# Average Accumulated Expenditures – Becker FAR MCQs

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Posts Anonymous
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On January 1, Year 3, Starlight Construction Co. began a construction project qualifying for capitalization of interest. The total amount spent on this project during Year 3 was \$250,000, spent uniformly during the year. To help pay for construction, \$200,000 was borrowed at 10% on January 1, Year 3, and funds not needed for construction were temporarily invested in short-term securities, yielding \$3,000 in interest revenue. Other than the construction funds borrowed, the only other debt outstanding during the year was a \$150,000, 10-year, 7% note payable dated January 1, Year 1. How much interest should be capitalized by Starlight during Year 3?

a. \$25,000
b. \$9,500
c. \$12,500
d. \$22,000

Explanation
Choice “c” is correct. The calculations are:
Total expenditures of \$250,000 ÷ 2 = \$125,000 Average accumulated expenditures
x .10 Interest rate on specific borrowing = \$12,500

Avoidable interest
Compare avoidable interest to actual total interest cost incurred and capitalize the lower amount.
Actual interest:
\$200,000 x .10 = \$20,000
\$150,000 x .07 = \$10,500

Total actual interest cost
= \$30,500 > \$12,500 avoidable interest

OK. My question is really on the first part; why is total expenditure divided by 2 = average accumulated expenditure? I am having a difficult time piecing together that when “\$250,000 is spent uniformly during the year”, dividing by 2 would yield the average accumulated expenditure….

The only reason that I can think of is that construction must have started during middle of the year, like on July 1st. Since only the interest expense during the construction period is capitalized, then the average accumulated expenditure must be the total amount, \$250,000, divided by 2.

Could someone please give me a clearer explanation than the one provided by in Becker? Anonymous
Inactive

source: Mcgraw Hill

because the amount of borrowing is spent OVER A PERIOD of time (in your case over the period of year 3 instead of ALL at once in Jan 1, Year 3), interest is capitalization is determined by averaging (0 + 250000)/2 = 125000*.1 = 12500.

this concept is very similar to weighted-average calculation for EPS in the outstanding shares area.

since the first 200,000 borrowed covers the 125,000 of average expenditures, you only use the 10% interest rate. when the average accumulated expend. exceeds 200,000 you use the next level of interest rates, which is 7% in this case.

Ah I didn't get this either. Thank you derf, this is why I come here. Anonymous
Inactive

When I open the link there are “X” where the “pictures” are supposed to be. Any idea how I can get the info to appear? I tried right clicking and choosing “show picture” but it doesn't work.

Any help will be much appreciated! Anonymous
Inactive

@DJN: lol, I have the same problem as well. I have tried different browsers and still couldn't open the pictures 🙁

I still don't get it. Why is the total spending \$250,000 divided by 2?

If you assume a monthly spending of 250,000/12, the weighted average of spending should be calculated as 250,000/12 x (12/12 +11/12 +10/12 + … +1/12), which is definitely not the same amount as 250,000/2

where did I get wrong?? Thanks!!

AUD: 64, 71, 73, 72, 78
FAR: 75 (expired), 79
BEC: 89
REG: 76

FINGERS CROSSED

The key issue here is not “Average” Accumulated Expenditure, it's the expenditures “generate” interest.

We all know the interest is calculated based on average accumulated expenditure. That means for every penny we spend on the project, we pay interest for it.

Back to the question, \$250,000 spent uniformly throughout the year, or we can say “evenly” throughout the year. That means we didn't spend the money at one single point of time. We split it. Let's assume we spend equal amount everyday, which means 250,000/365=684.93 everyday for entire year 3.

Notice, for expenditure spent on January 1, it generates interest for 365 days, on January 2, 364 days, January 3, 363 days…..December 31, 1 day. The rational behind this is the later we spend the money, the less interest we should pay for it.

Thus, the weighted average time period which our daily 684.93 generates interest is (365+364+363+…..+1)/365= 183 days.

Now let's calculate the total expenditures which generate interest: 684.93 x 183 = 125,342.19, which is approximately 250,000/2=125000.

