Consider the Rail Runner train service for the following questions. The New Mexi
ID: 2495111 • Letter: C
Question
Consider the Rail Runner train service for the following questions. The New Mexico Rail Runner is a publicly owned and operated intercity commuter
rail line that runs between Albuquerque and Santa Fe, New Mexico. The Rail Runner generally follows interstate highway 25 and has several stops in
-between Albuquerque (and a few south of Albuquerque) and Santa Fe. The service runs all week but is mainly focused on serving commuters during peak morning and evening travel times Monday through Friday.The project cost $400 million to build and about $20 million a year to operate. More informationabout the rail runner can be found here: http://www.nmrailrunner.com/
Assume that the annual net benefits of the Rail Runner are $35million and a 100-year analysis period.
a. What would the benefit cost ratio be using a 0.5% interest rate?
b. What would the benefit cost ratio be using a 10% interest rate?
c.How does the choice of the interest rate affect the cost benefitanalysis?
d.Why might you (or not) choose to use a very low interest rate versus a higher market based interest rate?
Explanation / Answer
Benefit-Cost ratio (BCR) = Present value (PV) of benefits / PV of costs
(a)
PV of benefits ($ million) = 35 x PVIFA(0.5%, 100) = 35 x 74.5826 (From PVIFA table) = 2,610.40
PV of costs ($ million) = 400 + [20 x PVIFA(0.5%, 100)] = 400 + (20 x 74.5826) = 400 + 1,491.7
= 1,891.7
BCR = 2,610.4 / 1,891.7 = 1.38
(b)
PV of benefits ($ million) = 35 x PVIFA(10%, 100) = 35 x 9.9993 (From PVIFA table) = 350
PV of costs ($ million) = 400 + [20 x PVIFA(10%, 100)] = 400 + (20 x 9.9993) = 400 + 200 = 600
BCR = 350 / 600 = 0.58
(c)
As interest rate increases (decreases), BC decreases (increases).
(d)
A market- based rate, even if relatively high, will reflect the true BCR to a bigger extent than the case if I choose a very low interest rate which yileds a higher BCR but is unrealistic. That is why, I may not choose a very low rate.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.