School

Royal Melbourne Institute of Technology **We aren't endorsed by this school

Course

BUSM 4129

Subject

Finance

Date

Oct 17, 2023

Pages

4

Uploaded by ChiefBoulder11774 on coursehero.com

Time Value of Money / Discounted Cash Flow
Basic Practice Questions
Practice Exercises
1.
You have $15,000 to invest for 4 years at 8% per annum. What is future value?
2.
You need $30,000 in 3 years time. The interest rate is 7% per annum. How much do you
need to invest now?
3.
You invested $8,967 at 6% per annum and now you have $12,000. For how long has your
money been invested?
4.
You invested $8,000 for 4 years and now have $9,910.60. What interest rate are you
receiving.
Questions 1 to 4 are of the type where there is just one initial amount. There are four
variables - PV, FV, interest rate and number of periods. If you know any three, you can find
the fourth.
5.
You will be receiving $1,000 in one year's time, $500 in two year's time and $800 in three
years time. What is the present value of this set of cash flows if the appropriate discount
rate is 5%?
6.
The stated annual rate of interest (Annual percentage rate - APR) for an investment is
5%. The compounding period is monthly. What is the effective annual rate (EAR)?
7.
You wish to provide a prize of $500 every year forever and ever. The first prize will be
awarded in exactly one year's time. How much do you need to provide now to fund this
prize? The appropriate discount rate
is 4% per annum.
8.
You wish to provide a prize every year for ever and ever. The first prize of $500 will be
awarded in exactly one year's time. To provide for inflation you specify that the value of
the prize is to grow by 3% every year i.e. the second prize will be $515. How much do you
need to provide now to fund this prize? The appropriate discount rate
is 4% per annum.
9.
You wish to receive $10,000 every year for 5 years. The first payment will be in exactly 1
year's time. The appropriate discount rate is 4%. How much do you need to invest now to
receive these cash flows?
10.
You take out a mortgage of $200,000 at 8% per annum. You will be making 20 annual
equal payments with the first payment in exactly 1 year's time. How much is each
payment?
11.
What is the present value of an annuity that pays $6,000 every year for 10 years, with the
first payment in one year's time? The discount rate is 8%.
12.
What is the present value of an annuity that pays $6,000 every year for 10 years, with the
first payment today? The discount rate is 8%.
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13.
What is the present value of an annuity that pays $6,000 every year for 10 years, with the
first payment two years from today? The discount rate is 8%.
14.
What is the value of a perpetuity of $70,000
if the discount rate is 11% and the first
payment is in one year's time?
15.
What is the value of a perpetuity of $70,000
if the discount rate is 11% and the first
payment is today?
16.
You are taking out a personal loan for $50,000 at an interest rate of 8% p.a. compounding
yearly. You will be making 10 equal yearly payments, with the 1st payment in one year's
time. What is the yearly payment?
17.
You are taking out a personal loan for $50,000 at an interest rate of 8% p.a. compounding
six monthly. You will be making 20 equal payments, with the 1st payment in 6 month's
time. What is the six monthly payment?
18.
What
is the value of a growing perpetuity where the first payment is $500, the growth
rate is 2.5% and the discount rate is 4.25%?
19.
What is the value of a growing perpetuity where the first payment is $500, the growth
rate is 2.5% and the discount rate is 4.25%?
20.
You are quoted an interest rate of 16% compounding quarterly. What is the effective
interest rate?
21.
A project has the following cash flows:
Y0
-$5,000
Y1
-$1,000
Y2
+$3,000
Y3
+$4,500
If the discount rate is 5%, what is the NPV?
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Time Value of Money / Discounted Cash Flow
Advanced Practice Questions
Practice Exercises
1.
John wants to have $25,000 in 3 years' time for a deposit on a house. He has recently won
$22,000 in a lottery and would like to travel overseas.
If he can invest money at 13%, how
much can he afford to spend now on travel?
2.
A man can buy a block of land for $17,000 cash or payments of $12,000 now and another
$11,500 at the end of 5 years. He can earn 13% if he invests his money.
Which plan is
better?
3.
What is the value now of the right to receive $3,000 per annum at the end of each year for
the next 3 years followed by $5,000 per annum received at the end of the next 4 years?
Use an interest rate of 9%.
4.
A company contributed $1,250 per annum into a fund for 5 years.
The fund earned 11%
per annum and the interest was compounded yearly. After 5 years the company made no
more payments but left its money in the fund. How much would be in the fund at the end
of 9 years?
5.
What is the future value of $27,300 per annum invested for 11 years at 12%?
6.
Your grandfather's family trust has decided to pay you $1200 pre quarter for the 4 years
that you will take to complete your degree at RMIT.
If a fund can earn 6.8% per annum
paid quarterly how much should the trust invest now in the separate account in order
that the quarterly payments can be made.
7.
John is entitled to the fee simple (ownership) of a property with a current market rental
value of $6,000 per annum, in advance, upon the death of Jack. Jack is 63 years old and
has a life expectancy of 12 years. John would like possession of the property today.
What
sum should he offer based on an interest rate of 9.5%?
(In advance implies Cash flows
occur at the beginning of the period and you have to set your calculator in Beginning Mode.
This is Annuity Due).
8.
A property is sold for $195,000, a deposit of $50,000 is paid at the date of purchase.
Under the contract the outstanding balance is payable by annual instalments over a
period of 10 years with interest at the rate of 14%.
At the beginning of the fifth year the
vendor sells his contract at a price that enables the purchaser of the contract to earn
16.75% on his investment. What amount does the purchaser of the contract pay?
9.
How much would you pay for an investment that will return $27,500 for the next 10 years
and then $36,000 for the next five years? Use an interest rate of 7.3%.
10.
A company has borrowed $250,000 on a mortgage against the assets of the business. The
loan is to be repaid by equal annual instalments over the 20-year life of the loan.
If the
interest rate is 14.25% what is the amount of the instalment? Calculate the interest
component of the first, third and fifth instalments.
What does the balance owe on the
mortgage at the start of the ninth year?
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