Accounting Assignment with Solution
1. A highway department is considering building a temporary bridge to cut travel time during the three years it will take to build a permanent bridge. The temporary bridge can be put up in a few weeks at a cost of $740,000.
At the end of three years, it would be removed and the steel would be sold for scrap. The real net cost of this would be $81,000.
Based on estimated time savings and wage rates, fuel savings, and reductions in risks of accidents, department analysts predict that the
benefits in real dollars would be $275,000 during the first year,
$295,000 during the second year, and
$315,000 during the third year.
Departmental regulations require use of a real discount rate of 5 percent.
- Calculate the present value of net benefits assuming that the benefits are realized at the end of each of the three years.
- Calculate the present value of net benefits assuming that the benefits are realized at the beginning of each of the three years.
- Calculate the present value of net benefits assuming that the benefits are realized in the middle of each of the three years.
- Calculate the present value of net benefits assuming that half of each year’s benefits are realized at the beginning of the year and the other half at the end of the year.
- Does the temporary bridge pass the net benefits test?
2. A government data processing center has been plagued in recent years by complaints from employees of back pain. Consultants have estimated that upgrading office furniture at a net cost of $425,000 would reduce the incidence and severity of back injuries, allowing the center to avoid medical care that currently costs $68,000 each year.
They estimate that the new furniture would also provide yearly benefits of avoided losses in work time and employee comfort worth $18,000.
The furniture would have a useful life of five years, after which it would have a positive salvage value equal to 10 percent of its initial net cost. The consultants made their estimates of avoided costs assuming that they would be treated as occurring at the beginning of each year.
In its investment decisions, the center uses a nominal discount rate of 9.5 percent and an assumed general inflation rate of 3 percent. It expects the inflation rate for medical care will run between 3 percent and 5 percent but is uncertain as to the exact rate. In other words, it is uncertain as to whether the cost of medical care will inflate at the same rate as other prices or rise 2 percent faster.
Should the center purchase the new furniture?
3. A town’s recreation department is trying to decide how to use a piece of land.
One option is to put up basketball courts with an expected life of eight years.
Another is to install a swimming pool with an expected life of 24 years.
The basketball courts would cost $180,000 to construct and yield net benefits of $40,000 at the end of each of the eight years.
The swimming pool would cost $2.25 million to construct and yield net benefits of $170,000 at the end of each of the 24 years.
Each project is assumed to have zero salvage value at the end of its life.
Using a real discount rate of 4 percent, which project offers larger net benefits?
Question 1 Solution
ANSWER (a)
Benefits accrue at the end of year:
PV(benefits)
= $275,000/(1+.05)1+ = $261,905
$295,000/(1+.05)2+ = $267,574
$315,000/(1+.05)3 = $272,109
= $801,588
NPV = $801,588-
$809,971 w1
= -$8,383
Working 1:
Begin by calculating the present value of the costs, which are realized at the beginning of year 1 and at the end of year 3:
PV(cost) = $740,000+$81,000/(1+.05)3
= $740,000+$69,971
= $809,971
ANSWER (b)
Benefits accrue at the beginning of year:
PV(benefits)
= $275,000+ = $275,000
$295,000/(1+.05)1+ = $280,952
$315,000/(1+.05)2 = $285,714
=$841,666
NPV
= $841,666-
$809,971
= $31,695
Answer (c)
Benefits accrue at mid-year:
PV(benefits)
= $275,000/(1+.05).5+ = $268,373
$295,000/(1+.05)1.5+ = $274,181
$315,000/(1+.05)2.5 =$278,829
= $821,383
NPV = $821,383-$809,971
= $11,412
ANSWER (d)
Benefits split equally between beginning and end of year:
PV(ben) = ($801,588 + $841,666)/2 = $821,627
NPV = $821,627-$809,971 = $11,656.
Alternatively, average the answers to parts a and b: ($-8,383 + $31,695)/2 = $11,656.
Answer (e)
The sign of the present value of net benefits depends on when the benefits are assumed to accrue. In this case, they accrue as various savings throughout the year, so either method (c) or (d) is most appropriate, and the temporary bridge passes the net benefits test.
