solluation

1. Solutions to Problems
P5-1. Usine a time line
LG 1; Basic
a b, and c
Compounding
P5—
2.
P5—
3.
Discountlng
d. Financial managers relv more on present value than future value because they
pically make decisions before the start of a pro ect. at time zero as does the
present value calculation.
Future value
calculation LG 2;
Basic
Case
A N - 2, I - 12%, PV - SI, Solve for FV =
1.2544 B N = 3, I = 6% PV = SI, Solve for FV
= 1.1910 C N = 2, I = 9%, PV = SI, Solve for
FV = 1.1881 D N = 4, I = 3% PV = SI, Solve for
FV = 1.1259
Time to double
LG 1; Basic
Case A: Computer Inputs: I=12%, PV=—S100, FV=
5200 Solve for N = 6.12 years
CaseB: Computer Inputs: I= S%,P4*= —$100: M" =
5200 O N = 11.90 years
It takes just short of tuice as lone to double in value. One reason for it beme shorter is
that in Case B there are more periods over o°hich compounding occurs.
Future
V8Iue

2. .S"ofr..’ You could use the "Rule of 72 to complete the problem Simply dii‘ide 72 by the
interest rate to net the number' of years it u‘ould take to double or initial balance.
Future i alues
LG 2; Intermediate
Case
.4 N = 20. I = 5%. PM" = S200
Soh e for FX' = S530.66
C N = 10 I = 9% PM’ =
S10.000 So1i‘e for FY' =
523.573.64
E N = . I = 11. PM’ =S37.000
Soh e for FX' = SS2.*47.IN
Personalfinance: Timex
alue LG 2; Intermediate
a. (I) N — 3. I — 7%. PX — S
I.J00 So1i‘e for FX'; —
S1.537.56
(?) N = 6. I = loo. PM' = S1
TOO
Sole efor FX'r S2 251 10
Case
B N = 7. I Y = 8%: PX' =
54500 Sol e for FT' = S7.
1.2.21
D N= 12 I = 10< . PX* =S2
5.000 So1i‘e forFT'=
578.460. 71
F N = 9. I = 12. PX =
540.000
Sol e forFT' = S1.10.92* 15
b. (1) Interest earned — F i^ —
PM
Interest earned — SI.83 7. 56
S1.500.00
S337 •,6
(2) Interest earned = I
— U; Interest
earned 52.251.10
(3) Interest earned — FVg —
lbs Interest earned S .
7.69
—So 2. 1. 10
S506 •,9
c. The fact that the louder' the investment period is. the larger the total amount of
interest collected will be. is not unexpected and is due to the Greater length of time
that the principal sum of 51.500 is nn‘ested. The mostsignificant ponit is that the
incremental interest eaiaied per 3-year period increases with each siibsequent 3-
year period. The total interest for the lust 3 x ears is S337.56: however. forthe
second3 ear's (from ;°eai' 3to 6)the additional interest earned is 5413.5fi. For the
third 3-year period. the incremental interest is SS 06.59. This iiicrrasine chance m
interest earned is due to compounding. the eaiaiing of interest on
pi'ex ions intei'est earned. The created the previous interest earned. the water' the
impactof compounding.

3. P5—
6.
Pmsoix4fnaime:Timeiflue
LG2;CAm¥eoge
a. (1) N = 5, I = 2P«, PV = $14,000 (2) N = 5, I = 4%, PV = $14,000
So1x'e for FV= $15,457.13 Solve for FV $17,033.14
b. The car wifi coat $1,576.01 more with a 4Po utBahon rate flian an inflafion rate
of 2%. This increase is 10.2% more ($1,576 + $15,457) trim would be paid with
only a 2% rale of
c. Future value at end of first 2
years: N = 2, I = 2%, PV =
$14,000 Solar for 2
$14,565.
Price rise at end of 5th year:
N = 3, I = 4%, PV =
$14,565.60 CO)¥'D f 5'
$16,384.32
As cue would expect, the forecast price is between the Blues calculated with 2%
and 4%
interest.
P5-7. Personal finance: Time value
LG 2; Challenge
Deposit Now: Deposit in 10 Years:
N = 40, I = 9%, PV = $10,000
Solve for FV = $314,094.20
N = 30, I = 9Wo, PV = $10,000
Solve for FV = $132,676.78
You would be better off by $181,417 ($314,094 — $132,677) by investing the
$10,000 now instead of citing for 10 years to makethe ink cut.
P5-8. Personal finance: Time value
LG 2; Challenge
P5—
9.
a. N = 5, PV = —$10,200, FV = 15,000
Solve for I = 8.02%
c. N = 5, PV = —$ 7150, FV= $15,000
Solve for I = 15.97%
Personal finance: Single-payment loan
repayment
LG 2; Intermediate
a. N = 1, I = 14%, PV = $200
Solve for FV = $228
c. N = 8, I = 14%, PV = $200
Solve for FVg = $570.52
b N = 5, PV = —$8,150, FV =
$15,000
Solve for I = 12 98Wo
b. N = 4, I = 14%, PV = $200
Solve for 4 - $3S7.79