Notice, the thing reaaaaaaaaally confused us in the explanation is the terminology of “average” accumulated expenditure. This is not a really good explanation. I know what are you thinking: the expenditure is the “expenditure”! Average expenditure should be the same amount of 250,000. What the hell of “divide by 2” coming from??? But, If we modify it to average accumulated expenditure which generates interest, then you will find it's actually easy to understand.

I hope you can figure it out now.

PS: You can explain the warranty type question with the same method which I mentioned above. The amount of capitalized interest is the lower of:
a. Avoidable interest = 125,000 x 10% = 12,500
Weighted average amount of accumulated expenditure
= 250,000/12 x (11.5/12 + 10.5/12 + 9.5/12 + 8.5/12…+ 0.5/12)
= 250,000/12 x 12×12/2 /12
= 250,000/12 x 6
= 250,000 x 6/12 = 125,000

b. Actual interest = 200,000 x 10% + 150,000 x 7% = 30,500

Capitalized interest = 12,500 (12,500 < 30,500) Anonymous
Inactive

250,000 x 6/12 = 125,000?

OR

250,000/2 = 125,00?

I’m still confused here.
How and why?

you can think of it like calculating weighted average shares outstanding with a catch, you have to weight the intra-monthly expense as well
250,000 is spent evenly throughout the year aka monthly expense is 250,000/12= 20,833.33
if this \$20,833 expense happened all on day 1, the expense would be outstanding for the full month or 30 days
however the tricky part is that this monthly expense occurs throughout the month, not all at the beginning of the month
on day 0 we have \$0 total expense and by day 30 we have the full amount of \$20,833 monthly expense
therefore the average days outstanding for this monthly expense is the beginning days (day 0, \$0) plus the ending days (day 30, full \$20,833) 0+30/2 = 15 days outstanding or .5 month
thus the january expense is outstanding 15 days in january + the full rest of the 11 months in the year for a total 11.5 months
the february expense is then outstanding 15 days in february + the full rest of the 10 months in the year for a total 10.5 months etc

january expense is outstanding for 11.5 months so 20,833.33 x 11.5/12 = 19965
february expense is outstanding for 10.5 months so 20,833.33 x 10.5/12 = 18229
march expense is outstanding for 9.5 months so 20,833.33 x 9.5/12 = 16493
20,833.33 x 8.5/12 = 14757
20,833.33 x 7.5/12 = 13021
20,833.33 x 6.5/12 = 11285
20,833.33 x 5.5/12 = 9548
20,833.33 x 4.5/12 = 7812
20,833.33 x 3.5/12 = 6076
20,833.33 x 2.5/12 = 4340
20,833.33 x 1.5/12 = 2604
the december expense is outstanding for only 15 days or .5 months so 20,833.33 x .5/12 = 868
total: 124,998 average accumulated expense for the year

as you can see it is much easier and faster to use the shortcut: beginning balance (0) + ending balance (250,000) /2 = \$125,000
this works because the expense occurs “uniformly” or “evenly” throughout the year, therefore
for every dollar spent on day 1 (365 days outstanding) there is a dollar spent on day 365 (0 days outstanding) 365+0 /2= 365/2 = .5 year average outstanding
for every dollar spent on day 2 (364 days outstanding) there is a dollar spent on day 364 (1 day outstanding) 364+1 /2 = 365/2 = .5 year average outstanding
for every dollar spent on day 3 (363 days outstanding) there is a dollar spent on day 363 (2 days outstanding) 363+2 /2 = 365/2 = .5 year average outstanding
thusly we can simply take the uniform expense and multiply by .5 year average outstanding
restated that is expense/2 = average accumulated expense

125000 x 10% interest = 12500 🙂

AUD :56, 72, 77!
FAR : 74, 77!
BEC : 72, 75!
REG : 72, 81! Anonymous
Inactive

@Jott, the explanation below enables me to grasp some of it:
As you can see it is much easier and faster to use the shortcut: beginning balance (0) + ending balance (250,000) /2 = \$125,000

So thanks a lot!

(BEgin interest 0+ end 365 )/2 that's the average JoCuatro