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 $5 million salvage value in this formula? Is my calculation correct?
I would calculated the future value at the end of the year 2048 ($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 $P_{2014}^T=\frac{C_{2048}^T}{1.08^{48-14}}$