4. PS—
10
PS—
11
Present value calculation. PDIF =
I
(i * )'
LG 2;
Basic
Case
.4 h = 4. I = FT' = Al 00. Sole e for Pfi*= TO 9?3S
B h = *. I = 10. FT' = Al00. Sole e for Pfi*= TO 8?64
C h — 3. I — 5 FT' — Al 00. Sole e for Pfi* — TO 8635
D h = *. I = l3. FT' = Al 00. So1i‘e for Pfi* = TO.7fi 31
LG 2; Basic
Case P’
Present value
concept LG 2;
Intermediate
a. N — 6. I — 12%. FT" —
56.000
Soli‘e for PM’ = S3.03 9
79
c. N 6. I 12%. FT"
S6.000
Soli‘e forPM’ =S3.039.79
b. N — 6. I — 12ââ. FX —
56.000 Sole-e Koi'PM” =
S3.039 79
d. The ariseer to all three parts is the same. In each casethe samequestion is being
asked hilt in a different wax.
Personal firorce. Time X
aliie LG 2; Basic
a. N = 3. I = 7%. FX* = 5500
Soli‘e for PM’ = 5408.15
b. Inn should be willing to pay no morethan 5408.15 for this future siim cixen
that his opportimin° cost is i%
c. If Jim pays less then 408.15. his rate of return will exceed 7°o.
Time value. Present valiie of a lump sum
LG 2; Intermediate
I = 6. I = 8. FX' = 5100
Solee for PX" = SS3.02
860.19613

5. Personal finance: Timexalue and discount
rates LG 2; Intermediate
a. (1) N = 10. I = 6%. M’ = S1.000.000
Soh e for PX' = SSS S.394. 7fi
(3) N 10. 1 1?to. FT" S1.000.000
Solee for PX'=S321973 24
b. (1) N — 15. I — 6%. M’ —
S1.000.000 So1i‘e for PX' =
541.7.265.06
(*) N = 15. I = IN to. Ffi* = S1.000.000
So1i‘e for PM' S182.696 26
(2) N = 10. I = 9 . FX = 51.000.000
Solve for PM’ = S422.410.8 1
(2)h- l:I-915F--51000000
SohefoiPV=S74biS0#
c. As the discount rate increases. the present x alue becomes smaller. This decrease
is dile to
the hieher opportiinin costassociated with the higher rate. Also. the longer the time
until the lotteo' patient is collected. the less the present value due to the gi'eater
time over u hich the opportiinin° costapplies. R other' words. the lamer the discount
rate and the lonser the time nntil the money is receix ed. the smallerwill be the
present x alue of a fiitiu'e payment.
Personal firorce. Timex alue comparisons oflump
sums LG 2; Intermediate
a. .t fi=?.I=11%.FX’=S?8.>00
Solve for PX — S 0.838. 95
C N= 20. I = 11%. FT’=
5160.000
Soleefor'PX S19.845.43
B N = 9. I = 11âfi. FX' = S5fi.000
Sole e for PX° — S21.109. 94
b. Alterriatix es Aand B are both worth sweater than 520.000 in term of the present
value
c. The best alternative is B becaiue the present value of Bis larger than either A or
Cand is also greater than the S20.000 offer.
Personal finance: Cashflowinvestment
decision LG 2; Intermediate
.4 N — 5. I — 10 . FX — 530.000
So1i‘e for PX" = 518.62 7 64
C N — 10. I — 10°t. FX*—
S10.000 Soh e for PX" =
S3.855.43
Purchase Do Not
Purchase A B
C D
Calculatmg deposit
needed LG 2; Challenge
B N — 20. I — 10 . FX — 53.000
So1i‘e for' PM" = 5445. 93
D h — 40. I — 10%. FT’ — 51.000
Sole e for PM’ = S331.4
Step 1: Determination of future v alue of initial tin

