PROBLEM 6.3
Time diagram (Bid A):
i = 9%
W69,000
PV – OA = R =
? 3,000 3,000 3,000 3,000 69,000 3,000 3,000 3,000 3,000 0
n = 9
W 69,000
PROBLEM 6.3 (Continued)
Time diagram (Bid B):
i = 9%
W126,000
PV – OA = R =
? 1,080 1,080 1,080 1,080 1,080 1,080 1,080 1,080 1,080 0
Present value of initial cost
12,000 X W10.50 = W126,000 (incurred today) …….
W126,000.00
Present value of maintenance cost
12,000 X W.09 = W1,080
R (PV – OA9, 9%) = W1,080 (5.99525) ……………………
PROBLEM 6.4
Lump sum alternative: Present Value = $500,000 X (1 – .46) = $270,000.
Annuity alternative: Payments = $36,000 X (1 – .25) = $27,000.
PROBLEM 6.5
(a) The present value of €55,000 cash paid today is €55,000.
(b) Time diagram:
i = 21/2% per quarter
PV – OA = €62,357
(c) Time diagram:
i = 21/2% per quarter
€18,000
PV – AD =
PROBLEM 6.5 (Continued)
Formula: PV – AD = R (PVF – ADn, i)
(d) Time diagram:
i = 21/2% per quarter
PV – OA = R =
? €1,500 €1,500 €1,500 €1,500
PV – OA = R =
? €4,000 €4,000 €4,000
0 1 11 12 13 14 36 37
PROBLEM 6.5 (Continued)
Present values:
(a) €55,000.
Time diagram:
i = 12%
PV – OA = ? R =
(€39,000) (€39,000) €18,000 €18,000 €68,000 €68,000 €68,000 €68,000 €38,000 €38,000 €38,000
€12,000)
€12,000)
€12,000)
Formulas:
PV – OA = R (PVF – OAn, i)
PV – OA = R (PVF – OAn, i)
PV – OA = R (PVF – OAn, i)
PV – OA =R (PVF – OAn, i)
PV – OA = (€39,000)(PVF – OA5, 12%)
PV – OA = €18,000 (PVF – OA10–5, 12%)
PV – OA = €68,000 (PVF – OA30–10, 12%)
PV – OA = €38,000 (PVF – OA40–30, 12%)
PV – OA = (€39,000)(3.60478)
PV – OA = €18,000 (5.65022 – 3.60478)
PV – OA = €68,000 (8.05518 – 5.65022)
PV – OA = €38,000 (8.24378 – 8.05518)
PV – OA = (€140,586)
PV – OA = €18,000 (2.04544)
PV – OA = €68,000 (2.40496)
PV – OA = €38,000 (.18860)
PV – OA = €36,818
PV – OA = €163,537
PV – OA = €7,167
Present value of future net cash inflows:
€(140,586)
36,818
Copyright © 2018 Wiley Kieso, IFRS, 3/e, Solutions Manual (For Instructor Use Only) 6-47
PROBLEM 6.7
(a) Time diagram (alternative one):
i = ?
PV – OA =
$600,000 R =
$80,000 $80,000 $80,000 $80,000 $80,000
7.50 is the present value of an annuity factor of $1 for 12 years
discounted at an interest rate of approximately 8%.
Time diagram (alternative two):
i = ?
PV = $600,000 FV = $1,900,000
PROBLEM 6.7 (Continued)
Future value approach
Present value approach
FV = PV (FVFn, i)
PV = FV (PVFn, i)
$1,900,000 = $600,000 (FVF12, i)
$600,000 = $1,900,000 (PVF12, i)
(b) Time diagram:
i = ?
($824,150 – $200,000)
PV – OA = R =
$624,150 $76,952 $76,952 $76,952 $76,952
PROBLEM 6.7 (Continued)
Formulas: PV – OA = R (PVF – OAn, i)
(c) Time diagram:
i = 5% per six months (10% ÷ 5)
PV = ?
PV – OA = R =
? $32,000 $32,000 $32,000 $32,000 $32,000 ($800,000 X 8% X 6/12)
PROBLEM 6.7 (Continued)
(d) Time diagram (future value of $200,000 deposit)
i = 21/2% per quarter (10% ÷ 4)
PV =
$200,000 FV = ?
Amount to which quarterly deposits must grow:
$1,300,000 – $537,012 = $762,988.
Time diagram (future value of quarterly deposits)
PROBLEM 6.7 (Continued)
Formulas: FV – OA = R (FVF – OAn, i)
PROBLEM 6.8
Vendor A:
£18,000
Annual Payment
X 6.14457
(PV of ordinary annuity 10%, 10 periods)
£110,602
+ 55,000
down payment
+ 10,000
maintenance contract
£175,602
total cost from Vendor A
Vendor B:
£9,500
semiannual payment
X 18.01704
(PV of annuity due *5%, **40 periods)
£171,162
*(10 ÷ 2) **(20 periods x 2)
Vendor C:
£1,000
X 3.79079
(PV of ordinary annuity of 5 periods, 10%)
£ 3,791
PV of first 5 years of maintenance
£2,000
[PV of ordinary annuity 15 per., 10% (7.60608) –
X 3.81529
PV of ordinary annuity 5 per., 10% (3.79079)]
£3,000
[(PV of ordinary annuity 20 per., 10% (8.51356) –
X .90748
PV of ordinary annuity 15 per., 10% (7.60608)]
£ 2,722
PV of last 5 years of maintenance
Total cost of press and maintenance Vendor C:
£150,000.00
cash purchase price
3,791
maintenance years 1–5
7,631
maintenance years 6–15
2,722
£164,144
PROBLEM 6.9
(a) Time diagram for the first ten payments:
i = 10%
PV–AD = ?
R =
$800,000 $800,000 $800,000 $800,000 $800,000 $800,000 $800,000
Formula for the first ten payments:
PV – AD = R (PVF – ADn, i)
Formula for the last ten payments:
PV – AD = R (PVF – ADn, i)
Note: The present value of an annuity due is used here, not the
present value of an ordinary annuity, although it may be used.
PROBLEM 6.9 (Continued)
The total cost for leasing the facilities is:
$5,407,216 + $1,042,360 = $6,449,576.
Formulas for the last ten payments:
(i) Present value of the last ten payments:
PV – A = R (PVF – ADn, i)
PROBLEM 6.9 (Continued)
(ii) Present value of the last ten payments at the beginning of current
year:
PV = FV (PVFn, i)
(b) Time diagram:
i = 11%
PV – OA = ?
R =
$15,000 $15,000 $15,000 $15,000 $15,000 $15,000 $15,000
PROBLEM 6.9 (Continued)
Formula: PV – OA = R (PVF – OAn, i)
(c) Time diagram:
Amount paid =
$792,000
If the company decides not to take the cash discount, then the company
can use the $792,000 for an additional 20 days. The implied interest
rate for postponing the payment can be calculated as follows:
(i) Implied interest for the period from the end of discount period to
the due date:
PROBLEM 6.9 (Continued)
(ii) Convert the implied interest rate to annual basis:
Daily interest = 0.010101/20 = 0.000505