Note that even more accurate methods of discounting would involve estimating the benefits on a monthly, weekly, or even daily basis. Such refinement in the specification of the timing of benefits, however, would usually amount to false precision, given uncertainties in their measurement and the appropriate social discount rate.
Question 2 Solution
Working in real dollars, the first task is to
convert the nominal discount rate to a real discount rate:
d = (.095-.03)/(1+.03)
= .063
A major benefit is avoided medical care costs.
If it is assumed that the price of medical care inflates at the same rate as the general price level, then all the costs and benefits are in real dollars and the present value can be calculated as:
NPV = (-$425,000 + $68,000 + $18,000)
+ ($68,000 + $18,000)/(1+.063)1
+ ($68,000 + $18,000)/(1+.063)2
+ ($68,000 + $18,000)/(1+.063)3
+ ($68,000 + $18,000)/(1+.063)4
+ ($42,500)/(1+.063)5
= -$339,000 + $80,903 + $76,108 + $71,598 + $67,354 + $31,313
= -$11,724.
If, instead, it is assumed that the price of medical care inflates 2 percent faster than the general price level, then the net benefits are calculated as follows:
NPV = (-$425,000 + $68,000 + $18,000)
+ ($69,360 + $18,000)/(1+.063)1
+ ($70,747 + $18,000)/(1+.063)2
+ ($72,162 + $18,000)/(1+.063)3
+ ($73,605 + $18,000)/(1+.063)4
+ ($42,500)/(1+.063)5
= -$339,000 + $82,183 + $78,539 + $75,063 + $71,744 + $31,313
= -$158
In this case, the purchase would not pass the net benefits test if it were assumed that medical care prices will rise at the general rate of inflation, or if it were assumed medical care prices will rise 2 percent faster than the general rate of inflation. Though medical care prices have appeared to rise substantially faster than other prices in recent years in the United States, some of the faster increase may result because medical care price indexes do not take full account of improvements in the quality of care.
If the consultants assumed instead that the avoided costs will occur at the end of each year instead of at the beginning of each year, the NPV would be lower. In fact, with medical care prices rising 2 percent faster than general inflation, the NPV would be:
NPV = -$425,000
+ ($69,360 + $18,000)/(1+.063)1
+ ($70,747 + $18,000)/(1+.063)2
+ ($72,162 + $18,000)/(1+.063)3
+ ($73,605 + $18,000)/(1+.063)4
+ ($75,077 + $18,000 + $42,500)/(1+.063)5
= -$425,000 + $82,183 + $78,539 + $75,063 + $71,744 + $99,889
= -$17,582.
Question 3 Solution
As only one of these projects can be built on the site, they are mutually exclusive. The comparison is complicated because the swimming pool has an expected life three times longer than the basketball courts.
Consider first the NPV of each project separately:
NPV(one basketball court project)
NPV(one swimming pool project)
If we choose on the basis of this comparison, then the swimming pool has a larger present value of net benefits. A proper comparison, however, would be between one swimming pool and three successive basketball court projects so that the site is used in each case for the same length of time.
NPV(three successive basketball court projects)
= $89,310 + $89,310/(1+.04)8 + $89,310/(1+.04)16
= $89,310 + $65,258 + $47,683
= $202,251
Equivalent Annualised Return
(EAR)
Thus, three successive basketball court projects offer a lower present value of net benefits than the swimming pool project. One should build the pool.
An alternative approach for comparing these projects of different lengths is to divide each project’s NPV by its appropriate annuity factor to find its equivalent annual net benefits, an approach called "amortization." The appropriate annuity factor in each case can be obtained by using the formula for the present value of an annuity found in Appendix 6a.
The 8-year annuity factor = [1-(1+.04)-8]/(.04) = 6.7327
Annualized NB for the basketball court = ($89,310)/6.7327 = $13,265
The 24-year annuity factor = [1-(1+.04)-24]/(.04) = 15.247
Annualized NB for the swimming pool = ($341,984)/(15.247) = $22,430
The basket ball court project offers net benefits equivalent to an annuity paying $13,265 each year over its life. The swimming pool offers net benefits equivalent to an annuity paying $22,430 each year over its life.
