1
School of Banking and Finance
FINS5514 Capital Budgeting and Financing Decisions

Tutorial Covering Week 2 - Investment Decision I

Multiple Choice Questions
1. Alpha Bank pays interest of 4 percent compounded annually. Beta Bank pays 4
percent simple interest. Which one of the following statements is true if you invest
$1,000 in each bank for five years?
a. Alpha Bank will pay you a total of $200 in interest over the five years.
b. Beta Bank will pay you more interest over the five years than Alpha Bank will.
c. Alpha Bank will pay you a total of $216.65 in simple interest.
d. Alpha Bank will pay you $16.65 of interest on interest.

Calculate the interest amounts:
Alpha Bank: ܥ݋݉݌݋ݑ݊݀ ܫ݊ݐ݁ݎ݁ݏݐ = ܨܸ − ܫ݊݅ݐ݈݅ܽ ܣ݉݋ݑ݊ݐ = ܸܲ(1 + ݎ)௧ −
ܫ݊݅ݐ݈݅ܽ ܣ݉݋ݑ݊ݐ
ܥ݋݉݌݋ݑ݊݀ ܫ݊ݐ݁ݎ݁ݏݐ = $1000(1.04)ହ − $1000 = $216.65

Beta Bank: ܵ݅݉݌݈݁ ܫ݊ݐ݁ݎ݁ݏݐ = ܫ݊݅ݐ݈݅ܽ ܣ݉݋ݑ݊ݐ × ݎ × ݐ
ܵ݅݉݌݈݁ ܫ݊ݐ݁ݎ݁ݏݐ = $1000(0.04)(5) = $200.00

Therefore, ܫ݊ݐ݁ݎ݁ݏݐ ݋݊ ݅݊ݐ݁ݎ݁ݏݐ = ܥ݋݉݌݋ݑ݊݀ ܫ݊ݐ݁ݎ݁ݏݐ − ܵ݅݉݌݈݁ ܫ݊ݐ݁ݎ݁ݏݐ
ܫ݊ݐ݁ݎ݁ݏݐ ݋݊ ݅݊ݐ݁ݎ݁ݏݐ = $216.65 − $200 = $16.65
Answer: d


2
2. Jim has $1,650 saved today. He wants to buy a different vehicle as soon as he
has $3,200 saved. How long does Jim have to wait to get his vehicle if he earns 7.5
percent compounded annually?
a. 8.67 years b. 9.08 years c. 9.16 years d. 9.23 years

Calculate the time given the PV and FV
ݐ = ln ቀܨ ௧ܸܲ ௧ܸቁln(1 + ݎ) = ln ൬$3,200$1,650൰ln(1 + 0.075) = 9.16
Answer: c


3. All else equal, the future value will _____ as the period of time increases.
a. increase b. decrease c. remain constant
Answer: a All else equal, the future value will increase as the period of time
increases.



4. You have been offered a business opportunity that will pay you $25,000 in five
years if you invest $10,000 today. What is the expected rate of return on this
investment?
a. 20.11 percent b. 25.74 percent c. 27.02 percent d. 30.00 percent

Calculate the interest rate
ݎ = ൬ܨ ௧ܸܲ ௧ܸ൰ଵ௧ − 1 = ቆ$25,000$10,000ቇଵହ − 1 = 0.2011
Answer: a




3

5. All else equal, the present value will _____ as the rate of return decreases.
a. increase b. decrease c. remain constant
Answer a. All else equal, the present value will increase as the rate of return
decreases.

6. Your grandmother deposited $1,000 into an account for you fifteen years ago.
Today, the account is worth $3,548. If interest is compounded annually, what rate
of return have you been earning on this money?
a. 8.75 percent b. 8.81 percent c. 8.95 percent d. 9.06 percent

Calculate the interest rate
ݎ = ൬ܨ ௧ܸܲ ௧ܸ൰ଵ௧ − 1 = ቆ$3,548$1,000ቇ ଵଵହ − 1 = 0.0881
Answer: b


Short answer questions
7. Martha wants to have $10,000 in her investment account ten years from now.
How much does she have to deposit today to achieve her goal if she can earn 8
percent compounded annually?

Calculate the Present Value of the investment.
ܲ ௧ܸ = ܨ ௧ܸ(1 + ݎ)௧ = $10,000(1 + 0.08)ଵ଴ = $4,631.93
Martha must invest $4,631.93 today to have $10,000 in 10 years time






4
8. Lewis borrows $10,000 today at 8.25 percent compounded annually. The terms
of the loan require Lewis to repay the principal and interest in one lump sum four
years from today. How much will Lewis have to pay in four years?

Calculate the future value of this investment:
ܨܸ = ܸܲ(1 + ݎ)௧ = $10,000(1.0825)ସ = $13,731.30
In four years time, the payment will be $13,731.30


9. You opened a savings account four years ago and deposited $200 at that time.
Three years ago, you added another $400 to the account. Last year, you deposited
an additional $100 into this account. The rate of return is 5 percent compounded
annually. How much is in your account today?

