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- 2. Topics • Uniform Gradient •Capitalized Cost • Annual Cost 2
- 3. Uniform Gradient -Arithmetic • An arithmetic gradient series is a cash flow series that either increases or decreases by a constant amount each period. The amount of change is called the gradient. 3
- 4. Uniform Gradient -Geometric • A geometric gradient series is a cash flow series that either increases or decreases by a constant percentage each period. The uniform change is called the rate of change. 4
- 5. Capitalized Cost Capitalized costis an application or perpetuity. • The capitalized cost of a project or structure is the sum of the first cost (FC) and the present worth of all future payments and replacements which is assumed to continue forever. If a project requires a first cost of FC, annual operation and maintenance of OM for n years, and a replacement cost of RC after every end of n years, and a replacement cost of RC after every end of n years, then the capitalized cost is 5 Capitalized cost may also be defined as the first cost plus the present worth of annual maintenance and operation cost plus the present worth of depreciation assumed to continue forever.
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- 7. Example 7 A machine costsP300,000.00 new, and must be replaced at the end of 15 years. If the annual maintenance required is P5,000.00, find the capitalized cost and annual cost, if money is worth 5% and the final salvage value is P50,000.00.
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- 9. Depreciation Depreciation refers tothe decrease in the value of an asset, due to usage of passage of time. An asset may depreciate physically or functionally. Elements of Depreciation FC = first cost SV = salvage value or trade-in value d = depreciation charge n = economic life of property in years m = any time before n BVm = book value after m years (BVm = FC – Dm) Dm = total depreciation for m years 9
- 10. Methods of Depreciation •Straight Line Depreciation (SLD) • Sinking Fund Method • Sum of the Years Digit Method (SYD) • Declining Balance Method 10
- 11. Straight Line Depreciation(SLD) • This is the most common method used in computing depreciation. In this methos, the cost of the property is assumed to vary linearly with time. 11 In some cases, the life n may be the number of outputs. An example of this is the copying machine (XEROX) where the life span is dependent on the number of copies made.
- 12. Example 12 What is thevalue of an asset after 8 years of use if it depreciates from its original value of P120,000.00 to its salvage value of 3% in 12 years?
- 13. Sinking Fund Method •In this method, an imaginary fund d called a sinking fund is invested yearly at a rate of i to amount to (FC-SV) at the end of the life of the property. 13
- 14. Example 14 An equipment costingP250,000 has an estimated life of 15 years with a book value of P30,000 at the end of the period. Compute the depreciation charge and its book value after 10 years using sinking fund method assuming i = 8%.
- 15. Sum of theYears Digit Method • To depreciate charge in this method is assumed to vary directly to the number of years and inversely to the sum of the year’s digit. 15
- 16. Example 16 An asset Ispurchased for P120,000.00. Its estimated economic life is 10 years, after which it will be sold for P12,000.00. Find the depreciation for the first year using the SYD.
- 17. Declining Balance Method •This method is based on the compound interest formula F = P(1+i)^n , where P is the first cost, FC, F is the book value at any time, and i .is the dedpreciation rate and is equal to –K. Then 17
- 18. Example 18 An equipment costingP250,000 has an estimated life of 15 years with a book value of P30,000 at the end of the period. Compute the depreciation charge and its book value after 10 years using declining balance method.