6. estment N = 7. I = 5%. PM’ = S10.000
Solve for FX" = S1fi.071 00

7. PS-
19
htep 2: Determination of future value of second ink
estinent S2 0.000 — S1fi.0 71 — 55.929
Step 3: Calculation of initial in estment
N = 4. I = 5%. FT’ = SJ.9 9
Sole e for PX" — 5487 7.80
Futiire i alue of an
aiming LG 3;
Intermediate
a. Future x alue of an ordinary annuit.' vs anniut'.' due
(1) Ordinarn‘ .4nnuitn (2) .4nnuiH Due
4 N = 10. I = go ;: PNfT = S2 500 536 2 16 41 x 1 08 = S?• 9.113. <2
Solve for FX = 536 216 41
B N = 6. I = 12 t. PñfT = 5500
Sole e for FX = Sfi.057. 9
C N = 5. I = 20o ;: PñfT = S30
000
Solve for FX = S223 245
D N= 8.I = 9°t. PS4T =
S11.500
Sole e for FX° = S126.fi 7.4
E N = 30. I = 14° t. PUT =
56.000 Solve for'FX —
S2.140.721.08
8221248x 120=8267S9T60
Si26I2:4: x 109=Si5i2419?
52.140.721.08 x 1.14 =
52.440.442 03
b. The anniut. due results in a greater future x alue in each case. By depositing the pan
ment at the be Drum ng rather than at the end of the year. it has one additional year
of compounding.
Presentvalue of an
annuiH LG 3;
Intermediate
a. Present x alue of or ordinan' annuiH x s annuity' due
(1) Ordinarn‘.4nnuio (2) .Annuity‘ Due
.4 N ?. I 7ho. PUT S1? 000 S31 491. 79 x 1 07 — S33 695 22
Sole e for PM’ = S31.491. 79
B N — 1•,. I — 12°t. PMT — SSS.000
Sole e for PM’ = S37fi. 597.5
C N — 9. I — 20%. PMT — 5700
Soli‘e for PM’ = S2.821.68
D N 7. 1 5to. PUT SI
40.000
Sole e for PM’ = SS10.09? 2
S
E N — 5. I — 10%. PMT — S2L
500
Soli‘e for PM’ = SSS.292.
70

8. l009l2SxL05 5550J9659
565 ?92. 70 x 1.1 — 593.821 97
b. The anniub due results in a greater present i alue in each case. By depositing the
payment at the beerm ne rather than at the end of the year. it has one less x'ear to
discount back*

9. Personal finance: Time x alue-
annuities
LG 3; Challenge
a. AnnuiH‘ C (Ordinam)
(1) N — 10. I — 10%. PMT —
52.500
Solve for FX = S39.843 56
(2) N = 10. I = 20%. PMT =
52.500
Sole e for' FX = S64.896. 71
.4nnuita D (Due)
N — 10.‘I — 10° t. PMT — S? 200
Sole e for FT’ = S3 .0S .*3
Drumm‘ Due Adjustment
S35.062.3 3 x 1.1 —
538.56fi.57 N = IO. I = 20°t.
PMT = S2.TOO
Solve for' FT’ = S5
7.109.10 AnnuiU Due
Adjustment
S•. <.109.10 x 1.2 = 568.5?• 0.92
b. (1) At the end of year 10. at a rate of 10° t. Annuit.' C has a created value (539.8fi3
. 6 xs.
(2) At the end of year 10. at a rate of 20° t. Grimm' D has a greater value
(565.530.92 v s.
564.596. 71).
c. .4nnuin‘ C (Ordiuau) .Annuity D (Due)
(1) N — 10. I — 10%. PMT — 52.500 N 10. 1 10°o. PMT SP.200
Sole e for PX* = SI ..361 14 Solve for PM’ = 51.518.05
Annuifi Due Adjustment
S l3.51fi.05 x 1.1 — S1fi.869.85
(2) N = 10. I = 2 0%. PMT =
52.500
Solve for PX* = S10.fi61. 18
N = l0. I = 20° t. PMT = S? 200
Solve for PM’ = S9 ?23 fi4
AnnuiU' Due Adjustment
59.223.44 x 1.2 = S11.065.13
d. (1) At the beoinnms of the 10 years. at a rate of 1Oââ. Aiimm‘ C has a n'eater
value
(2) At the beeinnine of the 10 years. at a rate of 20ââ. WirimN' D has a
gi'eater x alue (S1.1.068. l3 i s. S10.fi61.1 $)
e. nnui0' C. with an annual payment of SP.500 made at the end of the year. has a
higher present i‘aliie at 10° I than niiuiU' D with an annual payment of S2 ?00
made at the beeinnirie of the 'ear. ten the rate is increased to 20%. the shorter
period of time to discount at the higher rate results in a larger i‘alue for AnnuiU° D.
despite the lou‘er payment.
Personal firorce. Retirement
planning LG 3; Challenge
a. N = fi0. I = 10° t. PMT = 52.000 b. N = 30. I = 10° t. PUT = S? 000
Solee for M’ — SSfi5 185 11 Solve for FT’ — S328.98$ 0
c. By delaying the deposits by 10 years the total opportunio cost is S556.197. This
difference is due to both the lost deposits of 520.000 (S .000 x 10 years) and the
lost compounding of interest on all of the mone; for 10 years.
d AnnuiH‘ Due:

