MHB Applying the annuity method - how?

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The discussion revolves around evaluating the feasibility of expanding a food processing company's production facilities using the annuity method. Key financial figures include an initial outlay of €800,000, a further €600,000 investment in four years, and annual net returns of €220,000 over ten years, with a desired return rate of 13%. Participants clarify that both the annuity method and present value calculations can be utilized, emphasizing the importance of consistency in approach. The annuity method is suggested for calculating the present value of future cash flows, while also noting that the depreciation of the asset may not be critical for this analysis. Ultimately, the focus is on accurately assessing the cash flows to determine if the expansion is financially viable.
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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! :)
 
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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.
 
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