Applying the annuity method - how?

[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! :)

 

[tkhunny]

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.

 

[Wilmer]

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

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

Agree TK?

 

[tkhunny]

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.