Dillon Products manufactures various machined parts to customer specifications. The company uses a job- order costing system and applies overhead costs to jobs on the basis of machine-hours. At the beginning of the year, the company used a cost formula to estimate that it would incur $4,271,200 in manufacturing overhead cost at an activity level of 562,000 machine-hours The company spent the entire month of January working on a large order for 8,400 custom made machined parts. The company had no work in process at the beginning of January. Cost data relating to January follow: a. Raw materials purchased on account, $317,000 b. Raw materials requisitioned for production, $271,000 (80% direct and 20% indirect) c. Labor cost incurred in the factory, $174,000, of which $58,000 was direct labor and $116,000 was indirect labor. d. Depreciation recorded on factory equipment, $63,000. e. Other manufacturing overhead costs incurred, $86,000 (credit Accounts Payable). f. Manufacturing overhead cost was applied to production on the basis of 40,550 machine-hours actually worked during the month. g. The completed job was moved into the finished goods warehouse on January 31 to await delivery to the customer. (In computing the dollar amount for this entry, remember that the cost of a completed job consists of direct materials, direct labor, and applied overhead.) Required: 1. Prepare journal entries to record items (a) through (f above. re item (g) for the moment (If no entry is required for a transactionlevent, select \"No jo urnal entry required\" in the first account field. Do not round intermediate calculations.) view transaction view general journal st Transaction General Journal Debit Credit Raw materials 317,000 Accounts payable 317,000 Direct materials 212,800 212,800 Raw materials Indirect materials 53,200 53,200 Raw materials d. Direct labor 53,000 106,000 Indirect labor Wages and salaries payable 159,000 e. Depreciation 63,700 Accumulated depreciation 63,700 63,700 Depreciation 63,700 Depreciation
Solution
Preparation of journal entries
Cash/ Bank A/C
(To record bond purchase at fair value and not separted as bond premium)
3% Bond revaluation A/C = $ 314,140.38 - $ 313,000
3% Bond A/C
(To recoed interest and bond revaluation
Interest A/C
(To record the interest received)
Interest A/C
3% Bond A/C
(To record interest and revaluation)
Interest A/C
(To record interest received)
Interest A/C
(To sale of bond amount recognised)
3% Bond revalution A/C
(To record loss on Bond sale)
The single entry can be passed for december 31, 2017 to record transaction but separated for bettere understanding. The loss on bond can be charged to profit and loss account or to retain earning as per company policy but it is loss and interest credited to profit and loss account as income.
Total gain or loss from bond = interest income = $ 9,000 + $ 9,000 + $750 - $ 4,140.38 loss on valuation = $ 14,609.62 profit over the period.DateAccounts titles and explanationDebit in dollarsCredit in dollarsNov. 30 ,20153% Bond A/C$ 314,140.38
Cash/ Bank A/C
(To record bond purchase at fair value and not separted as bond premium)$ 314,140.38Dec. 31, 2015
3% Bond revaluation A/C = $ 314,140.38 - $ 313,000$ 1,140.38Accroued interest Interest A/C$750Interest A/C $300,000 * 3% /12 or $ 750$750
3% Bond A/C
(To recoed interest and bond revaluation$1,140.38Nov. 30, 2016Cash/ Bank A/C$9,000Accured interest A/C$750
Interest A/C
(To record the interest received)$8,250Dec. 31, 20163% Bond revaluation A/C $ 313,000 - $ 312,000$1,000Accrued interest A/C$750
Interest A/C$750
3% Bond A/C
(To record interest and revaluation)$1,000Nov. 30, 2017Cash/ Bank A/C$ 9,000Accrued interest A/C$ 750
Interest A/C
(To record interest received)$ 8,250Dec. 31, 2017Cash/ Bank A/C $ 310,000 + interest for one month $ 750$310,7503% Bond A/C$310,000
Interest A/C
(To sale of bond amount recognised)$ 750Dec. 31, 2017Profit / Loss on Bond A/C$4,140.383% Bond A/C $ 312,000 - $ 310,000$ 2,000
3% Bond revalution A/C
(To record loss on Bond sale)$ 2,140.38
