Question

Problem 3: Sensitivity of NPV to Discount Rates
A ski resort wants to expand by opening more trails and adding a new high-speed chair lift. The initial capital investment for the expansion is $150,000 in year 0 and the resort will not benefit financially until after the project is completed in year 3. After that the annual net benefits will be $20,000 at the end of each year. Assume a lifetime of 25 years for the expansion.
a) Is this investment NPV positive under a 5% discount rate? Under a 13% discount rate?
Note: You may use computer software for your calculation. If you do, please print out the NPV of each year’s annual benefit under each discount rate (i.e., two columns of NPVs). Please be sure to state any assumptions you make.
b) The resort invests in the expansion but ownership decides to sell five years later. Does this affect the NPV analysis? Why or why not? Please state your assumptions. Hint: You do not need to complete another quantitative analysis, and there is more than one right answer.

Answer 1

A) Cost: $150,000

PV of cost: $150,000

Revenue: $\sum$_{from 3 to 25} ($20,000)  

When discount rate, r=0.05

PV of revenue: $\sum$_{n= 3 to 25} ($20,000/(1+r)^n) = $244,600

Since PV of revenue> PV of cost by $94600

When discount rate r=0.13

PV of revenue: $\sum$_{n= 3 to 25} ($20,000/(1+0.13)^n) = $113200

PV of cost>PV of revenue

PV Costs exceed by $36800

B) If the resort sells ownership after 5 years, then the revenue/benefits realised will go to the new owner. Hence, in the present value analysis, the expected increase in revenue due to expansion should be taken into account i.e. the benefit that will incur to the new owner should be accounted for. Another method could be, to realise benefits the discount rate should be really low to be willing to invest in this expansion so that PV of benefits and cost equal in the five year span