10. N = fi0. I = 10° t. PMT = 52.000
Soli‘e for M’ = 5565.185.11
miiN' Due Adjustment: 5855.185.11 1.10 = 5973.703.62

11. N = 30. I = 10° t. PMT = 52.000
Sole e for M’ = S328.986.OF
nnriiH' Due Adjustment: 5328.98 $.OF 1.10 — S361.fi86.8
Both deposits mcreased due to the extra year of compounding h'om the
beginning-of-year deposits instead of the end-of-year deposits. However. the
incremental chanse in the 40-year annuiU is muchlarger than the incremental
compounding onthe 30-xear deposit (Sfi8.51fi ve. 532.898) due to the lamer sum
on which the last year of compounding occiirs.
Personal finance: X'a1ue of a retirement annuiH'
LG 3; Intermediate
N = 25. I = 9° t. PUT = 51.000
Sole e for PX' = 511.7.8 70.9S
Personal firono : Funding voiir retirement
LG 2, 3; Challenge
a. N — 30. I — 11° t. PMT — 520.000 b. N — 20. I — 9ââ. FX* — 5173.875.85
Sole e for PM’— 5173.8.75.8 . Solve for PM’ — S3 l 0?fi. fi2
c. Both values u‘oiild be lower In other words. a smallershun would be needed in 20 x
eari for the aiiiiuiH and a smaller amount would hai‘e to be put an ay toda to
accumulate the needed futilre snm
d. N — ?0. I — 10°o. PMT — 520.000 b. N — 20. I — 10°o. FX' — 5168.536
29
Sole e for PM’ = S1fi8.536. 9 Solve for PM’ = S fi 025. 02
Store money is ill be required to support the S20.000 annuio iii retirement. became
the initial amount will earn 1O f less per year. How ever. more less money will hat e
to be deposited during the next 20 }‘em. because the i'eturii on saved find will be
l% hishei.
Personal firono : ¥'alue of an anriuiH' i s. a single
amount LG 2, 3; Intermediate
a. N — 25. I — 5%. PMT — 540.000
Soli‘e for PM’ = S . 63./57.78
At 5%. takmg the award as an annum' is better the present value is S563. 760.
compared to receiime5500.000 as alump sum.However.one has toliieatleast 23.5
veari [25 — (63.753.38 excess 540.000)] to benefit more from the aiiriuiU' streairi
of payments
b. N = 5. I = 7%. PMT = 540.000
Sole e for APX' = 5466.1fi3.33
At ^%. taknig the award as a lump sum is better: the present alue of the annui0' is
only 5466.160. compared to the 5500.000 lump-sum payment.
c. X'ieiv this problem as oriris estment of 5000.000 to get a 25-year annuib of
540.000. The discount rate that equates the two sums is 6.24%. calculated at
follow‘s:
N = 5. PX = -S 00.000. PMT = Sfi0.000
Sole e for I = 6.2fi