練習和計算題 財-A 4990S053 陳柔穎
1. (1)FV=$10,000×FVIF(3,12%)=$10,000×1.4049=$14,049 (2)FV=$10,000×FVIF(6,6%)=$10,000×1.4185=$14,185 (3)FV=$10,000×FVIF(12,3%)=$10,000×1.4258=$14,258
(4)FV=$10,000×FVIF(36,1%)=$10,000×FVIF(30,1%)×FVIF(6,1%)
=$10,000×1.3478×1.0615=$14,308
2. $10,000×PVIF(3,10%)=$10,000*0.7513=$7,513
3. (1) FVA=$10,000×FVIFA(20,12%)=$10,000×72.052=$720,520 (2) FVA=$5,000×FVIFA(40,6%)=$5,000×154.76=$773,800 (3) FVA=$2,500×FVIFA(80,3%)
=$2,500×FVIFA(40,3%)×(FVIF(40,3%)+1)=$2,500×75.401×(3.2620+1)
=$2,500×321.359=$803,398
4. PVA=$5,000×PVIFA(36,1%)×(1+1%)=$5,000×(PVIFA(35,1%)+1)
=$5,000×(29.4086+1) = $152,043 5. (1)設可提n 次，則
$150,000×PVIFA(n,8%)=$1,283,922
則 PVIFA(n,8%)=8.55948 查年金現值表知，n=15 (2)設張三每年提PMT 元，則
PMT×PVIFA(20,8%)×(1+8%)=$1,283,922 因 PVIFA(20,8%)=9.8181 得 PMT=$130,771 即張三每年提$130,771
(3)設每年提PMT 元，則
PMT×PVIFA(15,8%)×(1+8%)=$1,283,922
因 PVIFA(15,8%)×(1+8%)=PVIFA(14,8%)+1=8.2442+1=9.2442 故 PMT=
9.2442
$1,283,922
=$138,889
即張三每年提$138,889
(4) PMT×PVIFA(19,8%)-PMT×PVIFA(4,8%)=$1,283,922 PMT(9.6036-3.3121)=$1,283,922
PMT=
6.2915
$1,283,922
=$204,073
或 PMT×PVIFA(15,8%)×PVIF(4,8%)=$1,283,922 因 PVIFA(15,8%)×PVIF(4,8%)=8.5595×0.7350
=6.2912325
∴ PMT=
6.2915
$1,283,922
=$204,073
即張三每年提$204,073
6. (1)設每期應攤還本息PMT 元，則 PMT×PVIFA(40,3%)=$1,000,000
因 PVIFA(40,3%)=23.114772 故 PMT=$43,262
(2)
期別 利息(1)=上期(3) ×0.03 償還之本金(2)=$43,262-(1) 剩餘應付本金(3)=上期(3)-(2) 0 $1,000,000
1 $30,000 $13,262 986,738 2 29,602 13,660 973,078 3 29,192 14,070 959,008 7. (1)市場利率為8%時，
本金$1,000,000，利率4%，20 期的複利現值
=$1,000,000×PVIF(20,4%)=$1,000,000×0.4564=$456,400 利息$50,000，利率4%，20 期的年金現值
=$50,000×PVIFA(20,4%)=$50,000×13.5903= $679,515 公司債的本金和利息現值合計 $1,135,915 分錄如下：
現金 1,135,915
應付公司債 1,000,000 應付公司債溢價 135,915
(2)因市場利率10%=票面利率10%，故無折、溢價。
分錄如下：
現金 1,000,000
應付公司債 1,000,000 (3)當市場利率為12%時，
本金$1,000,000，利率6%，20 期的複利現值
=$1,000,000×PVIF(20,6%)=$1,000,000×0.3118=$311,800 利息$50,000，利率6%，20 期的年金現值
=$50,000×PVIFA(20,6%)=$50,000×11.4699= $573,495 公司債的本金和利息現值合計 $885,295
分錄如下：
現金 885,295
應付公司債折價 114,705 應付公司債 1,000,000
8. (1)A=$2,000,000×FVIFA(5,10%)=$2,000,000×6.1051
