# Financial Exercises 5: Investment Timing

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by Clemens Werkmeister

### 1. Timing of a single investment

Ten years ago, John Walden planted Nordman fir trees. The plan is to fell them and sell them as christmas trees. For reasons of efficiency, it is best to fell the complete lot. But John can decide whether to harvest the trees early or to wait and get higher revenues for larger trees. The following table contains the expected revenues for felling the trees in the given year. Walden assumes a 10 % cost of capital.

 year alternative cash flows 0 100 1 125 2 145 3 160 4 170 0 180

a. Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15.
b. Calculate for years 11 to 15 the percentage change of revenues compared to the previous year.
c. Calculate the present values of felling in years 11 to 15.
d. Given your calculations, what is the best year for felling the trees?

### 2. Timing of replacement (the case of perpetual investment chains)

John Walden plans to reuse the area for the next generation of christmas trees of the same kind. Hence, the same expected revenues apply again after the life cycle of the trees.
a. Calculate the annuity of the revenues over the different lifetimes (11 to 15 years).
b. At what age is it best to fell the christmas trees in this case?

### 3. Life cycles of single investments and investment chains

Jim Weam produces premium wine whose extraordinary flavour depends on the old barrels he uses. The cost of grapes and processing are 150 € per barrel. Handling and preparing the barrel every other year of maturing costs 10 €. While maturing in barrels up to five years, the wine price increases. The following table lists the expected revenues per barrel if the wine is sold after x years of maturing:

 years of maturing cash flows if sold in year annual costs until sale 0 150 1 230 10 2 340 10 3 470 10 4 510 10 0 600

a. Forecast the cash flows for every year until the sales year.
b. Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?
c. Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.

### 4. Comparing investment proposals with different lifetimes

A ski resort plans to install a new lift and is analyzing two different proposals. Proposal A requires an initial investment of 5 million Euro and annual maintenance cost of 900,000 Euro. The corresponding figures for proposal B are 3 million Euro of initial investment and 1.2 million Euro of annual maintenance cost. Proposal A has to be replaced after nine years, proposal B after six years.
a. Calculate the NPV and the annuity (equal annual cost – EAC) of the lift proposals.
b. Which is the better project if you expect to quit operations after the economic lifetime of the lift?
c. What happens if we assume annual revenues of 2 million Euro, independent of the kind of lift?
d. Which lift would you buy if you plan to use similar lifts for at least 18 years?