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Q: A bridge upgrade would cost thirty million dollars in 2016.It would provide benefits, mainly the value of time saved by drivers, reduced gasoline consumption and reduced GHG emissions, of twelve million dollars in each of the following four years 2017, 2018, 2019 and 2020. The upgrade would require one-time maintenance spending of $5 million in 2019. The rate of interest is four per cent and there is no inflation. What is the net present value and should the bridge project go ahead?

A: this is what I have so far. As you can see, I am not sure whether I subtract the $30M from the NPV calculation or add it. Also I am not sure how to conclude whether or not we should go ahead with the bridge

Year 1 (2017): 12,000,000 / (1+0.04)^1 = 11,538,461.54

Year 2 (2018): 12,000,000 / (1+0.04)^2 = 11,094,674.56

Year 3 (2019): 12,000,000 / (1+0.04)^3 = 10,667,956.3

5,000,000 / (1+0.04)^3 = 4,444,981.79

10,667,956.3 - 4,444,981.79 = 6,222,974.51

Year 4 (2020): 12,000,000 / (1+0.04)^4 = 10,257,650.29

NPV: -30,000,000 + (11,538,461.54 + 11,094,674.56 + 6,222,974.51 + 10,257,650.29) = 9,113,760.90

2 Answers 2

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You need to subtract the $30$ million as that is a cost. As it is incurred immediately, you do not discount it. You also failed to take account of the maintenance spending, which does need to be discounted.

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    Thank you for your help. Sorry but what do you mean by 'discount it' and not? – 2017-02-03
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    That is the divisions you did by $1.04$ – 2017-02-03
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    Would I then calculate $5M/(1.04)^3 as year 3 is 2019, then subtract it from the year 3 calculation? – 2017-02-03
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    You would subtract it from the present value. Whether you do that by including it in 2019 or separately doesn't matter. – 2017-02-03
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    Ok makes sense. Thank you for your help! So we would assume the project is a yes and should be undertaken since you have a NPV of $9,113,760.90? – 2017-02-03
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$$ \mathrm{NPV}=-C_0+\sum_{t=1}^n\frac{C_t}{(1+i)^t}=-30+\frac{12}{1.04}+\frac{12}{1.04^2}+\frac{12-5}{1.04^3}+\frac{12}{1.04^4}\approx 9.11\, \text{millions} $$ $\mathrm{NPV}>0$ and then the bridge project sho go ahead because the actualized benefits ($39.11$ millions) are greater than the investment ($30$ millions).