<p>The state of Minnesota is considering building a highway through undeveloped wilderness. The construction will take 1 year and the construction costs are estimated at 10 million. The annual routine maintenance costs are expected to be 1 million per year. The relevant interest rate is 5%. The expected estimated annual benefits to the public and environment are $2 million per year. Assume an infinite project life.
 is my attempt on the first 3, feel free to correct me if I am wrong.*
I do not understand the parts d and e if anyone could shed some light on it.</p>

<p>PV = Present Value</p>

<p>a. Find the PV of the Costs of this project.</p>

<blockquote>
  <p>10,000,000 + 1/0.05 = 30000000</p>
</blockquote>

<p>b. The PV of the benefits of this project.</p>

<blockquote>
  <p>2,000,000/0.05 = 40000000</p>
</blockquote>

<p>c. The PV of the Benefits – PV of the Costs.</p>

<blockquote>
  <p>Subtract the above we get 10000000</p>
</blockquote>

<p>d. Find the annual value of benefits which generates a zero net present value.</p>

<p>e. Assuming an infinite project life, find the increase in annual routine maintenance costs that make the NPV = 0.</p>

CC BY-SA 3.0
2015-10-16T00:49:33.943Z
For part (d), you will want to remember that the costs are 10m + 1m/year, so you're trying to find a number that, at a 5% interest rate, will in perpetuity equal that 10m upfront + 1m/year... So it's a number x where (x-1) in perpetuity at a 5% discount rate will equal 10m today, right?
dismalscience
CC BY-SA 3.0
2015-10-16T00:56:36.997Z
I havent quite got it but would it be something on the lines of 40,000,000*x-30,000,000 = 0, so therefore the value of x = 0.75?
Dangerous Game
CC BY-SA 3.0
2015-10-16T01:02:10.507Z
So you can pretty much just subtract the annual costs from the annual benefits to get a net annual benefit, right? So it's just (x/yr - 1m/yr)/ 0.05 = 10m, right?
dismalscience
CC BY-SA 3.0
2015-10-16T01:15:35.360Z
what do u mean by x/yr? if yr is inifinity does this just mean x?
Dangerous Game
CC BY-SA 3.0
2015-10-16T01:22:19.620Z
No, the formula for the PV of a perpetual annual annuity (or whatever) A is just A/r. Where A is the payment/year. So I'm just saying you're trying to find (x-1m)/0.05=10m. You can subtract the annual costs from the annual benefits to find a net annual benefit, and you just need to compare the present value of that net annual benefit to the upfront cost.
dismalscience
CC BY-SA 3.0
2015-10-16T01:27:48.687Z
I see what you mean, so I guess that would make it x = 1050000
Dangerous Game
CC BY-SA 3.0
2015-10-16T01:51:01.090Z
Cool, now use the same understanding for part (e).
dismalscience
<microeconomics>
Present Value of Costs and Benefits
Dangerous Game
# Present Value of Costs and Benefits

(Asked by: username_0 on 2015-10-16)

The state of Minnesota is considering building a highway through undeveloped wilderness. The construction will take 1 year and the construction costs are estimated at 10 million. The annual routine maintenance costs are expected to be 1 million per year. The relevant interest rate is 5%. The expected estimated annual benefits to the public and environment are $2 million per year. Assume an infinite project life.
is my attempt on the first 3, feel free to correct me if I am wrong.\*
I do not understand the parts d and e if anyone could shed some light on it.

PV = Present Value

a. Find the PV of the Costs of this project.

> 10,000,000 + 1/0.05 = 30000000

b. The PV of the benefits of this project.

> 2,000,000/0.05 = 40000000

c. The PV of the Benefits – PV of the Costs.

> Subtract the above we get 10000000

d. Find the annual value of benefits which generates a zero net present value.

e. Assuming an infinite project life, find the increase in annual routine maintenance costs that make the NPV = 0.

**Tags:** microeconomics

> **Comments:**
> **username_1**: For part (d), you will want to remember that the costs are 10m + 1m/year, so you're trying to find a number that, at a 5% interest rate, will in perpetuity equal that 10m upfront + 1m/year... So it's a number x where (x-1) in perpetuity at a 5% discount rate will equal 10m today, right?  
> **username_0**: I havent quite got it but would it be something on the lines of 40,000,000*x-30,000,000 = 0, so therefore the value of x = 0.75?  
> **username_1**: So you can pretty much just subtract the annual costs from the annual benefits to get a net annual benefit, right? So it's just (x/yr - 1m/yr)/ 0.05 = 10m, right?  
> **username_0**: what do u mean by x/yr? if yr is inifinity does this just mean x?  
> **username_1**: No, the formula for the PV of a perpetual annual annuity (or whatever) A is just A/r. Where A is the payment/year. So I'm just saying you're trying to find (x-1m)/0.05=10m. You can subtract the annual costs from the annual benefits to find a net annual benefit, and you just need to compare the present value of that net annual benefit to the upfront cost.  
> **username_0**: I see what you mean, so I guess that would make it x = 1050000  
> **username_1**: Cool, now use the same understanding for part (e).  

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## 0 answers

