Problem 4 The Trust for Open Spaces purchases land within and around cities in a

Question

Problem 4 The Trust for Open Spaces purchases land within and around cities in an effort to preserve open spaces in otherwise urban settings. The Trust has a 10 year plan to purchase and restore 20,000 acres. . Th e land will be purchased in increments over a 5 year period. They are spending $2 million now (year 0) for a portion of the land. Total annual purchase amounts are expected to decrease $200,000 each year through the fifth year (i.e., the year 1 purchase price will be $1.8 million), at which point the land will have been completely purchased. At the end of year 3, the trust will spend $250,000 to restore the land to its native state. This value is expected to increase by $100,000 per year (as additional land is acquired) and will continue through year 10, when the land should be completely restored. hat is the equivalent uniform annual worth of these expenses over the next ten years nd of years 1-10)? Trust projects and funds are evaluated at 8% per year.

Explanation / Answer

The Trust has a plan to purchase and restore 20,000 acres. Hence, there are two kinds of expenses. We'll convert all of them to Present Valuce first, then to an equivalent uniform annual worth

1. Purchases:

Cost spent now (year 0) : $ 2 million

Then for coming 5 years, cost will reduce by $ 200,000.

So, we'll use ( P / G, i%, n) for $ 200,000 i.e. ( P / G , 8 % , (5-1) ) * ( $ 0.2 million ) = $ 0.93 million. This value is after 1 year, to bring it to year 0, we'll use ( P / F ) i.e. ( $ 0.93 million ) / ( 1.08 ) = $ 0.861 million

Then we'll use ( P / A, i%, n) for $ 2 million i.e. ( P / A , 8%, 5 ) * ( $ 2 million ) = $ 7.985 million

Hence, $ 7.985 - 0.861 million = $ 7.124 million

Total present value of purchases is : $ 7.124+ 2 million i.e. $ 9.124 million

2. Restoration:

At end of year 3, $ 250,000 will be spent for restoration, uptill the year 10 with an increament of $ 100,000 per year.

We'll use ( P / A , i%, n ) for % 250,000 i.e. ( $ 0.25 million ) * ( P / A , 8 % , ( 10 - 3 ) ) = $ 1.3 million

To bring it to year 0, we'll use ( P / F, i%, 3 ) = $ 1.032 million

For the increament, we'll use ( P / G , i% , (10-3-1) ) = $ 1.052 million

To bring it to year 0, we'll use ( P / F, i%, (3+1) ) = $ 0.773 million

Hence, total present value of restoration = $ 0.773 + $ 1.032 million = $ 1.805 million

Hence, total present value of expenses = $ 1.805 + $ 9.124 million = $ 10.929 million or $ 10.93 million

We'll use ( A / P , i% , 10 ) to get the uniform annual series for the total present value i.e $ 1.629 million.

Hence, the equivalent uniform annual worth of these expenses over the next ten years is $ 1.629 million.

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