LESSON 5
Suggested solutions
Question 1 (10 marks)
Computer solution
a. (6 marks)
Of the three GICs, GIC B (10.25%, compounded semi-annually) has the highest maturity
value of €82,419.52.
Excel formula: = FV(B15, B16,, – $B$4)
b. (4 marks)
At first glance, you could expect that either GIC A (with the highest interest rate) or
GIC C (with the most interest compounding periods in a year) would yield the best
return. However, due to the different interest compounding periods, the interest
accumulates in a different fashion for each of the three GICs. The worksheet reveals that
GIC B yields the best return; it has an optimal combination of interest rate and
compounding periods for this GIC compared with the other two.
Question 2 (30 marks)
Multiple choice (1 mark each)
a. 1)
Future values are higher than present values and a yearly amount for five years is higher
than one amount at the end of five years.
b. 4)
Future values are always greater than one. Present value of an annuity would normally be
greater than one unless the discount rate was very high and the number of payments was
very low.
c. 1)
Accounts receivable are short-term assets and therefore would not need to be discounted
in determining the value of consideration given in order to purchase the other assets.
d. 1)
For a single payment, PV = 1/FV and FV = 1/PV.
e. 3)
The first payment under an annuity due would be payable today and would have a
present value equal to its nominal value, whereas the first payment for an ordinary
annuity would be payable at the end of the period and would have a present value less
than its nominal value.
Financial Accounting: Assets
Suggested solutions 5  1
f. 4)
The future values for the four options are €160,471, €159,385, €157,352, and €168,896,
respectively.
g. 1)
€40,000  €25,000 = 1.6 FV for 12 quarters (3 years) at 4%.
h. 4)
€503,634  €200,000 = 2.51817 = FV factor for 8% for 12 semi-annual periods.
Therefore, annual rate is 8%  2 = 16%.
i. 2)
Items (1) and (4) involve present value calculations and item (3) does not need to be
discounted or compounded because it involves a short-term asset.
j. 3)
A euro to be received in a future year is worth less in today’s euro if the interest portion
of the euro increases and the principal portion decreases.
k. 4)
16% per year = 4% per quarter; 10 years has 40 quarters.
l. 3)
The first payment for an annuity due is payable on the first day of the period, need not be
discounted, and therefore, does not include any interest.
(2 marks each)
m. 1)
€60,000 (0.8333) + €100,000 (0.6944) + €75,000 (0.5787) + €10,000 (0.4823)
n. 3)
(€10,000  €4,000)  18.9139
o. 3)
€9,000  24%  1/12
p. 1)
€500  4.3553
q. 3)
[(€758,158 + €758,158  10%)  €200,000]  10%
Financial Accounting: Assets
Suggested solutions 5  2
r. 2)
€30,000 ÷ €5,000 = 6 = maximum factor for annuity at 8%.
Closest factor is 5.7466 for 8 years. Therefore, 8 payments of €5,000. The payment for
the ninth year: [€30,000  (€5,000  5.7466)]  (1.08)9
s. 3)
€4,984.88 ÷ €400 = 12.46 = factor for 20 years at 5%
€4,984.88 ÷ €700 = 7.12 = factor for approximately 9 years at 5%
20 years versus 9 years = 11  20 = 55% difference
t. 3)
(€160,000  6.2098) – €160,000  12%  1/2
u. 2)
[(€15,000  6.78641)  €15,000]  5% = €4,340;
(€86,796 + €4,340  €15,000)  5% = €3,807;
€4,340 + €3,807 = €8,147
1
Present value of annuity of 7 periods at 5% + 1 (since this is the present value of an
annuity due)
Question 3 (5 marks)
The time value of money, commonly called interest, is the cost of using money over time.
The higher the interest rate and the longer the time period, the greater the interest cost.
Because of the interest cost, a euro today is not equal in value to a euro of other years.
Question 4 (16 marks)
a. (4 marks)
It will take 19 years to repay the note because the annuity factor of €100,379 ÷ €12,000 =
8.36 falls on year 19 on the table for present value of an ordinary annuity.
b. (4 marks)
Linda must live at least 18 years to make the life annuity advantageous.
