Machine I cost X dollars, has a salvage value of X/8, and is to be depreciated o

Question

Machine I cost X dollars, has a salvage value of X/8, and is to be depreciated over 10 years using the declining balance method. Machine II costs Y dollars, has a salvage value of X/8, and is to be depreciated over 10 years using the sum-of-the-years digits method. The total amount of depreciation in the first 7 years for Machine I equals the total amount of depreciation in the first 7 years of Machine II. Calculate Y/X...

I know the answer is .986 but need help with the work to get there. Thanks!

Explanation / Answer

For Machine I, S = A(1 d)n gives that X

8 = X(1 d)10

So, 1 d = (1/8)1/10 = 0.1250.1.

Hence, B7 = A(1 d)7 = X(0.1250.7).

The total amount of depreciation in the first seven years is

A B7 = X X(0.1250.7) = X(1 (0.125)0.7).

For Machine II, the total amount of depreciation in the first seven years is

D1+D2+-----+D7 = j=17(y-x/8)*(2/(10)(11))*(11-j)

= (y-x/8)(1/55)(10+9+8+7+6+5+4) = (y-x/8)(49/55)

So, X(1 (0.125)0.7) =(Y X/8)(49/55)

y/x = 0.125+(55/49)(1 (0.125)0.7) = 0.9856

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