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I would like to know how to consider the "Salvage Value" in the following question while calculating the present and future values.

here is the question:

We are planning to build a new bridge. Construction is to start in 2015 and is expected to take 4 years at a cost of $25 million per year. After construction is completed, the cost of operation and maintenance is expected to be $2.5 million for the first year, and increase by 2.8% per year thereafter. The salvage value of the bridge at the end of year 2048 is estimated to be $5 million. Consider the present to be the end of 2013/beginning of 2014 and the interest rate to be 8%.

a- Draw a cash flow diagram for this project (from present till end of year 2048) b- find the Present Worth c- find the Future Worth

HERE IS WHAT I DID:

we need to find P2013 (Present Worth at this time) P2013 = P2015 (1+i)^n = P2015 (1+0.08)^2

P2015 = A1 (P1|A1 8%,33) + A2 (P2|A2 2.8%,8%,29) P2015 = $ 324,433,747.65

P2013 = P2015 (1+0.08)^2 = $ 378,419,523.26

Now the question is where to consider the $5 million salvage value in this formula? Is my calculation correct?

Vahid Garshasbi
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1 Answers1

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I would calculated the future value at the end of the year 2048 ($C_{2048}$) an and after that I would calculate the present value.

Construction costs:

The construction period goes from 2015 to 2018. $C_{2018}^C=25,000,000\cdot \frac{1-1.08^4}{1-1.08}$

$C_{2048}^C=25,000,000\cdot \frac{1-1.08^4}{1-1.08}\cdot 1.08^{48-18}=25,000,000\cdot \frac{1-1.08^4}{1-1.08}\cdot 1.08^{30}$

Costs of operation and maintanace

It has to be made 30(=48-19+1) payments. And the formula with increasing payments is

$C_n=r \cdot \frac{g^n-q^n}{g-q}$

$C_{2048}^{OM}=2,500,000\cdot \frac{1.028^{30}-1.08^{30}}{1.028-1.08}$

salvage value The salvage value at 2048 is just $P_{2048}^S=5,000,000$

The value of all cash flows in 2048 is $C_{2048}^T=-C_{2048}^C-C_{2048}^{OM}+C_{2048}^S$

The value of all cash flows at the beginning of 2014 is $P_{2014}^T=\frac{C_{2048}^T}{1.08^{48-14}}$

callculus42
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  • thank you so much.So the Future Worth will be negative, is the Present Worth negative as well? – Vahid Garshasbi Nov 20 '14 at 01:49
  • @VahidGarshasbi Sure. This is always the case. The general equation is $PW=\frac{FW}{(1+i)^t}$. $1+i$ is always positive. If the Future Worth is negative, then the Present Worth is negative as well. If If the Future Worth is positive, then the Present Worth is positive as well. That is one the reason, why you can judge a project by using the net present value method. – callculus42 Nov 20 '14 at 09:29
  • @VahidGarshasbi You are welcome. – callculus42 Nov 20 '14 at 20:42