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Finance - Tutorial 5 (79), Study Guides, Projects, Research of Finance

<div>In this document topics covered which are Department of Accounting and Finance,M.Sc. FinanceAndM.Sc. International Accounting and Financial Studies</div><div><br /></div>

Typology: Study Guides, Projects, Research

2010/2011

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M.Sc.
Finance
M.Sc. Investment &
Finance
M.Sc. International Banking &
Finance
M.Sc. International Accounting & Fina
nce
2009/20
10
40901 Finance I: Tutorial One
SOLUTIO
NS
Some straightforward questions on the use of future values and present
value factors.
Q1. a) You have £100 available today to invest for twenty years and the annual
interest rate is 8 per cent. The interest payments are to be reinvested, also
at a rate of 8 per cent. How much will you have available twenty years
from now?
100
(
1
+ .08
)
20
= 100
×
4.6610
=
466.10
b) Assume that the interest rate is 4 per cent rather than 8 per cent and
repeat the calculation carried out to answer part (a). [Observe the
difference in the sums available in year twenty.]
100
(
1
+ .04
)
20
= 800
×
2.1911
=
219.11
Sum accumulated at 4 per cent is less than 50 per cent of that built up at 8
per cent – reflects the lower interest rate and the effects of “compounding”
over time.
Q2. a) You decide to save £2,000 per annum and place the savings in a deposit
account at the end of each of the next five years. If you can invest your
savings at 12 per cent how much will you have accumulated by the end of
year five?
V5
= 2,000
×
FVAF5 / 0.12
= 2,000
×
6.3528
=
12705.69
b) You are given £500 today and decide to place this in a savings account
which will earn interest at 12 per cent. You decide to save £500 for each
of the next five years to add to the initial sum. How much will you have in
the savings account by the end of year five?
5
V5
= 500(1 +
0.12)
+ 500
×
FVAF5 / 0.12
= 500
×
1.7623
+ 500
×
6.3528
=
4057.57
pf3
pf4
pf5

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1

M.Sc. Finance

M.Sc. Investment & Finance

M.Sc. International Banking & Finance

M.Sc. International Accounting & Finance

40901 Finance I: Tutorial One

SOLUTIO

NS

Some straightforward questions on the use of future values and present

value factors.

Q1. a) You have £100 available today to invest for twenty years and the annual

interest rate is 8 per cent. The interest payments are to be reinvested, also

at a rate of 8 per cent. How much will you have available twenty years

from now?

20

= 100 × 4.6610 = 466.

b) Assume that the interest rate is 4 per cent rather than 8 per cent and

repeat the calculation carried out to answer part (a). [Observe the

difference in the sums available in year twenty.]

20

= 800 × 2.1911 = 219.

Sum accumulated at 4 per cent is less than 50 per cent of that built up at 8

per cent – reflects the lower interest rate and the effects of “compounding”

over time.

Q2. a) You decide to save £2,000 per annum and place the savings in a deposit

account at the end of each of the next five years. If you can invest your

savings at 12 per cent how much will you have accumulated by the end of

year five?

V

5

= 2 ,000 × FVAF

5 / 0.

= 2 ,000 × 6.3528 = 12705.

b) You are given £500 today and decide to place this in a savings account

which will earn interest at 12 per cent. You decide to save £500 for each

of the next five years to add to the initial sum. How much will you have in

the savings account by the end of year five?

5

V

5

= 500 ( 1 + 0 .12) + 500 × FVAF

5 / 0.

= 500 × 1.7623 + 500 × 6.

2

alternatively: divide through by 500

5

5

= 500 x 8. 1152 = 4057. 59

Q4. a) A loan of £30,000 is to be paid back in six annual and equal instalments.

Interest of 8 per cent is charged on the outstanding balance of the loan.

Determine the annual instalments. Present value of repayments must equal

the loan at the specified interest rate.

Instalment

Loan /

PVAF

Year Loan at

the start

of the

period

Interest 8%Loan at

the end

of the

period

Repayment

b) A loan of £30,000 is to be paid back in six equal instalments of

£7,297. Determine

the effective interest rate (i) on the loan.

If

Instalment = Loan / PVAF

PVAF = Loan / Instalment

and gives tables and values of PVAF and n it is possible to determine r

PVAF

6 / r

Using tables

PVAF

6 / r

r ≅ 12%

Year Loan at

the start

of the

period

Interes

t

Loan at

the end

of the

period

Repayment

YEAR NCF PVF(6%) PV

Present Value

Q5. a) The present value annuity factor for seven years at an interest rate of 9.

per cent is 4 .9088. Determine the annuity factors for years six and eight by

adjusting the given annuity value rather than by calculating new annuity

factors from scratch.

To determine the present value annuity factor for year 6 deduct the

discount factor for 7 from PVAF ( 7 ,9.7 5 %) , ie. 4.9088 – 0.5214 = 4.3874.

To determine the present value annuity factor for year 8 add the discount

factor for year 8 to the PVAF ( 7 ,9.75%) , ie. 4 .9088 + 0.4751 = 5.3839.

b) A contract specifies that a company will received £80,000 each year for

10 years, the first payment being received three years from now. What is the present value

of these payments if the interest rate is 6 per cent?

PVAF (3‐12, 6%) = PVAF (10,6%)

x PVF

PV of 80 , 000 in years 3‐12 = 80, 000 x 6.5505 = 524,