€125,000 ÷ €12,425 = 10.06, which is the present value factor of an annuity for 18 years
at 7%.
c. (4 marks)
Bond interest = €2,500,000  10% =
Sinking fund payment = €2,500,000 ÷ 54.865 =
Savings required
Financial Accounting: Assets
€ 250,000
45,567
€ 295,567
Suggested solutions 5  3
d. (4 marks)
Total interest will be (€636.46 × 50) – €20,000 = €11,823
€20,000 ÷ €636.46 = 31.4238, which is the present value factor of an annuity for
50 periods at 2%. Therefore, annual interest rate is 24%, compounded monthly.
Question 5 (23 marks)
a. (9 marks)
1. Assuming payments made at the end of each six-month period (PV of an ordinary
annuity):
PV ordinary annuity = annuity  PV rate
€120,000 = annuity  2.6730*
annuity = €120,000  2.6730
annuity = €44,893.38
* Appendix A, Table 2: 3 periods, 6% = 2.6730
2. Assuming payments made at the beginning of each six-month period (PV of an annuity
due):
PV annuity due = annuity  PV rate
€120,000 = annuity  2.8334*
annuity = €120,000  2.8334
annuity = €42,351.94
* Appendix A, Table 2: 2 periods, 6% = 1.8334 + 1 = 2.8334
b. (10 marks)
Debt payment schedules (n = 3; i = 6%):
1. Ordinary annuity:
Date
Principal balance
beginning of period Payment Interest
June 30/X5 120,000
Dec. 31
June 30
82,306.62
Dec. 31
42,351.64*
*difference due to rounding
Financial Accounting: Assets
Principal
Principal balance
end of period
44,893.38 7,200.00 37,693.38 82,306.62
44,893.38 4,938.40 39,954.98 42,351.64
44,893.38 2,541.01 42,352.37* 0
14,679.41
Suggested solutions 5  4
2. Annuity due:
Date
Principal balance
beginning of period Payment Interest
June 30/X5 120,000
Dec. 31
77,648.06
June 30
39,955.00*
*difference due to rounding
Principal
Principal balance
end of period
42,351.94
0
42,351.94 77,648.06
42,351.94 4,658.88 37,693.06 39,955.00
42,351.94 2,397.30 39,954.64* 0
7,056.18
c. (4 marks)
Interest expense if payments are made at period end equals €14,679.41 compared to
interest expense of €7,056.18 if payments are made at the beginning of the period.
Although both annuities are for the same principal amount, number of payments, and
interest rate, the interest expense is much higher if payments are made at the end of each
period. The interest expense is much higher because the funds are outstanding for
six months longer and the principal balance on which interest is accruing is higher at all
times throughout the period.
Question 6 (16 marks)
a. (8 marks)
1. January 1, 20X7
Land .......................................................................................
Building .................................................................................
Notes payable...................................................................
100,000
400,000
500,000
2. February 1, 20X7
Computers ..............................................................................
32,595 *
Discount on notes payable .....................................................
5,425
Notes payable...................................................................
PV = FV  PV rate (Lesson note, Appendix A. Table 1, 2 years, 8%)
PV = €38,020  0.8573
PV = €32,595
3. July 1, 20X7
Copyright ...............................................................................
Notes payable...................................................................
300,000
4. December 1, 20X7
Cash .......................................................................................
Bank loan payable............................................................
400,000
Financial Accounting: Assets
38,020
300,000
400,000
Suggested solutions 5  5
b. (8 marks)
1. December 31, 20X7
Interest expense .....................................................................
Notes payable.........................................................................
Cash .................................................................................
45,000 *
83,228 **
128,228
* To determine the interest rate:
PV annuity
= annuity  PV rate
€500,000 = €128,228  PV rate
PV rate = €500,000  €128,228
= 3.8993
Using Lesson note, Appendix A. Table 2, looking across five periods 3.8993
corresponds to an interest rate of 9%.
0.09  €500,000 = €45,000
** €128,228 – €45,000
2. December 31, 20X7
Interest expense* ...................................................................
Discount on note payable.................................................
* 0.08  €32,595  11/12
3. December 31, 20X7
Notes payable.........................................................................
Interest expense* ...................................................................
Cash .................................................................................
* 0.10  €300,000  6/12
4. December 31, 20X7
Interest expense* ...................................................................
Cash .................................................................................
* 0.10  €400,000  1/12
2,391
2,391
25,000
15,000
40,000
3,333
3,333
100
Financial Accounting: Assets
Suggested solutions 5  6