I am studying engineering economics and please help me solve this problem with s

Question

I am studying engineering economics and please help me solve this problem with step by step with explanations. Dont just write the solution please. Thanks
Q4Consider the following three depreciation schedules: Year A (S)B (S) C(S) 1323.3424.0 194.0 21258.7254.4194.0 3194.0152.6194.0 4129.3 91.6194.0 5 64.747.4194.0 970.01970.?970.0 They are based on the same initial cost and salvage value. Assume the useful life to be 5 years and the interest rate to be 12%. a) Calculate the initial cost and salvage value b) Identify each depreciation schedule

Explanation / Answer

I might not solve the two parts independently, since both of them are strongly related. But, despite that, I'll make sure you understand well. And please note that before going through such questions, you should be very clear about all kinds of depreciation schedule (well, especially the common ones, which are comparatively more important), so that an immediate pattern can be observed, and thus question can be solved accordingly.

So step 1: identify the pattern;

step 2: think of the depreciation method that syncs with the pattern;

step 3: verify by putting in the respective formula and arithmetic

Solution: Symbolizing initial cost by IC, and Salvage value by S

Given the depreciation schedules, for schedule C, we can see that a fixed amount of depreciation is charged every year. Thus, clearly Schedule C is a straight line depreciation schedule.

In straight line method, depreciation amount = (initial cost - salvage value)/ Years of use

In this case then, 194 = (IC - S)/5 giving us: IC - S = 970 ... (1)

Now, the remaining two schedules are a little twisted.

First we shall see a pattern in depreciation amounts for both:

For schedule A, 323.3 - 258.7 = 64.6

258.7 - 194 = 64.7

194 - 129.3 = 64.7

129.3 - 64.7 = 64.6. So, a little higher depreciation expense is incurred during initial years, while lower in the latter years, with not much difference in the amounts. This is sum-of-years-digits depreciation method.

In thiis case, depreciation amount = (remaining life years*(initial cost - salvage value))/ sum of years digits. Also, from the formula clearly, since in last year (of useful life), remaining life years = 0 (so, depreciation amount is 0 from 5th year onwards). Now since, all three methods are based on same IC and S, we have already calculated IC - S = 970. (which is of course constant for all years)

Now, total life = 5 years, then sum of years digits = 1 + 2 + 3 + 4 + 5 = 15

Now, for beginning of first year depreciation amount then, depreciation amount = 5(IC -S)/15

Depreciation amount = 970/3 = 323.3 (which is true from the table)

Similarly for second year, depreciation amount = 4*970/15 = 258.7 (again true)

For third year, 3*970/15 = 194; fourth year: 2*970/15 = 129.3; fifth year: 1*970/15 = 64.7 (so all values match from table). We can conclude schedule A follows sum-of-years-digits depreciation method.

For schedule B, 424 - 254.4 = 169.6

254.4 - 152.6 = 101.8

152.6 - 91.6 = 61

91.6 - 47.4 = 44.2. Thus, clearly, depreciation is decreasing at a decreasing rate. So, one possibility could be of double declining balance depreciation. In this method, there is a fixed rate of depreciation, which is charged on the asset value in the beginning of each year. Also, under double-declining balance depreciation method, rate of depreciation is 200% (2 times) the rate in Straight-line depreciation method.
Thus, in this case, Depreciation amount = 2*straight-line depreciation percent*asset value at beginning of year

where, 2*SL depreciation rate = depreciation rate under DDB depreciation method

straight-line depreciation percent = Depreciation amount under SL method/(IC - S) = 194/970 = 1/5 = 0.2

So, depreciation rate under DDB depreciation method = 2*0.2 = 0.4 or 40%

Then, for first year, depreciation amount = 0.4*IC

Or, 424 = 0.4*IC, giving us IC = 1060

Then for second year, depreciation amount = 0.4*(1060 - 424) = 254.4

For third year: 0.4*(1060 - 424 - 254.4) = 152.6; fourth year: 0.4*(1060 - 424 - 254.4 - 152.6) = 91.6; fifth year: 0.4*(1060 - 424 - 254.4 - 152.6 - 91.6) = 55 (So, verified with the table)

Using (1), 970 = IC - S

With IC = 1060, S = 1060 - 970 = 90

Of course there are plenty other ways of solving this question, I hope you find this method helpful. Thank you.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.