = 1 / 1.13, we have, simply:

Cost = 800000 + 600000v^4 - 200000v^10 - 220000(v + v^2 + v^3 + ... + v^10)

If you like, you can add up the last part, $220000\cdot\dfrac{v - v^{11}}{1-v}$

Seriously, just draw a time diagramme and put your cash flows on it. Is that the "Annuity Method"?

The "Annuity Method" may be a way to depreciate your initial asset, but since we are not valuing anything at any intermediate date, I'm not real clear on why we care how it depreciates. We just need to know where it ends up - which is given.

Outlay portion:
-800000(1.13)^10 - 600000(1.13)^6 + 200000

Revenue portion:
annual annuity of 220000: n=10, i=.13

Agree TK?

Wilmer said:
Outlay portion:
-800000(1.13)^10 - 600000(1.13)^6 + 200000

Revenue portion:
annual annuity of 220000: n=10, i=.13

Agree TK?

Whether you accumulate or discount, it is of no consequence. The conclusion is the same.

Whether payouts are positive or negative, and income is negative or positive, it is of no consequence. The conclusion is the same.

Just be consistent. Make up your mind what you are doing before you start writing and don't change the rules mid problem.

## 1. What is the annuity method?

The annuity method is a financial calculation used to determine the present value of a series of future cash flows, typically through regular payments over a set period of time. It takes into account the time value of money, or the concept that money is worth more in the present than in the future due to inflation and potential investment returns.

## 2. How is the annuity method applied?

To apply the annuity method, you will need to know the periodic payment amount, the interest rate, and the number of periods. You will then use a formula, such as the present value of an annuity formula, to calculate the present value of the future cash flows. This can be done manually or with the help of financial calculators or software.

## 3. Can the annuity method be used for any type of cash flow?

The annuity method is typically used for regular, fixed payments over a set period of time. This can include things like loan payments, rental payments, or pension payments. It may not be suitable for irregular or variable payments.

## 4. What is the difference between an annuity and a perpetuity?

An annuity is a series of fixed payments over a set period of time, while a perpetuity is a series of fixed payments that continue indefinitely. The annuity method can be used to calculate the present value of both annuities and perpetuities, but the formulas will differ slightly.

## 5. Are there any limitations to using the annuity method?

The annuity method is based on certain assumptions and may not always accurately reflect the true present value of future cash flows. It also does not take into account factors such as taxes, inflation, or changes in interest rates. It is important to consider these limitations and use the annuity method as just one tool in your financial analysis.

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