=$12,210,200 (2)設須n 年，則
A=$2,000,000×FVIFA(n,12%)=$20,178,024 得 FVIFA(n,12%)=10.089012
查年金終值表知，n=7 即須七年。
(3)設利率為i，則
A=$2,000,000×FVIFA(5,i)=$12,400,000 得 FVIFA(5,i)=6.2
查年金終值表知，FVIFA(5,10)=6.105100 FVIFA(5,12)=6.352847
利用插補法：
6.352847 6.105100 0.12 0.10
=
6.2 6.105100 0.10
i
得 i=10.77%
9.本題要從遞延普通年金現值的觀點來看。
大學四年所花的費用現值為：
$180,000×PVIFA(4,10%)=$180,000×3.169865=$570,576 而少赚的收入現值為
$60,000×PVIFA(4,10%)=$60,000×3.169865= $570,576 費用和收入的現值合計 $760,768
設王君至少須花n 年，方能赚回上述的費用和收入，則
$120,000×PVIFA(n,10%)×PVIF(4,10%)≧$760,768 得 PVIFA(n,10%)≧
$120,000 (4,10%)
$760,768
PVIF
=
$120,000 0.683013
$760,768
=9.28201
查年金現值表，知PVIFA(28,10%)=9. 306567>9. 28201 即王君至少要花28 年。
10. 應付公司債$2,000,000，利率8%，十期的複利現值為：
$2,000,000×PVIF(10,8%)=$2,000,000×0.463193
=$926,386
每期基金$100,000，利率8%，3 期的年金現值為：
$100,000×PVIF(3,8%)=$100,000×2. 577097
=$257,710
而未提撥基金的現值=$926,386-$257,710=$668,676 R×PVIFA(7,8%)×PVIF(3,8%)=$668,676
因 PVIFA(7,8%)×PVIF(3,8%)=5. 206370×0.793832=4.132983 得 R=$161,790。
11. (1)張三前期服務成本為：
$10,000×15×PVIFA(12,10%)×PVIF(25,10%)=$150,000×6.813692×0.092296
=$94,331
(2)公司在張三65 歲退休時全部服務年資所負擔的退休金成本為：
$10,000×40×PVIFA(12,10%)=$400,000×6.813692
=$2,725,477
08 年1 月1 日現值為$2,725,477×PVIF(25,10%)=$251,551 (3)假設公司每年提撥基金R，則
R×FVIFA(25,10%)=$2,725,477 因 FVIFA(25,10%)=98.347059 得 R=$27,713
即每年應提基金$27,713。
12. (1)收入現值：
$200,000×PVIFA(5,8%)=$200,000×3.992710= $798,542
$250,000×PVIFA(5,8%)×PVIF(5.8%)=$250,000×3.992710×0.680583= $679,343
$300,000×PVIFA(10,8%)×PVIF(10,8%)=$300,000×6.710081×0.463193=$932,419
$150,000×PVIFA(10,8%)×PVIF(20,8%)=$150,000×6.710081×0.214548=$215,945 收入現值合計： $2,626,249
(2)成本支出現值：
($50,000+$60,000)×PVIFA(308%)=$110,000×11. 257783
=$1,238,356
根據(1)、(2)，若王五向李四頂讓這塊果園，則其合理價格為$1,387,893
即$2,626,249-$1,238,356
13. (1)科瑞公司在第三十五年底所累積的數額
= $300,000×FVIFA(30,12%)=$300,000×241.332684
=$72,399,805
其在第一年年底的現值
=$72,399,805×PVIF(35,12%)=$72,399,805×0.018940
=$1,371,252
(2)科瑞公司再第五年年底的現值
=$300,000×PVIFA(30,12%)=$300,000×8.055184
=$2,416,555
其在第一年年底的現值
=$2,416,555×PVIF(5,12%)=2,416,555×0.567427
=1,371,218
註：兩法計算結果應相同，上述(1)與(2)不同係因小數點進位產生的差異。