Calculate the future value of these cash flows using the differing amounts. Note
there is no deposit from the year before last.
ܨ݅ݎݏݐ ݀݁݌݋ݏ݅ݐ ܨܸ = ܸܲ(1 + ݎ)௧ = $200(1.05)ସ = $243.10
ܵ݁ܿ݋݊݀ ݀݁݌݋ݏ݅ݐ ܨܸ = ܸܲ(1 + ݎ)௧ = $400(1.05)ଷ = $463.05
ܮܽݏݐ ݀݁݌݋ݏ݅ݐ ܨܸ = ܸܲ(1 + ݎ)௧ = $100(1.05)ଵ = $105.00

The total investment is simply the sum of these future values:
ܶ݋ݐ݈ܽ ܨܸ = $243.10 + $463.05 + $105.00 = $811.15










5
10. You have won a lottery. You can either choose to take the money as a lump
sum of $5,000,000 today or you can have it paid to you in equal amounts of
$250,000 at the beginning of each year over the next 25 years (an instalment plan).
The appropriate discount rate is 5%. Which of these options should you accept?
Why?

This is an annuity due so we need to calculate the present value accordingly. The CF
= 250,000, r = 0.05 and t = 25

> @ 45.660,699,3$)05.1(05.0105.0
1
05.0
1000,250)1(
1
11
25 ¸¸¹
·
¨¨©
§
¸¸¹
·¨¨©
§
rrrrCPVA tt


If you accept the instalment plan, this is the amount you are going to get in today's
terms. Clearly it is less than the lump sum of $5million. The difference is
$1,300,339.

You should accept the lump sum as the more profitable outcome.


11. Extending on your answer to question 10, imagine that you accept the
instalment plan. In each period you immediately invest each instalment at 7.5%
(compounded yearly) for 20 years. How much will it be worth at the end of this
time? Would this change your mind about how to accept the money?

Now we calculate the future value if we invest the instalments at 7.5% for 20 years.

CF = 250,000, r = 0.075, t =20
> @ > @ 10.133,638,11$)075.01(
075.0
1075.01000,250)1(11
20
¸¸¹
·
¨¨©
§ ¸¸¹
·
¨¨©
§ r
r
rCFVA
t
t


If the instalments are invested at this rate the total will be worth $6,638,133 more
than the lump sum so you should consider changing your answer to question 10,
take the instalment plans and invest it as here.
However, remember that you might also invest the lump sum and you are not given
any information here to calculate that possible future value which you would need
for a complete analysis of your options.
6 
 
Chapter 6 Questions  
 
20. You want to buy a car for $83,500 and the finance office has offered you a loan of 6.5% APR 
for 60 months. What will your monthly payments be? What is the effective annual interest rate 
on this loan?  
 
This is an annuity in which we know the PVA, the duration of the loan and the interest rate. 
Therefore, we solve for the payment, remembering to adjust the APR to a monthly rate.  
 
If the APR is 6.5%, then the monthly rate is 6.5% / 12 = 0.00542 
௧ ൌ ൬1 െ 1ሺ1 ൅ ሻ௧൰ ൌ $83,500 
௧ ൌ ൬ 10.00542 െ 10.00542ሺ1 ൅ 0.00542ሻ଺଴൰ ൌ $83,500 
௧ ൌ ሺ51.10868ሻ ൌ $83,500 and therefore,   ൌ ଼ଷ,ହ଴଴ହଵ.ଵ଴଼଺଼ ൌ $1,633.77 
And the EAR is 
ൌ ൬1 ൅ ൰௠ െ 1 ൌ ൬1 ൅ 0.06512 ൰ଵଶ െ 1 ൌ 6.7%  
 
22. You are offered a $3 loan if you repay $4 in one weeks’ time. What is the annual rate (APR) 
and what is the Effective Annual Interest rate (EAR)?  
 
Calculate the interest rate using the PV and FV. 
ൌ ൬௧௧൰
ଵ
௧ െ 1 ൌ ቆ$4$3ቇଵଵ െ 1 ൌ 33.33%  
The interest rate is 33.33% per week. To find the annual rate, we multiply this rate by the number 
of weeks in a year, so:  
 
ሺሻ ൌ 52 ൈ 33.33% ൌ 1,733.33% 
 
Calculating the Effective Annual Interest Rate: 
ൌ ൬1 ൅ ൰௠ െ 1 ൌ ൬1 ൅ 52 ൈ 0.333352 ൰ହଶ െ 1 ൌ 313,916,516%  
 
7 
 
54. You wish to buy a car for $78,000. The contract is a 60‐month annuity due at 7.25% APR. What 
will your monthly payments be?  
 
Here we use the equation for the present value of an annuity due, adjusting the APR to reflect the 
monthly payment scheme. So, the equation is: 
ௗ௨௘ ൌ ሺ1 ൅ ሻ ൌ ሺ1 ൅ ሻ ൈ ൬1 െ 1ሺ1 ൅ ሻ௧൰ 
ௗ௨௘ ൌ 78,000 ൌ ሺ1 ൅ 0.072512 ሻ ൈ ቌ 10.072512 െ 10.072512 ሺ1 ൅ 0.072512 ሻ଺଴ቍ 
ℎ, ൌ $1,544.38