Question

Jensen Company owns a building in a suburban industrial park. It purchased the building four years ago for $3 million. It is now deciding whether to lease the building or to use it as a distribution center. It could be leased immediately. Given today’s market conditions, lease income of $120,000 per year would be expected. To convert the building to make it useful as a distribution center would require an immediate expenditure of $400,000. Having the distribution center at this location would provide Jensen with $140,000 per year in cost savings, at today’s prices. The cash flows associated with this decision are not very risky, so a real discount rate of just 3% per year is required. Inflation of 2% per year is expected in the future. For simplicity, assume that: (i) there are no taxes, (ii) the building could be leased or used as a distribution center forever, (iii) ongoing cash flows, including rents and distribution cost savings, would increase with the overall inflation rate, and (iv) all cash flows except the initial $400,000 would occur at year end. (the last assumption implies that one year of inflation would affect the first lease payment and distribution cost saving) (a) Provide a NPV analysis and a recommendation of how the building should be used.(b) Is the outcome of your NPV analysis sensitive to changes in the assumed inflation rate?

Answer 1

Part (a)

Initial cost of land of $ 3 mn is sunk now and irrelevant for the purpose of decision making. Hence, they will not be considered anywhere in the NPV analysis.

All analysis is in real terms, without taking into impact of inflation. All financials are in $.

If the land is leased, Annual Lease income in real terms = L = 120,000

Real discount rate, R = 3%

Hence, NPV of leasing option = NPV_Lease = PV of perpetuity of L = L / R = 120,000 / 3% = 4,000,000

If land is converted into a distribution centre,

Annual cost savings in real terms, S = 140,000

Initial investment, C₀ = 400,000

Hence, NPV of distribution center option = NPV_DC = - C₀ + PV of perpetuity of S = - C₀ + S / R = - 400,000 + 140,000 / 4% =  4,266,667

Since NPV_DC > NPV_Lease, hence the building should be used as distribution center.

Part (b)

The outcome of our NPV analysis is not sensitive to changes in the assumed inflation rate, because inflation is impacting the financials and the discount rate alike. Hence in the calculation of PV of a perpetuity, the numerator and denominator both are increasing by a factor of (1 + inflation). And they eventually cancel out. Hence, the NPV analysis is independent of assumed inflation rate.