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Chapter 5: Q. 49 (page 350)

The number of years n for a piece of machinery to depreciate to a known salvage value can be found using the formula, n=logs-logilog(1-d), where s is the salvage value of the machinery, i is its initial value, and d is the annual rate of depreciation.

(a) How many years will it take for a piece of machinery to decline in value from \(90,000 to \)10,000 if the annual rate of depreciation is 0.20 (20%)?

(b) How many years will it take for a piece of machinery to lose half of its value if the annual rate of depreciation is 15%?

Short Answer

Expert verified

Part (a) Number of years for a piece of machinery to decline in value from $90,000 to $10,000 at annual rate of depreciation of 20% is : 9.85years

Part (b) Number of years for a piece of machinery to lose half of its value at annual rate of depreciation of 15% is : 4.27years

Step by step solution

01

Part (a) Step 1. Given information  

The number of years n for a piece of machinery to depreciate to a known salvage value can be found using the formula, n=logs-logilog(1-d), where s is the salvage value of the machinery, i is its initial value, and d is the annual rate of depreciation.

02

Part (a) Step 2. Finding number of years for a piece of machinery to depreciate from $90000 to $10000 at 20% 

Given, n=logs-logilog(1-d)

Put s=90000,i=10000,d=0.2

n=log10000-log90000log(1-0.2)

鈬�n=log1000090000log0.8

鈬�n=log0.1111log0.8

鈬�n=-0.9542-0.0969

鈬�n=9.85

03

Part (b) Step 1. Number of years for a piece of machinery to lose half of its value at 15% depreciation

Given, n=logs-logilog(1-d)

Put s=i2,d=0.15

n=logi2-logilog(1-0.15)

鈬�n=logi2脳1ilog0.85

鈬�n=log0.5log0.85

localid="1646619719042" 鈬�n=-0.3010-0.0705

鈬�n=4.27

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